New in SG-Lib 4.9 | SG-Lib • Solid Geometry Library Toolbox for Generative AI

Last change of this documentation page: 2022-06-02 of SolidGeometry 4.9

CVLzseparate(CVLz,i)- returns a sliced CVL/CPL for a given z value

% CVLzseparate(CVLz,i) - returns a sliced CVL/CPL for a given z value
% (by Tim Lueth, VLFL-Lib, 2020-AUG-23 as class: CLOSED POLYGON LISTS)
%
% for sliced CVL, i.e. CPL with an added z value, this fnctn returns only
% the contours that have the same z value
% CVLzseparate works with an index
% CVLofSGslices works with z values
% (Status of: 2020-08-25)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CVLofSGslices, SGofCVLslices, CVLseparatez, CPLofSGsliceauto,
% CVLzofSGsliceauto, CVLzaddauxpoints, CVLzofSGsliceauto, CVLzplot,
% CVLzplotasCPS, CVLzplotui, CVLzremovearea, CVLzsimplifyAmin, CVLzsweep,
% exp_2017_07_18
%
% CVL=CVLzseparate(CVLz,[i])
% === INPUT PARAMETERS ===
% CVLz: Slices CVL
% i: simple index in zz list
% === OUTPUT RESULTS ======
% CVL: just the contour with the nth z value
%
% EXAMPLE:
% CVL=CVLofSGslices(SGsample(5),10);
% CVLzseparate(CVLzofSGsliceauto(SGsample(5)),2)
%
% See also: CVLofSGslices, SGofCVLslices, CVLseparatez, CPLofSGsliceauto,
% CVLzofSGsliceauto, CVLzaddauxpoints, CVLzofSGsliceauto, CVLzplot,
% CVLzplotasCPS, CVLzplotui, CVLzremovearea, CVLzsimplifyAmin, CVLzsweep,
% exp_2017_07_18
%
%
% Copyright 2020 Tim C. Lueth

CVLzremovearea(res)- removes areas with a small distance to the opposite wall

% CVLzremovearea(res) - removes areas with a small distance to the opposite wall
% (by Tim Lueth, VLFL-Lib, 2020-AUG-23 as class: CLOSED POLYGON LISTS)
%
% Uses CPLfindsmalldist
% (Status of: 2020-08-25)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLfindsmalldist, CVLzaddauxpoints, CVLzofSGsliceauto,
% CVLzplot, CVLzplotasCPS, CVLzplotui, CVLzseparate, CVLzsimplifyAmin,
% CVLzsweep, exp_2017_07_18
%
% CVLN=CVLzremovearea([res])
% === INPUT PARAMETERS ===
% res: minimal required distance to survive as contour
% === OUTPUT RESULTS ======
% CVLN: CVL with removed areas the will creates problems during printing
% or SG reconstruction
%
% EXAMPLE: SG=SGservosample(1); CVLz=CVLzofSGsliceauto(SG);
% SGfigure; CVLzplotasCPS(CVLzseparate(CVLz,1),'r',1); shg; grid off
% SGfigure; CVLzplotasCPS(CVLzremovearea(CVLzseparate(CVLz,1),0.3),'r',1); shg; grid off
%
% See also: CPLfindsmalldist, CVLzaddauxpoints, CVLzofSGsliceauto,
% CVLzplot, CVLzplotasCPS, CVLzplotui, CVLzseparate, CVLzsimplifyAmin,
% CVLzsweep, exp_2017_07_18
%
%
% Copyright 2020 Tim C. Lueth

CVLzaddauxpoints(CVLz,d)- adds points to CVL z sorted contours

% CVLzaddauxpoints(CVLz,d) - adds points to CVL z sorted contours
% (by Tim Lueth, VLFL-Lib, 2020-AUG-22 as class: CLOSED POLYGON LISTS)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLaddauxpoints, GPLauxgridpointsCL, PLELaddauxpoints,
% GPLauxgridpointsPLEL, RLaddauxpoints, CVLzofSGsliceauto, CVLzplot,
% CVLzplotasCPS, CVLzplotui, CVLzremovearea, CVLzseparate,
% CVLzsimplifyAmin, CVLzsweep, exp_2017_07_18
%
% CVLz=CVLzaddauxpoints(CVLz,[d])
% === INPUT PARAMETERS ===
% CVLz: CVL z sorted contour
% d: forced maximum distance of points; default is smin
% === OUTPUT RESULTS ======
% CVLz: modified an corrected CPLz
%
% EXAMPLE:
% SG=SGservosample(2); CVLz=CVLofSGslices(SG,10);
% CVLzaddauxpoints(CVLz);
%
%
% See also: CPLaddauxpoints, GPLauxgridpointsCL, PLELaddauxpoints,
% GPLauxgridpointsPLEL, RLaddauxpoints, CVLzofSGsliceauto, CVLzplot,
% CVLzplotasCPS, CVLzplotui, CVLzremovearea, CVLzseparate,
% CVLzsimplifyAmin, CVLzsweep, exp_2017_07_18
%
%
% Copyright 2020 Tim C. Lueth

CVLzplotasCPS(CVLz,c,a,e)- similar to CVLplot but separates the z values just in case somebody forgot nan nan

% CVLzplotasCPS(CVLz,c,a,e) - similar to CVLplot but separates the z values just in case somebody forgot nan nan
% (by Tim Lueth, VLFL-Lib, 2020-AUG-22 as class: VISUALIZATION)
%
% This procedure is based on VLFLofCVLdelaunay2D
% (Status of: 2022-05-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CVLzplot, CVLzplothatched, CVLzplotui, VLELplots, CPLplot,
% PLplot, VLplot, CVLplots, CVLplot, CVLzaddauxpoints, CVLzofSGsliceauto,
% CVLzplot, CVLzplotui, CVLzremovearea, CVLzseparate, CVLzsimplifyAmin,
% CVLzsweep, exp_2017_07_18
%
% h=CVLzplotasCPS(CVLz,[c,a,e])
% === INPUT PARAMETERS ===
% CVLz: Several closed vertex list separated by nan
% c: Optional color of CPS; default changing colors
% a: Optional facete alpha
% e: Optional line color
% === OUTPUT RESULTS ======
% h: handle to drawing elements
%
% EXAMPLE:
% SG=SGservosample(2); CVLz=CVLofSGslices(SG,10)
% SGfigure(-30,30); CVLzplotasCPS(CVLz,'',1)
% SGfigure(-30,30); CVLzplotasCPS(CVLz,'',1,'k')
% SG=SGservosample(1); CVLz=CVLofSGslices(SG,10); SGfigure(-30,30); CVLzplotasCPS(CVLz,'',1);
%
%
%
% See also: CVLzplot, CVLzplothatched, CVLzplotui, VLELplots, CPLplot,
% PLplot, VLplot, CVLplots, CVLplot, CVLzaddauxpoints, CVLzofSGsliceauto,
% CVLzplot, CVLzplotui, CVLzremovearea, CVLzseparate, CVLzsimplifyAmin,
% CVLzsweep, exp_2017_07_18
%
%
% Copyright 2020-2022 Tim C. Lueth

VLcorrelate(NVL,VL);- returns the indices of a list in another list

% VLcorrelate(NVL,VL); - returns the indices of a list in another list
% (by Tim Lueth, VLFL-Lib, 2020-AUG-22 as class: AUXILIARY PROCEDURES)
%
% This fnctn finds the indices of some vertices in a longer list. For a
% complete remapping use fnctn "maprows".
% bi=findVL(VL,ai); bi=ai(bi)
% maprows is extremely and unbeatable fast (Status of: 2020-08-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: maprows, findVL, reversesortindex, VLFLreorder
%
% vi=VLcorrelate(NVL,VL);
% === INPUT PARAMETERS ===
% NVL: Long vertex list to search in; must not be unique, first entry is
% returned
% VL: Second vertex list to find in NVL
% === OUTPUT RESULTS ======
% vi: index in NVL
%
% EXAMPLE:
% VL1=rounddiv(rand(20,3)*100,5)-50, VL2=rounddiv(rand(20,3)*100,5)-50
% VLcorrelate(VL1,ELunsort(VL1))
% VLcorrelate([VL1;VL2],ELunsort(VL1))
% VLcorrelate([VL1],[ELunsort(VL1);ELunsort(VL2)])
%
% See also: maprows, findVL, reversesortindex, VLFLreorder
%
%
% Copyright 2020 Tim C. Lueth

Fofbendinggirder(l,h,b,s,E,Slim)- returns binding force of a bended girder

% Fofbendinggirder(l,h,b,s,E,Slim) - returns binding force of a bended girder
% (by Tim Lueth, VLFL-Lib, 2020-AUG-21 as class: MECHANICAL PROCEDURES)
%
% Helpful parameter:
% Steel Slim=355; E=200000
% PA12 Slim=36; E=1240 (PA2200 called at EOS)
% The length of a bar which cross section is [h x b] that will be bended
% distance s (related to h) if a force F is applied?
% the less force F is applied the longer the length is
% the less distance s is requested the shorter the length is
% The force to deflect a bending beam in the order of its height is
% reduced with the 4th power when the height is halved. So to push in an
% enclosure with half its wall thickness 1/16 of the force is sufficient.
% Two fingers can apply 50N when gripping. 5N, i.e. 500 grams are no
% problem. We can even apply 10N to a thin bar of it in continuous load.
% (Status of: 2020-09-09)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% bofbendinggirder
%
% [F,alpha,Smax,r,c]=Fofbendinggirder([l,h,b,s,E,Slim])
% === INPUT PARAMETERS ===
% l: length of the bended beam
% h: height of the cross section of bended beam; default i 1.5
% b: width of the bended beam; default is h
% s: bending distance; default h
% E: E modulus default 1200 MPa (Polyamid PA12)
% Slim: Limit of bending stress
% === OUTPUT RESULTS ======
% F: bending force to achieve distance s
% alpha: bending angle
% Smax: bending stress
% r: bending radius
% c: bending contour
%
% EXAMPLE:
% Fofbendinggirder(6,1.5,1.5,2.0) % clip width length 6 and wall thickness 1.5 and pin of 0.5
%
% See also: SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% bofbendinggirder
%
%
% Copyright 2020 Tim C. Lueth

exp_2020_08_20_snapper- This experiment is used to determine the excess length of snap hooks

% exp_2020_08_20_snapper - This experiment is used to determine the excess length of snap hooks
% (by Tim Lueth, VLFL-Lib, 2020-AUG-21 as class: EXPERIMENTS)
%
% A bracket is designed for the SGmotorN20, which can be 3D-printed for
% this purpose if you do not have the original. The fnctn uses slfit to
% design a clearance fit before the snap hooks are applied. (Status of:
% 2020-09-18)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsnaprivet, slfit, DIN4AMfitting, exp_2020_08_18_snapper,
% SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% bofbendinggirder, Fofbendinggirder
%
% LITERATURE:
% - Fischer et al. (2011): Tabellenbuch Metall, Verlag Europa-Lehrmittel,
% Nourney, 45. Auflage,
%
% SGC=exp_2020_08_20_snapper
% === OUTPUT RESULTS ======
% SGC: Snapper for SGmotorN20
%
% EXAMPLE:
% slfit('set formiga'), slfit('c'), slfit('set form3b'), slfit('c')
%
% exp_2020_08_18_snapper
%
%
% See also: SGsnaprivet, slfit, DIN4AMfitting, exp_2020_08_18_snapper,
% SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% bofbendinggirder, Fofbendinggirder
%
%
% Copyright 2020 Tim C. Lueth

userip- return internal and externam ip address of the used computer

% userip - return internal and externam ip address of the used computer
% (by Michael Kleder and Stephen LL, VLFL-Lib, 2020-AUG-20 as class:
% AUXILIARY PROCEDURES)
%
% Michael Kleder of 2005-08-16 and Stephen LL of 2005-08-08 (Status of:
% 2020-08-20)
%
% See also: whoisPID, whoisTCP, whoisIP, lastlogins, userIP
%
% [ipi,ipe]=userip
% === OUTPUT RESULTS ======
% ipi: internal ip address
% ipe: externally seen ip address
%
% EXAMPLE:
% userIP
% [i,e]=userIP
%
% See also: whoisPID, whoisTCP, whoisIP, lastlogins, userIP
%

SGcolorsample()- creates boxes in colors with text

% SGcolorsample() - creates boxes in colors with text
% (by Tim Lueth, VLFL-Lib, 2020-AUG-20 as class: SURFACES)
%
% This fnctn is slow if it creates text, therefor it was extracted from
% SGsample
% This fnctn checks wether the color code is correct (Status of:
% 2020-08-20)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsample
%
% SG=SGcolorsample([])
% === PROPERTY NAMES =====
% 'text' : if 'text' is used asl argument, the boxes show text descriptors
% === OUTPUT RESULTS ======
% SG: Colored Boxes
%
% EXAMPLE:
% SGcolorsample
% SGcolorsample('text')
%
% See also: SGsample
%
%
% Copyright 2020 Tim C. Lueth

bofbendinggirder(h,l,s,F,E,Slim)- returns the width of a bended girder

% bofbendinggirder(h,l,s,F,E,Slim) - returns the width of a bended girder
% (by Tim Lueth, VLFL-Lib, 2020-AUG-19 as class: MECHANICAL PROCEDURES)
%
% Helpful parameter:
% Steel Slim=355; E=200000
% PA12 Slim=36; E=1240 (PA2200 called at EOS)
% The length of a bar which cross section is [h x b] that will be bended
% distance s (related to h) if a force F is applied?
% the less force F is applied the longer the length is
% the less distance s is requested the shorter the length is (Status of:
% 2020-09-18)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% Fofbendinggirder
%
% [b,alpha,Smax,r,c]=bofbendinggirder([h,l,s,F,E,Slim])
% === INPUT PARAMETERS ===
% h: height of the cross section of bended beam
% l: length of the bended beam
% s: bending distance; default h
% F: bending force to achieve distance s; default 10 N
% E: E modulus default 1200 MPa (Polyamid PA12)
% Slim: Limit of bending stress
% === OUTPUT RESULTS ======
% b: width of cross section of a bended girder
% alpha: bending angle
% Smax: bending stress
% r: bending radius
% c: bending contour
%
% EXAMPLE:
% bofbendinggirder(1.5,10,1.5+1) % clip width length 10 and wall thickness 1.5 and pin of 1
%
% See also: SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% Fofbendinggirder
%
%
% Copyright 2020 Tim C. Lueth

CVLzplot(CVL,c,w,t,b,f)- similar to CVLplot but separates the z values just in case somebody forgot nan nan

% CVLzplot(CVL,c,w,t,b,f) - similar to CVLplot but separates the z values just in case somebody forgot nan nan
% (by Tim Lueth, VLFL-Lib, 2020-AUG-18 as class: VISUALIZATION)
%
% =======================================================================
% OBSOLETE (2022-05-21) - USE 'CVLplot' INSTEAD
% =======================================================================
%
% This procedure is different to VLELplot (Status of: 2020-08-25)
%
% Introduced first in SolidGeometry 4.9
%
% See also: [ CVLplot ] ; CVLzplot, CVLzplotasCPS, CVLzplothatched,
% CVLzplotui, VLELplots, CPLplot, PLplot, VLplot, CVLplots, CVLplot,
% CVLzaddauxpoints, CVLzofSGsliceauto, CVLzplotasCPS, CVLzplotui,
% CVLzremovearea, CVLzseparate, CVLzsimplifyAmin, CVLzsweep,
% exp_2017_07_18
%
% CVLzplot(CVL,[c,w,t,b,f])
% === INPUT PARAMETERS ===
% CVL: Several closed vertex list separated by nan
% c: Optional color of desired edges; default changing colors
% w: Optional line width; default is 1
% t: Size of a cone shaped arrow tip, default is ''=invisible
% b: Size of a cube showing the start point; default is ''=invisible
% f: Size of a ring showing the end point; default is ''=invisible
%
% EXAMPLE:
% SGfigure; view(-30,30); CVLplots(VLsample(18),'',3,1);
% SGfigure; view(-30,30); CVLplots(VLsample(18),'',3,1,1);
% SGfigure; view(-30,30); CVLplots(VLsample(18),'',3,1,1,1);
%
% See also: [ CVLplot ] ; CVLzplot, CVLzplotasCPS, CVLzplothatched,
% CVLzplotui, VLELplots, CPLplot, PLplot, VLplot, CVLplots, CVLplot,
% CVLzaddauxpoints, CVLzofSGsliceauto, CVLzplotasCPS, CVLzplotui,
% CVLzremovearea, CVLzseparate, CVLzsimplifyAmin, CVLzsweep,
% exp_2017_07_18
%
%
% Copyright 2020-2022 Tim C. Lueth

exp_2020_08_18_snapper- This experiment is used to determine the excess length of snap hooks

% exp_2020_08_18_snapper - This experiment is used to determine the excess length of snap hooks
% (by Tim Lueth, VLFL-Lib, 2020-AUG-18 as class: EXPERIMENTS)
%
% A bracket is designed for the SGmotorN20, which can be 3D-printed for
% this purpose if you do not have the original. The fnctn uses slfit to
% design a clearance fit before the snap hooks are applied. (Status of:
% 2020-08-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% bofbendinggirder, Fofbendinggirder
%
% LITERATURE:
% - Fischer et al. (2011): Tabellenbuch Metall, Verlag Europa-Lehrmittel,
% Nourney, 45. Auflage,
%
% exp_2020_08_18_snapper
%
% EXAMPLE:
% slfit('set formiga'), slfit('c'), slfit('set form3b'), slfit('c')
%
% exp_2020_08_18_snapper
%
%
% See also: SGsnaprivet, lofbendinggirder, sofbendinggirder, rofcircbend,
% bofbendinggirder, Fofbendinggirder
%
%
% Copyright 2020 Tim C. Lueth

Dashboard- just opens the web side for formlab dashboard

% Dashboard - just opens the web side for formlab dashboard
% (by Tim Lueth, VLFL-Lib, 2020-AUG-17 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: Wegertseder, Norelem
%
% Dashboard
%
% See also: Wegertseder, Norelem
%
%
% Copyright 2020 Tim C. Lueth

saveTL(vname,fname,copyn)- a modified version of the save command

% saveTL(vname,fname,copyn) - a modified version of the save command
% (by Tim Lueth, VLFL-Lib, 2020-AUG-17 as class: AUXILIARY PROCEDURES)
%
% Matlab save command uses the first argument as name of the file and
% further arguments as names of variables. In contrast, this fnctn takes
% the name of a variable and saves it under the same filename (Status of:
% 2020-09-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: save
%
% saveTL(vname,[fname,copyn])
% === INPUT PARAMETERS ===
% vname: variable name to save under the same name as .mat file
% fname: filename
% copyn: if true; the variable name changes to fname
%
% EXAMPLE:
% A=SGbox
% saveTL(A) % in file A.mat is only variable A
% clear all; load A; whos
% saveTL(A,'B',false) % in file B.mat is only one variable A
% clear all; load B; whos
% saveTL(A,'B') % in file B.mat is only one variable B
% clear all; load B; whos
%
% See also: save
%
%
% Copyright 2020 Tim C. Lueth

exp_2020_08_17_fittings- EXPERIMENT To create a set of fitting cylinders with different slot sizes between the walls

% exp_2020_08_17_fittings - EXPERIMENT To create a set of fitting cylinders with different slot sizes between the walls
% (by Tim Lueth, VLFL-Lib, 2020-AUG-17)
%
% a) The Experiment for testing t20 different parts to be assembled
% afterwards
% (Status of: 2020-08-17)
%
% Introduced first in SolidGeometry 4.9
%
% exp_2020_08_17_fittings
%
% EXAMPLE: Just try
% exp_2020_08_17_fittings
%
%
%
% Copyright 2020 Tim C. Lueth

CPLconvexhullfillgap(CPL,d,ftyp,keep)- returns the convex hull for a CPL

% CPLconvexhullfillgap(CPL,d,ftyp,keep) - returns the convex hull for a CPL
% (by Tim Lueth, VLFL-Lib, 2020-AUG-16 as class: CLOSED POLYGON LISTS)
%
% The fnctns are based on the planar CPLfnctns
% - CPLconvexhullfillgap - closes gaps and try to find a SINGLE OUTLINE
% contour
% - CPLoutlinecontour - just returns ALL OUTLINE contours
% - CPLfillgap -just fillgapsb etween contours (Status of: 2021-04-13)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLrack4PL, CPLconvexhull, CPLconvexhulldelaunay,
% delaunayofCPL, CPLharbour, CPLfillin, CPLfillinside, CPLfillgap,
% CPLoutlinecontour
%
% [CPLD,dn]=CPLconvexhullfillgap(CPL,[d,ftyp,keep])
% === INPUT PARAMETERS ===
% CPL: CPL
% d: distance to fill the gap; default is 0.1
% ftyp: edge type 'default is 'square'
% keep: colinear points; default is false
% === OUTPUT RESULTS ======
% CPLD: convex hull of the delaunay triangulation
% dn:
%
% EXAMPLE:
% CPLconvexhulldelaunay(CPLsample(14));
% CPLconvexhulldelaunay(CPLsample(19));
% CPLconvexhulldelaunay(CPLsample(21));
% CPLfillgap(CPLsample(21),3)
% CPLconvexhullfillgap(CPLaddauxpoints(CPLsample(14),0.5),'','miter',true)
%
% See also: CPLrack4PL, CPLconvexhull, CPLconvexhulldelaunay,
% delaunayofCPL, CPLharbour, CPLfillin, CPLfillinside, CPLfillgap,
% CPLoutlinecontour
%
%
% Copyright 2020-2021 Tim C. Lueth

CPLconvexhulldelaunay(CPL)- returns the convex hull for a CPL

% CPLconvexhulldelaunay(CPL) - returns the convex hull for a CPL
% (by Tim Lueth, VLFL-Lib, 2020-AUG-16 as class: CLOSED POLYGON LISTS)
%
% based on delaunayofCPL (Status of: 2020-08-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLconvexhull, delaunayofCPL, CPLharbour, CPLfillin,
% CPLfillinside, CPLfillgap
%
% CPLD=CPLconvexhulldelaunay(CPL)
% === INPUT PARAMETERS ===
% CPL: CPL
% === OUTPUT RESULTS ======
% CPLD: convex hull of the delaunay triangulation
%
% See also: CPLconvexhull, delaunayofCPL, CPLharbour, CPLfillin,
% CPLfillinside, CPLfillgap
%
%
% Copyright 2020 Tim C. Lueth

SGcopypatternXYZ(SG,cp,dd,fuse)- returns a cell list of xyz copies or a fused solid of SG

% SGcopypatternXYZ(SG,cp,dd,fuse) - returns a cell list of xyz copies or a fused solid of SG
% (by Tim Lueth, VLFL-Lib, 2020-AUG-16 as class: SURFACES)
%
% was existing by Lauren de Smedt as SGpatternXYZ but forgotten and
% implemented from SGofCPLcommand (Status of: 2020-08-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGboxing, SGpatternRotz, SGcopyrotZ, SGarrangeSG,
% SGarrangeSGC, SGCaddSGn, SGCaddSG, SGstackn, SGcopyVL, SGsurfaces
%
% SG=SGcopypatternXYZ(SG,[cp,dd,fuse])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% cp: number of copies in [x y z]
% dd: distance between the copies
% fuse: if true; SG is struct not cell; default is true
% === OUTPUT RESULTS ======
% SG: cell list of SG
%
% EXAMPLE: Create copies at ten random positions
% SGcopypatternXYZ(SGcylinder,[1 1 3],4)
% SGcopypatternXYZ(SGcylinder,[1 1 3],4,true)
%
% See also: SGboxing, SGpatternRotz, SGcopyrotZ, SGarrangeSG,
% SGarrangeSGC, SGCaddSGn, SGCaddSG, SGstackn, SGcopyVL, SGsurfaces
%
%
% Copyright 2020 Tim C. Lueth

PoseofCPLcutui(CPL,CPLW)- allows the interactive shaping and move of poses of contours

% PoseofCPLcutui(CPL,CPLW) - allows the interactive shaping and move of poses of contours
% (by Tim Lueth, VLFL-Lib, 2020-AUG-16 as class: KINEMATICS AND FRAMES)
%
% This fnctn is helpful if you want to cut out from a background
% used first in exp_2019_01_27_chair
% (Status of: 2020-08-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: Poseofimageui, Poseorderchange, Posetransui, PoseofCPLui,
% exp_2019_01_27_chair
%
% PS=PoseofCPLcutui(CPL,[CPLW])
% === INPUT PARAMETERS ===
% CPL: Effektor contour
% CPLW: Background Contour
% === OUTPUT RESULTS ======
% PS: Pose Struct include A, B, CPLE, CPLB, CPLW
%
% EXAMPLE:
% CPL=PLcircle(70,'','',80); CPLW=PLcircle(60,'','',70); CPL=[CPL; nan nan; CPLW];
% PoseofCPLcutui (CPL,CPLW); PS=ans
%
% See also: Poseofimageui, Poseorderchange, Posetransui, PoseofCPLui,
% exp_2019_01_27_chair
%
%
% Copyright 2020-2021 Tim C. Lueth

SGButtonDownFcn(srch,cbdat)- Callback Fnct for current axis and all polygons inside

% SGButtonDownFcn(srch,cbdat) - Callback Fnct for current axis and all polygons inside
% (by Tim Lueth, VLFL-Lib, 2020-AUG-15 as class: USER INTERFACE)
%
% This fnctn installs the callback uipolygonmoveWindowButtonDownFcn if
% required
% This fnctn can be attached to gca and polygons (Status of: 2020-08-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: rotate3d, SGWindowButtonMotionFcn
%
% SGButtonDownFcn(srch,cbdat)
% === INPUT PARAMETERS ===
% srch: callback arg 1
% cbdat: callback arg 2
%
% EXAMPLE:
% set(gca,'ButtonDownFcn',@SGButtonDownFcn)
% set(findobj(gca,'Type','polygon'),'ButtonDownFcn',@SGButtonDownFcn,'selected','off')
%
%
% See also: rotate3d, SGWindowButtonMotionFcn
%
%
% Copyright 2020 Tim C. Lueth

SGWindowButtonMotionFcn(srch,cbdat)- implements the concept of get(gca,'CurrentPoint') also for rotate3d on

% SGWindowButtonMotionFcn(srch,cbdat) - implements the concept of get(gca,'CurrentPoint') also for rotate3d on
% (by Tim Lueth, VLFL-Lib, 2020-AUG-15 as class: USER INTERFACE)
%
% It seems that in 2019a in combination with some updates the behaviour
% of get(gca,'CurrentPoint') changed. It is not possible anymore within a
% ButtonDownFcn callback any other Currentpoint than the point of the
% first hit of the fnctn. This is a problem for some fnctn such as
% uipolygonmoveWindowButtonDownFcn. Therefor this fnctn, if installed as
% WindowButtonMotionFcn callback creates a global variable named
%
% get_gca_CurrentPoint which is the same as get(gca,'CurrentPoint')
%
% but works also for rotate3D on. (Status of: 2020-08-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: rotate3d, SGButtonDownFcn
%
% h=SGWindowButtonMotionFcn(srch,cbdat)
% === INPUT PARAMETERS ===
% srch:
% cbdat:
% === OUTPUT RESULTS ======
% h: global variable get_gca_CurrentPoint
%
% EXAMPLE:
% set(gcf,'WindowButtonMotionFcn',@SGWindowButtonMotionFcn);
%
%
% See also: rotate3d, SGButtonDownFcn
%
%
% Copyright 2020 Tim C. Lueth

SGdesignSupplement(S,F,w)- creates cylinders or CPLs that are big enough to encapsulate the fixture elements

% SGdesignSupplement(S,F,w) - creates cylinders or CPLs that are big enough to encapsulate the fixture elements
% (by Tim Lueth, VLFL-Lib, 2020-AUG-13 as class: AUTOMATIC DESIGN)
%
% THIS IST DIFFERENT TO SGsupplement
% This fnctn is used in combination with the creation of subtraction
% solid for fixations for instance such as SGdesignDIN912DIN985 or
% SGdesignDIN912DIN985ballbearing
% The SGdesignSupplement has to be ADDED to a solid. Afterwards it is
% possible to SUBTRACT the Subtraction solids (Status of: 2021-03-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdesignDIN912DIN985, SGdesignDIN912DIN985ballbearing
%
% [SGHS,SGNS]=SGdesignSupplement([S,F,w])
% === INPUT PARAMETERS ===
% S: Screw or Fiaxtion type using a Frame 'C' as separation
% F: Frame Name default is 'C'
% w: minimum wall size
% === OUTPUT RESULTS ======
% SGHS: Solid for Head SGdesignSupplement, green
% SGNS: Solid for Nut SGdesignSupplement, yellow
%
% EXAMPLE:
% [H,N,S]=SGdesignDIN912DIN985ballbearing([2.5 7 3.5],[10 +1])
% [SGHS,SGNS]=SGdesignSupplement(S)
% SG=SGsubtract(SGHS,H,'alignT',{'C','C'}); SGfigure; view(-30,30); SGTplotalpha(SG,'g',0.8); SGTplotalpha(S,'','','',SG,'alignT',{'C','C'});
% SG=SGsubtract(SGNS,N,'alignT',{'C','C'}); SGfigure; view(-30,30); SGTplotalpha(SG,'y',0.8); SGTplotalpha(S,'','','',SG,'matchT',{'C','C'});
%
%
% [H,N,S]=SGdesignDIN912DIN985([2.5 8])
% [SGHS,SGNS]=SGdesignSupplement(S)
% SGManipulatorLink(40,'',5.2,2); SA=ans;
% SA=SGunion(SA,SGNS,'center','matchT',{'C','B'}); SA=SGunion(SA,SGHS,'center','matchT',{'C','F'});
% SGfigure;view(-30,30); SGTplot(SA);
% SG=SGsubtract(SA,H,'alignT',{'C','F'}); SGfigure; view(-30,30); SGTplotalpha(SG,'g',0.8);
% SG=SGsubtract(SG,N,'alignT',{'C','B'}); SGfigure; view(-30,30); SGTplotalpha(SG,'g',0.8);
%
%
% See also: SGdesignDIN912DIN985, SGdesignDIN912DIN985ballbearing
%
%
% Copyright 2020-2021 Tim C. Lueth

exp_2020_08_13_refresh- creates an experiment compared to the ones almost 8 years ago

% exp_2020_08_13_refresh - creates an experiment compared to the ones almost 8 years ago
% (by Tim Lueth, VLFL-Lib, 2020-AUG-13 as class: EXPERIMENTS)
%
% This fnctn not only design a link between two frames, it also makes
% sure that it can be screwed by using norm elements such a DIN912 screw
% and a DIN985 nut (Status of: 2020-08-13)
%
% Introduced first in SolidGeometry 4.9
%
% See also: exp_2012_12_12, exp_2012_11_11_03
%
% exp_2020_08_13_refresh
%
% See also: exp_2012_12_12, exp_2012_11_11_03
%
%
% Copyright 2020 Tim C. Lueth

FLofVLFLinVLFL(VLA,FLA,VLB,FLB,flp)- searches for identical facets of B in A (slow)

% FLofVLFLinVLFL(VLA,FLA,VLB,FLB,flp) - searches for identical facets of B in A (slow)
% (by Tim Lueth, VLFL-Lib, 2020-AUG-13 as class: SURFACES)
%
% =======================================================================
% OBSOLETE (2020-08-13) - USE 'findfacetsinVLFL' INSTEAD
% =======================================================================
%
% Good example for a fnctn not implemented better as second try - Compare
% with findfacetsinVLFL which is more flexible in Version SG-Lib 4.9
% (Status of: 2020-08-13)
%
% Introduced first in SolidGeometry 4.9
%
% See also: [ findfacetsinVLFL ] ; SGcolorcopy, findfacetsinVLFL,
% ismemberFL
%
% [fia,fib,ci]=FLofVLFLinVLFL(VLA,FLA,VLB,[FLB,flp])
% === INPUT PARAMETERS ===
% VLA: Vertex list A or SGA
% FLA: Facet list A
% VLB: Vertex list B or SGB
% FLB: Facet list B
% flp: not in use
% === OUTPUT RESULTS ======
% fia: faces of A used in B
% fib: faces of B used in A
% ci: face correspondance list
%
% EXAMPLE:
% SGbox([15*dofn(6)*2 20 10]); A=ans;
% SGtransP(SGcylinder(20,10,6),[0 0 -5]); B=ans;
% A=SGcolorfaces(A,'g'); B=SGcolorfaces(B,'y');
% [a,b,c]=FLofVLFLinVLFL(A,'',B)
% SGcolorcopy(A,B); SGfigure(ans); view(30,30)
% findfacetsinVLFL(A.VL,A.FL,B.VL,B.FL)
%
% See also: [ findfacetsinVLFL ] ; SGcolorcopy, findfacetsinVLFL,
% ismemberFL
%
%
% Copyright 2020 Tim C. Lueth

SGbearingslide(Sz,fit)- erzeugt ein Gleitlager nach Spezifikationen für einen AM Printer

% SGbearingslide(Sz,fit) - erzeugt ein Gleitlager nach Spezifikationen für einen AM Printer
% (by Tim Lueth, VLFL-Lib, 2020-AUG-12 as class: PARAMETRIC DESIGN)
%
% Unter einem Durchmesser von 3mm gibt es kaum Gleitlager und Wälzlager
% werden extrem teuer. Nicht zuletzt deshalb bietet es sich an, die
% Gleitlager selbst zu drucken in den Größenordnung der verfügbaren
% Wälzlager
% Diese Funktion unterstützt unterschiedliche Passungen zwischen den
% beiden Lagerhälften. (Status of: 2020-08-12)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbearing
%
% [SGI,SGO]=SGbearingslide([Sz,fit])
% === INPUT PARAMETERS ===
% Sz: Size of the Sliding Bearing
% fit: 'c form2b' transition fit for formlab 2
% === OUTPUT RESULTS ======
% SGI: Inner Part for the Screw or Shaft
% SGO: Outer Part for "Interference Fit"
%
% EXAMPLE:
% SGbearingslide([2.5 8 1.6],'t formiga') % Transition fit for EOS Formiga100 Printer
% SGbearingslide([2.5 8 1.6],'c form3b') % Clearance fit for Formlab FORM3B Printer
%
% See also: SGbearing
%
%
% Copyright 2020 Tim C. Lueth

SGManipulatorDIN912DIN985ballbearing(LL,LR,LH,BS,SS)- returns all the parts of a 7DoF manipulator than can be assembled by screws and ballbearings

% SGManipulatorDIN912DIN985ballbearing(LL,LR,LH,BS,SS) - returns all the parts of a 7DoF manipulator than can be assembled by screws and ballbearings
% (by Tim Lueth, VLFL-Lib, 2020-AUG-11 as class: AUTOMATIC DESIGN)
%
% Writes also all solid geometries on disk.
% Be careful that the dimensions of Manipulator arm segments are not
% multiples or integer fractions of the length of screws or ball bearings
% (Status of: 2020-08-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGManipulator04Basem, SGManipulator04Link
%
% [A,B,C,D,U,E]=SGManipulatorDIN912DIN985ballbearing([LL,LR,LH,BS,SS])
% === INPUT PARAMETERS ===
% LL: Distance between Axis; default is 40
% LR: Radius; default is 5.1
% LH: Height default is 7.1
% BS: Ball Bearing size (Ri, RO, W] default is [2.5 7 3.5]
% SS: Screw Seize {L oh] Length overhead default is [8 -1]
% === OUTPUT RESULTS ======
% A: Baser plate
% B: 1st link and 4th link
% C: optiona 7DoF
% D: 2nd link
% U: 3rd link and 5th link
% E: 6th link end effector
%
% EXAMPLE:
% [A,B,C,D,H,EF]=SGManipulatorDIN912DIN985ballbearing;
% SGTchain({A,B,C,D,H,B,H,EF},[pi pi 0 pi 0 pi 0]); SGn=ans; SGfigure; SGplotalpha(SGn,'w'); view(-30,30); fullview(0.5)
% SGfigure; view(-30,30); SGplotalpha(SGn);
%
%
% See also: SGManipulator04Basem, SGManipulator04Link
%
%
% Copyright 2020 Tim C. Lueth

slfit(typ,name)- returns the slot size value for a desired fitting during programmed design procedures

% slfit(typ,name) - returns the slot size value for a desired fitting during programmed design procedures
% (by Tim Lueth, VLFL-Lib, 2020-AUG-11 as class: MECHANICAL PROCEDURES)
%
% It is not a perfect method. Better it would be to use frames that
% explain the fitting by a letter such as
% 'fit-c' or 'fit-cx' if several frames are used or a combination of 'c'
% and arbitray frame name
% fittings {'c','0123'} with the number as fitting frame name
% The results using a FORM2 Printer with clear Resin V4 and 50µm
% resolution were on Aug. 16 2020 by Tim Lueth for bore hole radius
% oversize (plus == increase of bore hole radius):
% +0.05mm not to be pressed in at all by hand - probably destroyed by
% hammering
% +0.10mm Difficult to push in by hand and difficult to remove even with
% a hammer
% +0.15mm Easy to press in by hand and can only be easily removed by hand
% +0.20mm easy to join by hand and falls out by itself when shaken
% +0.25mm falls out by turning under its own weight
% The results using a FORM3B Printer with MOdel Resin V2 and 50µm
% resolution were on Aug. 11 2020 by Tim Lueth for bore hole radius
% oversize (minus == increase of bore hole radius
% +0.05mm Difficult to push in by hand and difficult to remove even with
% a hammer
% +0.10mm Difficult to push in by hand and difficult to remove even with
% a hammer
% +0.15mm Easy to press in by hand and can only be easily removed by hand
% +0.20mm easy to join by hand and falls out by itself when shaken
% +0.25mm falls out by turning under its own weight
% (Status of: 2020-08-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: DIN4AMfitting, islfit, FLofSGcolor
%
% LITERATURE:
% - Fischer et al. (2011): Tabellenbuch Metall, Verlag Europa-Lehrmittel,
% Nourney, 45. Auflage,
%
% [sl,Printer]=slfit([typ,name])
% === INPUT PARAMETERS ===
% typ: clearance type such as 'c', 't', 'i'
% name: name fo a printer such as FORM2
% === OUTPUT RESULTS ======
% sl: slot size ==> deivide by 2 for radius
% Printer: exact printer name
%
% EXAMPLE:
% slfit('set formiga');
% Ri=3; [sl,AM]=slfit('c','FORM3B') % try 'c' and 't' and 'i'
% A=SGofCPLz([PLsquare([8 8]);nan nan;PLcircle(Ri+sl); nan nan; PLcircle(Ri)],10); A.designed4=AM;
% SGdimensioning4(A);
%
% See also: DIN4AMfitting, islfit, FLofSGcolor
%
%
% Copyright 2020-2021 Tim C. Lueth

SGgrowVLFLfi(VL,FL,fi,dt)- moves facets of an indexed surface along the normal vectors

% SGgrowVLFLfi(VL,FL,fi,dt) - moves facets of an indexed surface along the normal vectors
% (by Tim Lueth, VLFL-Lib, 2020-AUG-10 as class: SURFACES)
%
% Just a first approach - There is a lot to improve (Status of:
% 2020-08-10)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGgrow, SGgrowinsideFS, SGgrowinsideoutside
%
% [VL,FL]=SGgrowVLFLfi(VL,FL,fi,dt)
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% fi: Facet Indices
% dt: distance to grow
% === OUTPUT RESULTS ======
% VL: New Vertex list
% FL: Same Facet list
%
% EXAMPLE:
% SGfittingsample; A=ans; FSofSGT(A,'F',-1); fi=ans;
% SG=SGcolorfaces(A,'r',fi); SGfigure; view(-30,30); SGplotalpha(SG);
% fi=FLofSGcolor(SG,'r');
% SGgrowVLFLfi(SG.VL,SG.FL,fi,-1.5)
%
% See also: SGgrow, SGgrowinsideFS, SGgrowinsideoutside
%
%
% Copyright 2020 Tim C. Lueth

FLofSGcolor(SG,col)- finds the faced of a specified color

% FLofSGcolor(SG,col) - finds the faced of a specified color
% (by Tim Lueth, VLFL-Lib, 2020-AUG-10 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGcolorfaces
%
% fi=FLofSGcolor(SG,col)
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% col: search color
% === OUTPUT RESULTS ======
% fi: facet index in SG
%
% EXAMPLE:
% SGfittingsample; A=ans; FSofSGT(A,'F',-1); fi=ans; SGcolorfaces(A,'dp',fi); SG=ans, % deep purple
% FLofSGcolor(SG,'dp') % logical faces of SG.FL
% FLofSGcolor(SG,'r');
%
% See also: SGcolorfaces
%
%
% Copyright 2020 Tim C. Lueth

PLshaft(r,d,b)- creates a PL for a contour for SGofCPLrot

% PLshaft(r,d,b) - creates a PL for a contour for SGofCPLrot
% (by Tim Lueth, VLFL-Lib, 2020-AUG-10 as class: CLOSED POLYGON LISTS)
%
% =======================================================================
% OBSOLETE (2022-01-16) - USE 'PLshaftrad' INSTEAD
% =======================================================================
%
% will be removed! (Status of: 2022-01-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: [ PLshaftrad ] ; CPLmotorshaft
%
% PL=PLshaft([r,d,b])
% === INPUT PARAMETERS ===
% r: [r1 r2 r3 ....] radius
% d: distance between radius
% b: radius for breaking the edges; default is 0.3
% === OUTPUT RESULTS ======
% PL: Point list of a shaft
%
% EXAMPLE:
% PLshaft([6 3 6],5,1); PL=ans; SGofCPLrot(fliplr(PL))
% PLshaft([6 3 6],5,0); PL=ans; SGofCPLrot(fliplr(PL))
%
% See also: [ PLshaftrad ] ; CPLmotorshaft
%
%
% Copyright 2020-2022 Tim C. Lueth

SGfittingsample(d)- returns a solid for fitting experiments

% SGfittingsample(d) - returns a solid for fitting experiments
% (by Tim Lueth, VLFL-Lib, 2020-AUG-08 as class: MODELING PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbox, SGsample
%
% SG=SGfittingsample([d])
% === INPUT PARAMETERS ===
% d: [d r1 r2 r3 ....] distance and radius
% === OUTPUT RESULTS ======
% SG: Solid Geometry
%
% EXAMPLE:
% SGfittingsample([5 1 2 3])
%
% See also: SGbox, SGsample
%
%
% Copyright 2020 Tim C. Lueth

SGmotorN20()- returns just the Geometry of a N20 motor

% SGmotorN20() - returns just the Geometry of a N20 motor
% (by Tim Lueth, VLFL-Lib, 2020-AUG-06 as class: MODELING PROCEDURES)
%
% Extraction of the N20 motor from the SGmotorSolExpert fnctn (Status of:
% 2020-08-10)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbatteriepack, SGmotorSolExpert, SGcapontop, SGmotorshaft,
% SGmotorhousing
%
% SG=SGmotorN20([])
% === OUTPUT RESULTS ======
% SG: Solid Geometry of a N20 Motor
%
% EXAMPLE:
% SGmotorN20; SG=ans;
% SGmotorN20('encoder'); SG=ans; SGdimensioning4(SG);
% SGmotorhousing(SGgrow(SG,0.5),1.4);
%
% See also: SGbatteriepack, SGmotorSolExpert, SGcapontop, SGmotorshaft,
% SGmotorhousing
%
%
% Copyright 2020 Tim C. Lueth

DIN4AMfitting(M,Q)- DIN similar table for fitting offsets with different AM-Printers

% DIN4AMfitting(M,Q) - DIN similar table for fitting offsets with different AM-Printers
% (by Tim Lueth, VLFL-Lib, 2020-AUG-05 as class: MECHANICAL PROCEDURES)
%
% The data was measured with
% - 5mm holes and 5mm dowel pins
% - 2.5mm hexagonal bits
% clearance_fit', => Spielpassung
% 'transition_fit', => Übergangspassung
% 'interference_fit'=> Presspassung
% See also Fischer et al (2011), Page 99ff. (Status of: 2020-08-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DIN985, DINfindinTab,
% DIN, 433, DINhelp, DINthreadtorque, DIN4AMFitting, slfit
%
% LITERATURE:
% - Fischer et al. (2011): Tabellenbuch Metall, Verlag Europa-Lehrmittel,
% Nourney, 45. Auflage,
%
% [M,TL,Taborder]=DIN4AMfitting(M,[Q])
% === INPUT PARAMETERS ===
% M: Search term such as "Formiga'
% Q: Optional search term in Taborder
% === OUTPUT RESULTS ======
% M: Number oder Char such as "Formiga'
% TL: Table or table entry if Q is used
% Taborder: Name of Table cols
%
% EXAMPLE:
% DIN4AMfitting
% [M,TL]=DIN4AMfitting ('FORM2')
% [M,TL]=DIN4AMfitting ('FORM3B','trans')
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DIN985, DINfindinTab,
% DIN, 433, DINhelp, DINthreadtorque, DIN4AMFitting, slfit
%
%
% Copyright 2020 Tim C. Lueth

SGdesignDIN912DIN985radialbearing(bbb,sdl,ins,tpl,W)- creates subtraction solids for a bearing connection at a specific frame position of a solid

% SGdesignDIN912DIN985radialbearing(bbb,sdl,ins,tpl,W) - creates subtraction solids for a bearing connection at a specific frame position of a solid
% (by Tim Lueth, EXPERIMENT, 2020-AUG-05 as class: AUTOMATIC DESIGN)
%
% Former name (4.9 and 5.0) was SGdesignDIN912DIN985ballbearing
% If two elements should be connected using a ball bearing, this fnctn
% helps to create the subtraction solids to achive a fnctnal connection
% using standard machine elements. (Status of: 2022-01-15)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdesignDIN912DIN985, SGdesignBallbearing, SGdesignSupplement
%
% [H,N,S,mt,parts]=SGdesignDIN912DIN985radialbearing([bbb,sdl,ins,tpl,W])
% === INPUT PARAMETERS ===
% bbb: [Ri Ro Width] of the ball bearing
% sdl: [length overize] length and oversize of the screw DIN912
% ins: "TT", "TP, "PT", "PP"; Default is "TT"
% tpl: Length of Insertion T/P for [HEAD NUT]; default is 10 10
% W: Rotation angle for the depth of the pocket
% === OUTPUT RESULTS ======
% H: Subtraction Solid for plug side including frame 'C'
% N: Subtraction Solid for bearing side including frame 'C'
% S: Geometry of Plug including frame 'C'
% mt: remaining material width
% parts: parts list for assembly of one connection
%
% EXAMPLE:
% SGdesignDIN912DIN985radialbearing
% [P,N,S]=SGdesignDIN912DIN985radialbearing([2.5 7 3.5],[8 -1],'T',20);
% SG=SGManipulatorLink('',true);
% SG=SGsubtract(SG,P,'alignT',{'C','B'});
% SG=SGsubtract(SG,N,'alignT',{'C','F'}); SGfigure(SG);
%
% See also: SGdesignDIN912DIN985, SGdesignBallbearing, SGdesignSupplement
%
%
% Copyright 2020-2022 Tim C. Lueth

DIN433(M)- returns the DIN433 table for a 2D Metric Washer

% DIN433(M) - returns the DIN433 table for a 2D Metric Washer
% (by Tim Lueth, VLFL-Lib, 2020-AUG-05 as class: AUXILIARY PROCEDURES)
%
% 'M','Inner_Diameter','Outer_Diameter','Height'
% The inner diameter is also the norm diameter for a drilling hole for a
% screw of this size. I.e. for M5 screws use a 5.3mm diameter for the
% drilling hole (Status of: 2020-08-05)
%
% Introduced first in SolidGeometry 4.9
%
% See also: DIN13, DIN336, IN464, DIN912, DIN913, DIN985, DINfindinTab,
% DINhelp, DINthreadtorque
%
% [M,TL,Taborder]=DIN433(M)
% === INPUT PARAMETERS ===
% M: Desired metric diameter
% === OUTPUT RESULTS ======
% M: Metric Diameter in Tab
% TL: Table row
% Taborder: Table colum names
%
% EXAMPLE:
% DIN433
% DIN433(2.3)
% DIN_433=DIN433; DINfindinTab(2.3,DIN_433)
%
% See also: DIN13, DIN336, IN464, DIN912, DIN913, DIN985, DINfindinTab,
% DINhelp, DINthreadtorque
%
%
% Copyright 2020 Tim C. Lueth

FLinsideSurfaceofSG(SG,seper,maxtry,wlim,ilim)- Returns the Facet Indices of inside surfaces

% FLinsideSurfaceofSG(SG,seper,maxtry,wlim,ilim) - Returns the Facet Indices of inside surfaces
% (by Tim Lueth, VLFL-Lib, 2020-AUG-04 as class: EXPERIMENTS)
%
% Uses SGinsideSurface
% In contrast to SGinsideSurface, this fnctn first of all splits a
% geometry into independent surfaces, which were possibly only combined
% with SGconcat. To avoid STL reading errors it is recommended to use the
% SGshortopti fnctn for CATIA/SOLIDWORS exported models.
% Afterwards the inner faces are detected for each of these surfaces.
% It is not always useful to disassemble the surfaces first, so there is
% an option to switch this off (Status of: 2020-08-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGcheckfacedist, SGinsidesurface
%
% [FLi,SG]=FLinsideSurfaceofSG(SG,[seper,maxtry,wlim,ilim])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% seper: separate into independent surfaces first; default is true
% maxtry: Number of tries to find an opponing facet; default is 10
% wlim: warning limit; default is 0.7 mm
% ilim: intended limit; distance that is intended; default is 0.1mm
% === OUTPUT RESULTS ======
% FLi: Facet surface index list
% SG: inside index of feature surface
%
% EXAMPLE:
% load JACO_robot.mat
% SG=SGsurfaces(JC3,3)
% FLinsideSurfaceofSG(SG);
%
% FLinsideSurfaceofSG(SG); fi=ans; fi=find(fi); fi=fi(1), T=Tof3P(SG.VL(SG.FL(fi,:),:)); tplot(T,100); FSofSGT(SG,T,'',.1)
% FLinsideSurfaceofSG(SG); fi=ans; SGN=SG; SGN.FL=SG.FL(fi,:); SGsurfaces(SGN)
%
% See also: SGcheckfacedist, SGinsidesurface
%
%
% Copyright 2020 Tim C. Lueth

SGDIN464(M,L,H)- SG of a knureld screw

% SGDIN464(M,L,H) - SG of a knureld screw
% (by Tim Lueth, VLFL-Lib, 2020-AUG-03 as class: MODELING PROCEDURES)
%
% M2.5 V2A => M7 PA (Status of: 2020-08-03)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGDIN912, SGDIN985, SGDIN433, SGDIN9021
%
% [SG,M]=SGDIN464([M,L,H])
% === INPUT PARAMETERS ===
% M: Metric Diameter
% L: Length of Screw
% H: Optional knurled head size
% === OUTPUT RESULTS ======
% SG: Solid Geomtry
% M:
%
% EXAMPLE:
% SGDIN464(5,8) % M5 x 8 NORM
% SGDIN464(5,8,10) % M5 x 8 Knureled heigh 10mm
%
%
% See also: SGDIN912, SGDIN985, SGDIN433, SGDIN9021
%
%
% Copyright 2020 Tim C. Lueth

DIN464(M)- returns the DIN464 table for a metric threads with knureld head

% DIN464(M) - returns the DIN464 table for a metric threads with knureld head
% (by Tim Lueth, VLFL-Lib, 2020-AUG-03 as class: AUXILIARY PROCEDURES)
%
% 'M','Knurled_Diameter','Knurled_Height','Socket_Diameter','Head_Height'
% (Status of: 2020-08-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: DIN13, DIN336, DIN912, DIN913, DIN985, DINfindinTab, DINhelp,
% DINthreadtorque
%
% [M,TL,Taborder]=DIN464(M)
% === INPUT PARAMETERS ===
% M: Desired metric diameter
% === OUTPUT RESULTS ======
% M: Metric Diameter in Tab
% TL: Table row
% Taborder: Table colum names
%
% See also: DIN13, DIN336, DIN912, DIN913, DIN985, DINfindinTab, DINhelp,
% DINthreadtorque
%
%
% Copyright 2020 Tim C. Lueth

PLknurled(R,n,k,m)- returns a sinus contour on a circle

% PLknurled(R,n,k,m) - returns a sinus contour on a circle
% (by Tim Lueth, VLFL-Lib, 2020-AUG-03 as class: CLOSED POLYGON LISTS)
%
% USED in SGDIN464 (Status of: 2021-01-24)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLknurled, PLstar, SGDIN464
%
% PLK=PLknurled([R,n,k,m])
% === INPUT PARAMETERS ===
% R: Radius
% n: nofrd(R)
% k: number of waves
% m: offset to R;
% === OUTPUT RESULTS ======
% PLK: CPLof of knureld contour
%
% EXAMPLE:
% PLknurled(5)
% PLstar(5,100,'','','',0.95);
%
% See also: PLknurled, PLstar, SGDIN464
%
%
% Copyright 2020-2021 Tim C. Lueth

SGslidingcoverofCPLz(CPL,w,T,op)- returns the part of a plane sliding cover for a solid with defined wall sizes

% SGslidingcoverofCPLz(CPL,w,T,op) - returns the part of a plane sliding cover for a solid with defined wall sizes
% (by Tim Lueth, VLFL-Lib, 2020-AUG-02 as class: AUTOMATIC DESIGN)
%
% w wall thickness
% h Height
% e Extension length
% s Slot size
% format [w [h e s]] (Status of: 2020-08-02)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGcapontop
%
% SG=SGslidingcoverofCPLz(CPL,[w,T,op])
% === INPUT PARAMETERS ===
% CPL: Contour of a convex hull
% w: [w h e sl] wall thickness of the walls ; height of the plate
% T: Frame to align the cover; not supported yet
% op:
% === OUTPUT RESULTS ======
% SG: Plate consisting of at least three parts
%
% EXAMPLE:
% SGslidingcoverofCPLz (PLsquare(10,20),[2 4]); % Contour with wall thickness 2 and desired height 4
% %% Create a housing for a motor with an sliding cover
% SGmotorSolExpert; M=ans; [C,~,CPL]=SGcapontop(M,[inf 2],'','simple'); SGplotalpha(C,'w',0.2);
% SGslidingcoverofCPLz(CPL,[2 4]); P=ans; % Create a Slidung Cover
% SGtransrelSG(P,C,'under'); P=ans; % Position Sliding Cover
% SGanalyzeGroupParts({P,C}); SG=ans; % Fuse Parts
% SGunion(SG.SG); SGanalyzeGroupParts(ans) % Show the new solids
% SGslidingcoverofCPLz(CPLradialEdges(CPLofPL(PLsquare(20))),[1 4 2 ],'',[9 1]); % with opening
%
% See also: SGcapontop
%
%
% Copyright 2020 Tim C. Lueth

SGmotorhousing(M,w,D)- returns a housing betwenn Base frame 'B' and end of motor

% SGmotorhousing(M,w,D) - returns a housing betwenn Base frame 'B' and end of motor
% (by Tim Lueth, VLFL-Lib, 2020-AUG-01 as class: AUTOMATIC DESIGN)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGcapontop, SGslidingcoverofCPLz
%
% [C,P]=SGmotorhousing(M,[w,D])
% === INPUT PARAMETERS ===
% M: SG Model of Motor
% w: wall width of housing; default is 2mm [w e sl]
% D: Diameter of hole at front side; default is 9mm; 0 and inf is possible
% === OUTPUT RESULTS ======
% C: Cell array of housing and slinder
% P:
%
% EXAMPLE:
% SGmotorSolExpert; M=ans;
% SGmotorhousing(SGgrow(M,.05),2); C=ans % Growing of 1/10 is required for formlab
%
% See also: SGcapontop, SGslidingcoverofCPLz
%
%
% Copyright 2020 Tim C. Lueth

SGcablewinch(wsz,drl)- creates a solid for a cable winch

% SGcablewinch(wsz,drl) - creates a solid for a cable winch
% (by Tim Lueth, VLFL-Lib, 2020-AUG-01 as class: AUTOMATIC DESIGN)
%
% If an optional length is specified, it is possible to set outer Radius
% or Height to Zero to get an automatic design of the cable winch (Status
% of: 2020-08-06)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGmotorSolExpert, SGmotorshaft
%
% [SG,nl]=SGcablewinch([wsz,drl])
% === INPUT PARAMETERS ===
% wsz: [Ri Ro H] Inner Outer Diameter and Height
% drl: [D l] Diameter of cable and optional length
% === OUTPUT RESULTS ======
% SG: Solid Geometry
% nl: Cable length
%
% EXAMPLE:
% SGcablewinch([5 15 5],1) % Winch for 1mm cable [ri ro h]
% SGcablewinch([5 0 5],[1 400]) % calc outer diameter for at least 40 cm
% SGcablewinch([5 10 0],[1 400]) % calc Height for at least 40 cm
%
% See also: SGmotorSolExpert, SGmotorshaft
%
%
% Copyright 2020 Tim C. Lueth

SGhook4rail(DR,WS,DL)- returns a solid for a rail hook looking to face

% SGhook4rail(DR,WS,DL) - returns a solid for a rail hook looking to face
% (by Tim Lueth, VLFL-Lib, 2020-AUG-01 as class: SURFACES)
%
% Can be used for a Motorcycle helmet at an 30mm IKEA Rail - Printing
% Time 4h (Status of: 2020-08-01)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbitISO1173
%
% SG=SGhook4rail([DR,WS,DL])
% === INPUT PARAMETERS ===
% DR: Diameter of Rail; default is 30mm
% WS: Wall size; default is DR/3
% DL: Elongation for hook; default is DR/2
% === OUTPUT RESULTS ======
% SG: Hook for a Rail
%
% EXAMPLE:
% SGhook4rail(30,6,'','Biker''s Dream'); SG=ans
%
% See also: SGbitISO1173
%
%
% Copyright 2020 Tim C. Lueth

SGrepairFLsimple(SG)- returns a solid with closed FL of the simpliest condition

% SGrepairFLsimple(SG) - returns a solid with closed FL of the simpliest condition
% (by Tim Lueth, VLFL-Lib, 2020-AUG-01 as class: SURFACES)
%
% Simply uses FLrepair.
% This fnctn closes obvious missing triangles in a facet list. It has
% clear limitations if a surface has edge facets with more than 90 degree
% angle. (Status of: 2020-08-01)
%
% Introduced first in SolidGeometry 4.9
%
% See also: FLrepair
%
%
% SG=SGrepairFLsimple(SG)
% === INPUT PARAMETERS ===
% SG: Solid Geometry SG.VL,SG.FL
% === OUTPUT RESULTS ======
% SG: Repaired Solid
%
% EXAMPLE:
% SGsphere(5); X=ans % Create a shpere
% X.FL=X.FL([1:615,617:end],:) % remove one facet
% SGcheckmeshlab(X); % Analyze the error
% SGrepairFLsimple(X); Y=ans % Close the facet
%
% See also: FLrepair
%
%
%
% Copyright 2020 Tim C. Lueth

SGTswap(SG,FA,FB);- Swaps two frames of a Solid

% SGTswap(SG,FA,FB); - Swaps two frames of a Solid
% (by Tim Lueth, VLFL-Lib, 2020-JUL-31 as class: KINEMATICS AND FRAMES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGTget, SGTset
%
% SGN=SGTswap(SG,FA,FB);
% === INPUT PARAMETERS ===
% SG: Solid
% FA: Frame name A
% FB: Frame name B
% === OUTPUT RESULTS ======
% SGN: Solid with swapped frame names
%
% EXAMPLE:
% SG=SGcylinder(10,40); SG=SGTset(SG,'F',TofFS(SG,[0 0 1])); SG=SGTset(SG,'B',TofFS(SG,[0 0 -1]));
% SGTswap(SG,'F','B')
%
% See also: SGTget, SGTset
%
%
% Copyright 2020 Tim C. Lueth

randol(r,c,rmin)- return an random number with at least a minimum value unit the next perdecimal

% randol(r,c,rmin) - return an random number with at least a minimum value unit the next perdecimal
% (by Tim Lueth, VLFL-Lib, 2020-JUL-31 as class: AUXILIARY PROCEDURES)
%
% helpful for random overlap intervalls (Status of: 2020-07-31)
%
% Introduced first in SolidGeometry 4.9
%
% See also: randsupp, randminv
%
% r=randol([r,c,rmin])
% === INPUT PARAMETERS ===
% r: rows or minimum number
% c: col
% rmin: minimum number; default is 0.01
% === OUTPUT RESULTS ======
% r: randum number, or matrix
%
% EXAMPLE:
% randol(4,4,.2) % 4x4 matrix, numbers between [0.2 and 0.3[
%
% See also: randsupp, randminv
%
%
% Copyright 2020 Tim C. Lueth

exp_2020_07_31_LinkBallbearing- Experiment to print dummyplugs for bearing links

% exp_2020_07_31_LinkBallbearing - Experiment to print dummyplugs for bearing links
% (by Tim Lueth, VLFL-Lib, 2020-JUL-31 as class: EXPERIMENTS)
%
% ..writes directly on disk (Status of: 2020-07-31)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGManipulatorLink, SGdesignDIN912DIN985, SGbearing
%
% exp_2020_07_31_LinkBallbearing
%
% See also: SGManipulatorLink, SGdesignDIN912DIN985, SGbearing
%
%
% Copyright 2020 Tim C. Lueth

SGTplotalpha(SG,c,a,e,relSG,relpos)- plots a solid including all frames and supports directly color and alpha value

% SGTplotalpha(SG,c,a,e,relSG,relpos) - plots a solid including all frames and supports directly color and alpha value
% (by Tim Lueth, VLFL-Lib, 2020-JUL-31 as class: USER INTERFACE)
%
% Just one successive call of SGplotalpha und SGTframeplot
% Changes SG-Lib 5.2: Automatically includes also position of frames into
% sizze for SGTframeplot (Status of: 2020-07-31)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGplot, setplotlight, SGplotalpha
%
% h=SGTplotalpha(SG,[c,a,e,relSG,relpos])
% === INPUT PARAMETERS ===
% SG: SOlid Geometry
% c: color; default is [];
% a: alpha value; default is 1;
% e: edge color; default is [];
% relSG: Solid as Position reference
% relpos: relative positioning like SGtransrelSG
% === OUTPUT RESULTS ======
% h: handle to graphics object patch
%
% EXAMPLE:
% SGfigure; view(-30,30); SGTplotalpha(SGcylinder(10,20,6),'b',.2);
% SGfigure; view(-30,30); SGTplotalpha(SGcylinder(10,20,6),'b',.2,'r');
% SGfigure; view(-30,30); SGTplotalpha({SGbox,SGcylinder(5)},'r',0.4,'g'); shg
% SGfigure; view(-30,3); SGTplotalpha(SGbox,'r',1,'',SGbox,'ontop',20); shg
%
% See also: SGplot, setplotlight, SGplotalpha
%
%
% Copyright 2020-2022 Tim C. Lueth

SGManipulatorBase(LL,Shap,LD,LH)- Plate, Base, and Hand for Manipulator Design # 4

% SGManipulatorBase(LL,Shap,LD,LH) - Plate, Base, and Hand for Manipulator Design # 4
% (by Tim Lueth, VLFL-Lib, 2020-JUL-30 as class: KINEMATICS AND FRAMES)
%
% Those parts can be assembled using screws, spacer, and nut of DIN DIN
% 912, DIN 985, DIN 433 using Diameter 2.5mm and 8mm length and a ball
% bearing S692-X-2Z (2.50 Euro /Stück) with inside 2.5mm, outside 7mm and
% width 3.5mm
% (Status of: 2020-08-01)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdimensioning4, SGdesignBallbearing, SGdesignDIN912DIN985,
% SGManipulatorLink
%
% [A,B,K,U,E]=SGManipulatorBase([LL,Shap,LD,LH])
% === INPUT PARAMETERS ===
% LL: Length of Base and Hand; default is 40
% Shap: Surface shaping; default is true
% LD: Radius of the tips; default is 5mm
% LH: Height of the parts; default is 6mm
% === OUTPUT RESULTS ======
% A: Base PLate
% B: Base
% K: 7 DoF
% U: Hand
% E: Effektor
%
% EXAMPLE: Create all parts of a 7DoF Manipulator
% SGManipulatorBase('',false); % Just no surface shaping
% [A,B,C,H,EF]=SGManipulatorBase
% D=SGManipulatorLink % Link and link extender
% SGTchain({A,B,C,D,H,B,H,EF},[pi pi 0 pi 0 pi 0]); SGn=ans; SGfigure; SGplotalpha(SGn,'w'); view(-30,30); fullview(0.5)
% SGfigure; view(-30,30); SGplotalpha(SGn)
%
% See also: SGdimensioning4, SGdesignBallbearing, SGdesignDIN912DIN985,
% SGManipulatorLink
%
%
% Copyright 2020 Tim C. Lueth

SGManipulatorLink(LL,Shap,LD,LH,DD)- Link with 2 Frames to create mechanisms or

% SGManipulatorLink(LL,Shap,LD,LH,DD) - Link with 2 Frames to create mechanisms or
% (by Tim Lueth, VLFL-Lib, 2020-JUL-28 as class: KINEMATICS AND FRAMES)
%
% This is just a simple design of a mechanical link with desired
% dimensions including 2 frames (Status of: 2021-01-07)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGlinkage, SGdimensioning, SGdesignBallbearing,
% SGdesignDIN912DIN985, SGManipulatorBase
%
% SG=SGManipulatorLink([LL,Shap,LD,LH,DD])
% === INPUT PARAMETERS ===
% LL: Axis Distance; default is 40; or [Startpoint;Endpoint]
% Shap: if true; the links are shaped; default is false
% LD: Radius of the Tip rounding; default is 5
% LH: Height of the Elements also used as shaping Radius; default is 6
% DD: if true; the shape is doubled for chaining; default is false
% === OUTPUT RESULTS ======
% SG: Link Geometry
%
% EXAMPLE:
% SGManipulatorLink(40,true); SG=ans;
% SGdimensioning4(SG);
% [P,N]=SGdesignBallbearing([2.5 7 3.5]); % Create Space for Shaft
% SG=SGsubtract(SG,P,'alignT',{'C','B'});
% SG=SGsubtract(SG,N,'alignT',{'C','F'}); SGfigure(SG);
% SGManipulatorLink(40,true); SG=ans;
% [P,N,S]=SGdesignDIN912DIN985([3 10 0],'TT',40,pi/2);
% SG=SGsubtract(SG,P,'alignT',{'C','B'});
% SG=SGsubtract(SG,N,'alignT',{'C','F'}); SGfigure(SG);
%
% See also: SGlinkage, SGdimensioning, SGdesignBallbearing,
% SGdesignDIN912DIN985, SGManipulatorBase
%
%
% Copyright 2020-2021 Tim C. Lueth

CPLTopCM_SUN(CPL,h,E0,nu,fixeddomain,loaddomain,loadvec,spring,pout,poutxy,poutdir,cons,VolFrac,MaxIter)- automatic design of a compliant mechanism based on topology optimization techniques.

% CPLTopCM_SUN(CPL,h,E0,nu,fixeddomain,loaddomain,loadvec,spring,pout,poutxy,poutdir,cons,VolFrac,MaxIter) - automatic design of a compliant mechanism based on topology optimization techniques.
% (by Yilun Sun, VLFL-Lib, 2020-JUL-28 as class: AUTOMATIC DESIGN)
%
% Very Powerful fnctn to create soft kill option topology optimization
% for large displacements
% SKOLD (Status of: 2020-08-30)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGshapeOptiCAO, SGshapeOptiSKO
%
% [CPL4,z,fem,Vcell,farray]=CPLTopCM_SUN(CPL,h,E0,nu,fixeddomain,loaddoma
% in,loadvec,spring,pout,poutxy,poutdir,cons,VolFrac,MaxIter)
% === INPUT PARAMETERS ===
% CPL:
% h:
% E0:
% nu:
% fixeddomain:
% loaddomain:
% loadvec:
% spring:
% === OUTPUT RESULTS ======
% CPL4: extracted 2D contour from the density distribution
% z: optimized density distribution (design variable)
% fem: FEM model of the optimized structure
% Vcell: logged information of the density distribution in each iteration
% farray: logged information of the objective fnctn in each iteration
%
% EXAMPLE: [h E0 nu]
%
%
% See also: SGshapeOptiCAO, SGshapeOptiSKO
%

isemptycell(A)- similar to isempty but works with cells

% isemptycell(A) - similar to isempty but works with cells
% (by Tim Lueth, VLFL-Lib, 2020-JUL-27 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: isempty
%
% e=isemptycell(A)
% === INPUT PARAMETERS ===
% A: cell
% === OUTPUT RESULTS ======
% e: logical list
%
% EXAMPLE:
% A=SGsample(20), isemptycell(A)
%
% See also: isempty
%
%
% Copyright 2020 Tim C. Lueth

SGdesignBallbearing(sdl,ins,tpl)- creates subtraction solids for a bearing connection at a specific frame position of a solid

% SGdesignBallbearing(sdl,ins,tpl) - creates subtraction solids for a bearing connection at a specific frame position of a solid
% (by Tim Lueth, VLFL-Lib, 2020-JUL-27 as class: AUTOMATIC DESIGN)
%
% If two elements should be connected using a ball bearing, this fnctn
% helps to create the subtraction solids to achive a fnctnal connection
% using standard machine elements. (Status of: 2020-07-29)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdesignDIN912DIN985, SGbearing
%
% [P,N,S,B]=SGdesignBallbearing([sdl,ins,tpl])
% === INPUT PARAMETERS ===
% sdl: [Ri Ro Width Ol]
% ins: Insertion Tunnel
% tpl: Length of Insertion T/P for [HEAD NUT]; default is 10 10
% === OUTPUT RESULTS ======
% P: Subtraction Solid for plug side including frame 'C'
% N: Subtraction Solid for bearing side including frame 'C'
% S: Geometry of Plug including frame 'C'
% B: Bearing Model
%
% EXAMPLE:
% SGdesignBallbearing;
% [P,N]=SGdesignBallbearing([2.5 7 3.5]); % Create Space for Shaft
% [P,N]=SGdesignBallbearing([2.5 7 3.5],'S'); % Create Spave for Nuts and Screw Heads
% SG=SGManipulatorLink('',true);
% SG=SGsubtract(SG,P,'alignT',{'C','B'});
% SG=SGsubtract(SG,N,'alignT',{'C','F'}); SGfigure(SG);
%
% See also: SGdesignDIN912DIN985, SGbearing
%
%
% Copyright 2020-2021 Tim C. Lueth

SGManipulator07Link(LL,Shap,m)- Link and Link extender for Manipulator Design # 4

% SGManipulator07Link(LL,Shap,m) - Link and Link extender for Manipulator Design # 4
% (by Tim Lueth, VLFL-Lib, 2020-JUL-27 as class: KINEMATICS AND FRAMES)
%
% In contrast to the original design #4, this design number 7 is just
% created by a different strategy, that ist independent on the screw
% diameter and shaping.
% Since V2A screws are much more strength than polyamid , the is no real
% need to increase the size of the screw diameter (Status of: 2020-07-27)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdimensioning, SGManipulator04Base, SGManipulator04Link
%
% SL=SGManipulator07Link([LL,Shap,m])
% === INPUT PARAMETERS ===
% LL: Axis Distance; default is 40
% Shap: if true; the links are shaped; default is false
% m: screw diameter; default is 2.5
% === OUTPUT RESULTS ======
% SL: Link 2.5mm screw and 2.5mm Nut
%
% EXAMPLE:
% [A,B,C,H,EF]=SGManipulator07Base
% [D]=SGManipulator07Link % Link and link extender
% SGTchain({A,B,C,D,H,B,H,EF},[pi pi 0 pi 0 pi 0]); SGn=ans; SGfigure; SGplotalpha(SGn,'w'); view(-30,30); fullview(0.5)
% SGfigure; view(-30,30); SGplotalpha(SGn);
%
%
% See also: SGdimensioning, SGManipulator04Base, SGManipulator04Link
%
%
% Copyright 2020 Tim C. Lueth

TofTrel(T,rel,gap)- creates a HT matrix relative to a frame

% TofTrel(T,rel,gap) - creates a HT matrix relative to a frame
% (by Tim Lueth, VLFL-Lib, 2020-JUL-26 as class: ANALYTICAL GEOMETRY)
%
% Introduced first in SolidGeometry 4.9
%
% See also: TofP, TofR, TofT
%
% T=TofTrel(T,[rel,gap])
% === INPUT PARAMETERS ===
% T: Original frame
% rel:
% gap:
% === OUTPUT RESULTS ======
% T: New Frame
%
% EXAMPLE:
% TofTrel(eye(4),'transz',10,'roty',pi/4)
%
% See also: TofP, TofR, TofT
%
%
% Copyright 2020 Tim C. Lueth

SGdesignDIN912DIN985(sdl,ins,tpl,W)- creates subtraction solids for a screw fixation at a specific frame position of a solid

% SGdesignDIN912DIN985(sdl,ins,tpl,W) - creates subtraction solids for a screw fixation at a specific frame position of a solid
% (by Tim Lueth, VLFL-Lib, 2020-JUL-25 as class: AUTOMATIC DESIGN)
%
% THIS FNCTN USES FITTINGS by fnctn slfit und DIN4AMfitting
% If two elements should be connected using a DIN912 Screw and a DIN985
% Nut, this fnctn helps to create the subtraction solids to achive a
% fnctnal connection using standard machine elements.
% Pocket holes modified for clearancefit in height (2022-01-09)
% (Status of: 2022-01-09)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGDIN912, SGDIN985, SGdesignBallbearing, SGdesignSupplement
%
% [H,N,S,mt,parts]=SGdesignDIN912DIN985([sdl,ins,tpl,W])
% === INPUT PARAMETERS ===
% sdl: [M L d] = Metrix Length and delta in nut for screw connection
% ins: Characters for "T"unnel or "P"ocket; default is 'TP' for [HEAD NUT]
% tpl: Length of Insertion T/P for [HEAD NUT]; default is 10 10
% W: Rotation angle for Pocket if required; default is 0;
% === OUTPUT RESULTS ======
% H: Subtraction Solid for Head side including frame 'C'
% N: Subtraction Solid for Nut side including frame 'C'
% S: Srew and Nut for Visualziation including frame 'C'
% mt: remainig wall thickness
% parts: parts list for assembly of one connection
%
% EXAMPLE:
% clc; [H,N,S]=SGdesignDIN912DIN985([5 10 0],'TT',40);
% SGsubtract(SGbox,H,'alignT',{'C','Y-'})
% SGsubtract(SGbox,N,'alignT',{'C','Y-'})
% clc; [H,N,S]=SGdesignDIN912DIN985([3 10 0],'TP',40,pi/2);
% SGsubtract(SGbox,H,'alignT',{'C','Y-'})
% SGsubtract(SGbox,N,'alignT',{'C','Y-'})
%
% See also: SGDIN912, SGDIN985, SGdesignBallbearing, SGdesignSupplement
%
%
% Copyright 2020-2022 Tim C. Lueth

Wegertseder(text)- just opens the website of company Wegertseder for often used normed elements

% Wegertseder(text) - just opens the website of company Wegertseder for often used normed elements
% (by Tim Lueth, VLFL-Lib, 2020-JUL-25 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: firmen, DIN912, SGDIN912
%
% Wegertseder([text])
% === INPUT PARAMETERS ===
% text: string or number of DIN norm such as 7979 or '7979'
%
% EXAMPLE:
% Wegertseder('912')
%
% See also: firmen, DIN912, SGDIN912
%
%
% Copyright 2020 Tim C. Lueth

SGpintorquegauge(d,l,m)- Creates a pin with a defined diameter and height with a torque-loadable head

% SGpintorquegauge(d,l,m) - Creates a pin with a defined diameter and height with a torque-loadable head
% (by Tim Lueth, VLFL-Lib, 2020-JUL-23 as class: MODELING PROCEDURES)
%
% When load tests are carried out with torques, the plastic at the point
% of engagement of the torque wrench deforms long before the actual
% interesting torque occurs. (Status of: 2020-07-23)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGDIN912head, SGpinwrenchsize
%
% SG=SGpintorquegauge([d,l,m])
% === INPUT PARAMETERS ===
% d: diameter
% l: length
% m: metric Nut and Scre concept for DIN985, DIN912
% === OUTPUT RESULTS ======
% SG: Solid Geometry (white)
%
% EXAMPLE:
% SGpintorquegauge (5,10)
%
% See also: SGDIN912head, SGpinwrenchsize
%
%
% Copyright 2020 Tim C. Lueth

ismemberincell(C,c,csens,fullc)- finds the logical indices of an member inside a cell list of DIFFERENT types

% ismemberincell(C,c,csens,fullc) - finds the logical indices of an member inside a cell list of DIFFERENT types
% (by Tim Lueth, VLFL-Lib, 2020-JUL-22 as class: AUXILIARY PROCEDURES)
%
% This fnctn is for cell lists with DIFFERENT types
% for strings in cell list think about
% - contains(l,'.m:%')
% - startsWith(l,'SG')
% - ismember
% there is no need for ismemberincell for identical types
% Failed in 'R2020b Update 6' and was repaired in SG-LIB 5.1 by
% introducing fnctn celltype
% (Status of: 2020-09-13)
%
% Introduced first in SolidGeometry 4.9
%
% See also: ismemberincell, celltype
%
% a=ismemberincell(C,c,[csens,fullc])
% === INPUT PARAMETERS ===
% C: Cell list
% c: Single entry to find
% csens: character sensitive; default is false
% fullc: full compare instead of starting chars; default is false
% === OUTPUT RESULTS ======
% a: logical field
%
% EXAMPLE:
% A={'A', 0, pi, {'A','B'}}
% ismemberincell(A,pi)
% ismemberincell(A,'A')
% ismemberincell(A,{'A','B'})
%
% See also: ismemberincell, celltype
%
%
% Copyright 2020-2021 Tim C. Lueth

SGshapecylindric(SG,ez,ce,R)- shapes a solid with a cylindrical intersection

% SGshapecylindric(SG,ez,ce,R) - shapes a solid with a cylindrical intersection
% (by Tim Lueth, VLFL-Lib, 2020-JUL-22 as class: MODELING PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGshapeOptiCAO
%
% SGN=SGshapecylindric([SG,ez,ce,R])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% ez: shaping direction;default is [1 0 0]; x axis
% ce: centered or not centered; default is false
% R: option Radius if not calculated from Solid;
% === OUTPUT RESULTS ======
% SGN: Final Solid
%
% EXAMPLE:
% SGshapecylindric(SGtransP(SGTremove(SGbox,'all'),[0 0 5]),[ 1 0 0],true)
% SGshapecylindric(SGtransP(SGTremove(SGbox,'all'),[0 0 5]),[ 1 0 0],false)
%
% See also: SGshapeOptiCAO
%
%
% Copyright 2020 Tim C. Lueth

SGmotorshaft(D,L,r,ol)- returns a solid geometry for a motor shaft with undercut

% SGmotorshaft(D,L,r,ol) - returns a solid geometry for a motor shaft with undercut
% (by Tim Lueth, VLFL-Lib, 2020-JUL-21 as class: MODELING PROCEDURES)
%
% Originally created for Dr. Franz Irlinger (Status of: 2020-07-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: exp_2020_07_08_franz, SGpinwrenchsize
%
% [SG,PL]=SGmotorshaft([D,L,r,ol])
% === INPUT PARAMETERS ===
% D: Diamater, default is 0.25
% L: Length, default is D
% r: Undercut, default is .25
% ol: Step, default is r
% === OUTPUT RESULTS ======
% SG: Solid Geometry including Frames
% PL: Point List
%
% EXAMPLE:
% SGmotorshaft(2.5,4,0.1,[0 4])
%
% See also: exp_2020_07_08_franz, SGpinwrenchsize
%
%
% Copyright 2020 Tim C. Lueth

CPLxor(A,B);- returns a Boolean exclusive or of 2 CPLs

% CPLxor(A,B); - returns a Boolean exclusive or of 2 CPLs
% (by Tim Lueth, VLFL-Lib, 2020-JUL-20 as class: CLOSED POLYGON LISTS)
%
% simply based on CPLbool (Status of: 2020-07-20)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLbool, CPLsubtract, CPLunion, CPLintersect
%
% CPL=CPLxor(A,B);
% === INPUT PARAMETERS ===
% A: CPL A
% B: CPL B
% === OUTPUT RESULTS ======
% CPL: Resulting Boolean
%
% EXAMPLE:
% CPLxor(PLcircle(10,6),PLcircle(5,6)+[7 0]);
%
% See also: CPLbool, CPLsubtract, CPLunion, CPLintersect
%
%
% Copyright 2020 Tim C. Lueth

CPLintersect(A,B);- returns a Boolean intersection of 2 CPLs

% CPLintersect(A,B); - returns a Boolean intersection of 2 CPLs
% (by Tim Lueth, VLFL-Lib, 2020-JUL-20 as class: CLOSED POLYGON LISTS)
%
% simply based on CPLbool (Status of: 2020-07-20)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLbool, CPLsubtract, CPLunion, CPLxor
%
% CPL=CPLintersect(A,B);
% === INPUT PARAMETERS ===
% A: CPL A
% B: CPL B
% === OUTPUT RESULTS ======
% CPL: Resulting Boolean
%
% EXAMPLE:
% CPLintersect(PLcircle(10,6),PLcircle(5,6)+[7 0]);
%
% See also: CPLbool, CPLsubtract, CPLunion, CPLxor
%
%
% Copyright 2020 Tim C. Lueth

CPLunion(A,B,sr)- returns a Boolean addition of 2 CPLs

% CPLunion(A,B,sr) - returns a Boolean addition of 2 CPLs
% (by Tim Lueth, VLFL-Lib, 2020-JUL-20 as class: CLOSED POLYGON LISTS)
%
% simply based on CPLbool
% CPLadd works different and protects all hole in the CPLs (Status of:
% 2021-01-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLadd, CPLbool, CPLsubtract, CPLintersect, CPLxor, CPLconcat
%
% CPL=CPLunion(A,B,[sr])
% === INPUT PARAMETERS ===
% A: CPL A
% B: CPL B
% sr: spatial relation for CPLtransrelCPL
% === OUTPUT RESULTS ======
% CPL: Resulting Boolean
%
% EXAMPLE:
% CPLunion(PLcircle(10,6),PLcircle(5,6)+[7 0]);
% CPLunion(PLcircle(10,6),{PLcircle(5,6)+[7 0], PLstar(3)});
%
% See also: CPLadd, CPLbool, CPLsubtract, CPLintersect, CPLxor, CPLconcat
%
%
% Copyright 2020-2021 Tim C. Lueth

CPLsubtract(A,B);- returns a Boolean subtraction of 2 CPLs

% CPLsubtract(A,B); - returns a Boolean subtraction of 2 CPLs
% (by Tim Lueth, VLFL-Lib, 2020-JUL-20 as class: CLOSED POLYGON LISTS)
%
% simply based on CPLbool (Status of: 2020-07-20)
%
% Introduced first in SolidGeometry 4.9
%
% See also: CPLbool, CPLunion, CPLintersect, CPLxor
%
% CPL=CPLsubtract(A,B);
% === INPUT PARAMETERS ===
% A: CPL A
% B: CPL B
% === OUTPUT RESULTS ======
% CPL: Resulting Boolean
%
% EXAMPLE:
% CPLsubtract(PLcircle(10),PLcircle(5)+[7 0]);
%
% See also: CPLbool, CPLunion, CPLintersect, CPLxor
%
%
% Copyright 2020 Tim C. Lueth

SGpinwrenchsize(D,H,n,B,W)- creates a pin/heaxagon pin for a specified metric wrench size

% SGpinwrenchsize(D,H,n,B,W) - creates a pin/heaxagon pin for a specified metric wrench size
% (by Tim Lueth, VLFL-Lib, 2020-JUL-20 as class: MODELING PROCEDURES)
%
% This fnctn can be used to create bore holes for nuts or screws if 'c'
% or 'n' is used , DIN 912 or DIN985 is used for the diameter of screw
% head and nut
% (Status of: 2020-07-23)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGDIN912head, SGpintorquegauge
%
% SG=SGpinwrenchsize([D,H,n,B,W])
% === INPUT PARAMETERS ===
% D: Metric Diameter
% H: Length of pin or 'c'(cylinder) for 'n'(ut)
% n: number of edges
% B: Width as subtraction sold
% W: Angle for rotation
% === OUTPUT RESULTS ======
% SG: Solid Geometry
%
% EXAMPLE:
% SGpinwrenchsize(5,10); % 5mm x 10 mm
% SGpinwrenchsize(5,10,6); % 5mm x 10 mm - Inbus
% SGpinwrenchsize(5,10,6,20); % 5mm x 10 mm - Inbus subtraction solid
% SGpinwrenchsize(5,5,6,20,pi/2); % 5mm x 10 mm - Inbus subtraction solid rotated
% SGpinwrenchsize([ 5 2.5 4 ],[5 10 5 ],[6 0 6],20);
%
% See also: SGDIN912head, SGpintorquegauge
%
%
% Copyright 2020 Tim C. Lueth

DIN985(M)- returns the DIN985/ISO476 table for a metric threads

% DIN985(M) - returns the DIN985/ISO476 table for a metric threads
% (by Tim Lueth, VLFL-Lib, 2020-JUL-20 as class: MECHANICAL PROCEDURES)
%
% The table DIN985/ISO4762 has the following columns. All values are
% given in millimeter
% M InbusWrench InbusDiameter WrenchHeight NutHeight (Status
% of: 2020-08-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DINfindinTab, DINhelp,
% DINthreadtorque
%
% [M,TL]=DIN985(M)
% === INPUT PARAMETERS ===
% M: metric treat diameter
% === OUTPUT RESULTS ======
% M: M that was used for the table entry
% TL: Table entry for M
%
% EXAMPLE:
% DIN985;
% [M,TL]=DIN985(2.5)
% Wegertseder(985)
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DINfindinTab, DINhelp,
% DINthreadtorque
%
%
% Copyright 2020 Tim C. Lueth

DINthreadtorque(m,mat)- returns the DIN912 torque for tightening screw threads

% DINthreadtorque(m,mat) - returns the DIN912 torque for tightening screw threads
% (by Tim Lueth, VLFL-Lib, 2020-JUL-18 as class: MECHANICAL PROCEDURES)
%
% http://www.schrauben-lexikon.de/td3-werkstoffe-stahl.asp
% https://schraube-mutter.de/drehmoment-tabelle-drehmoment-berechnung-din
% -912/
% https://www.schweizer-fn.de/maschinenelemente/schraube/schraubenverbind
% ung.php#ma
% (Status of: 2020-08-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DIN985, DINfindinTab,
% DINhelp
%
% [Tq,TL]=DINthreadtorque(m,[mat])
% === INPUT PARAMETERS ===
% m: metric diameter
% mat: material; default is V2A
% === OUTPUT RESULTS ======
% Tq: Torque
% TL: Table
%
% EXAMPLE:
% DINthreadtorque(3,'PA')
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DIN985, DINfindinTab,
% DINhelp
%
%
% Copyright 2020 Tim C. Lueth

SGDIN912head(M,Tp)- creates a Solid Geometry of a screw head with respect to DIN 912

% SGDIN912head(M,Tp) - creates a Solid Geometry of a screw head with respect to DIN 912
% (by Tim Lueth, VLFL-Lib, 2020-JUL-18 as class: MODELING PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGiso4026, SGiso4762, SGDIN433, SGDIN912
%
% SGDIN912head([M,Tp])
% === INPUT PARAMETERS ===
% M: Diameter metric
% Tp: Length metric mm
%
% EXAMPLE:
% SGDIN912head(5)
%
% See also: SGiso4026, SGiso4762, SGDIN433, SGDIN912
%
%
% Copyright 2020 Tim C. Lueth

SGbearing(Sz,Tp,Ax)- returns the SG of a simple bearing

% SGbearing(Sz,Tp,Ax) - returns the SG of a simple bearing
% (by Tim Lueth, VLFL-Lib, 2020-JUL-18 as class: MODELING PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbearing2012, SGunion, SGdesignBallbearing
%
% SG=SGbearing([Sz,Tp,Ax])
% === INPUT PARAMETERS ===
% Sz: [Di Do H os] oversize default is 0
% Tp: 'plain', '2012',
% Ax: axis to left and right
% === OUTPUT RESULTS ======
% SG: Solid Geometry
%
% EXAMPLE:
% SGbearing([2.5 6 1.8])
% SGbearing([2.5 6 1.8],'plain',[1 2])
% SGbearing([2.5 6 1.8],'plug',[4 2]); SG=ans; SGunion(SG)
%
% See also: SGbearing2012, SGunion, SGdesignBallbearing
%
%
% Copyright 2020 Tim C. Lueth

SGdimensioningSide(SG,pnt,acc)- Creates a Front View Dimensioning Figure

% SGdimensioningSide(SG,pnt,acc) - Creates a Front View Dimensioning Figure
% (by Tim Lueth, VLFL-Lib, 2020-JUL-18 as class: VISUALIZATION)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioning4, SGdimensioningTop,
% SGdimensioningFront
%
% CPL=SGdimensioningSide(SG,[pnt,acc])
% === INPUT PARAMETERS ===
% SG: Solid geometry
% pnt: crossing point
% acc: accuracy; default is 0.1
% === OUTPUT RESULTS ======
% CPL: CPL of Side-view
%
% EXAMPLE:
% SGsample(27); SG=ans;
% SGdimensioningSide(SG);
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioning4, SGdimensioningTop,
% SGdimensioningFront
%
%
% Copyright 2020 Tim C. Lueth

SGdimensioningFront(SG,pnt,acc)- Creates a Side View Dimensioning Figure

% SGdimensioningFront(SG,pnt,acc) - Creates a Side View Dimensioning Figure
% (by Tim Lueth, VLFL-Lib, 2020-JUL-18 as class: VISUALIZATION)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioning4, SGdimensioningTop, SGdimensioningSide
%
% CPL=SGdimensioningFront(SG,[pnt,acc])
% === INPUT PARAMETERS ===
% SG: Solid geometry
% pnt: crossing point
% acc: accuracy; default is 0.1
% === OUTPUT RESULTS ======
% CPL: CPL of Side-view
%
% EXAMPLE:
% SGsample(27); SG=ans;
% SGdimensioningSide(SG);
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioning4, SGdimensioningTop, SGdimensioningSide
%
%
% Copyright 2020 Tim C. Lueth

SGdimensioningTop(SG,pnt,acc)- Creates a Front View Dimensioning Figure

% SGdimensioningTop(SG,pnt,acc) - Creates a Front View Dimensioning Figure
% (by Tim Lueth, VLFL-Lib, 2020-JUL-18 as class: VISUALIZATION)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioning4, SGdimensioningSide,
% SGdimensioningFront
%
% CPL=SGdimensioningTop(SG,[pnt,acc])
% === INPUT PARAMETERS ===
% SG: Solid geometry
% pnt: crossing point
% acc: accuracy; default is 0.1
% === OUTPUT RESULTS ======
% CPL: CPL of Topview
%
% EXAMPLE:
% SGsample(27); SG=ans;
% SGdimensioningTop(SG);
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioning4, SGdimensioningSide,
% SGdimensioningFront
%
%
% Copyright 2020 Tim C. Lueth

SGDIN985(M)- creates a Solid Geometry with respect to DIN 985

% SGDIN985(M) - creates a Solid Geometry with respect to DIN 985
% (by Tim Lueth, VLFL-Lib, 2020-JUL-16 as class: MODELING PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGiso4026, SGiso4762, SGDIN433, SGDIN912, DIN985
%
% SG=SGDIN985(M)
% === INPUT PARAMETERS ===
% M: Diameter metric
% === OUTPUT RESULTS ======
% SG: Solid Geometry including Frames
%
% EXAMPLE:
% SGDIN985(2.5)
%
% See also: SGiso4026, SGiso4762, SGDIN433, SGDIN912, DIN985
%
%
% Copyright 2020 Tim C. Lueth

SGconcat(A,B,relpos)- Simple Concatenation of Solid Geometries

% SGconcat(A,B,relpos) - Simple Concatenation of Solid Geometries
% (by Tim Lueth, VLFL-Lib, 2020-JUL-15 as class: SURFACES)
%
% Sometimes there is no possibility to boolean unite solids but the
% calling code of SGunion is already written. In this case there is a
% compatible fnctn SGconcat for simple concatenation that also supports
% relative positioning. This fnctn is based on SGcat2 and SGtransrelSG.
% (Status of: 2021-01-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbool, SGtransrelSG, SGboolh, SGintersect, SGsubtract,
% SGunion, SGxor, SGsupplement
%
% SG=SGconcat([A,B,relpos])
% === INPUT PARAMETERS ===
% A: Solid A
% B: Solid B
% relpos: list of relative positions for SGtransrelSG
% === OUTPUT RESULTS ======
% SG: Concatenation Result of A+B
%
% EXAMPLE:
% SGconcat(SGboxsphere([30,20,10],4,10))
% SGconcat(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','left',-2)
% SGconcat(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','infront',-2)
%
% See also: SGbool, SGtransrelSG, SGboolh, SGintersect, SGsubtract,
% SGunion, SGxor, SGsupplement
%
%
% Copyright 2020-2021 Tim C. Lueth

SGfittinggauge- creates a solid for testing fits on a 3D printer

% SGfittinggauge - creates a solid for testing fits on a 3D printer
% (by Tim Lueth, VLFL-Lib, 2020-JUL-15 as class: MODELING PROCEDURES)
%
% This fnctn was rewritten because there were problems with ball bearings
% when fitting in manipulators printed on the Formlab FORM2. (Status of:
% 2020-07-15)
%
% Introduced first in SolidGeometry 4.9
%
% See also: exp_2012_04_10
%
% SGF=SGfittinggauge
% === OUTPUT RESULTS ======
% SGF: Solid
%
% EXAMPLE:
% SGfittinggauge
%
%
% See also: exp_2012_04_10
%
%
% Copyright 2020 Tim C. Lueth

SGDIN912(M,L)- creates a Solid Geometry with respect to DIN 912

% SGDIN912(M,L) - creates a Solid Geometry with respect to DIN 912
% (by Tim Lueth, VLFL-Lib, 2020-JUL-14 as class: MODELING PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGiso4026, SGiso4762, SGDIN433
%
% SG=SGDIN912([M,L])
% === INPUT PARAMETERS ===
% M: Diameter metric
% L: Length metric mm
% === OUTPUT RESULTS ======
% SG: Solid Geometry including Frames
%
% EXAMPLE:
% SGDIN912(2.5,8)
%
% See also: SGiso4026, SGiso4762, SGDIN433
%
%
% Copyright 2020 Tim C. Lueth

SGDIN433(M)- creates a Solid Geometry with respect to DIN 433

% SGDIN433(M) - creates a Solid Geometry with respect to DIN 433
% (by Tim Lueth, VLFL-Lib, 2020-JUL-14 as class: MODELING PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGiso4026, SGiso4762, SGDIN912
%
% SG=SGDIN433([M])
% === INPUT PARAMETERS ===
% M: Diameter metric
% === OUTPUT RESULTS ======
% SG: Solid Geometry including Frames
%
% EXAMPLE:
% SGDIN433(1.9)
%
% See also: SGiso4026, SGiso4762, SGDIN912
%
%
% Copyright 2020 Tim C. Lueth

DINfindinTab(M,Tab,takelarg)- searches an entry with in a table name

% DINfindinTab(M,Tab,takelarg) - searches an entry with in a table name
% (by Tim Lueth, VLFL-Lib, 2020-JUL-14 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DIN985, DINhelp,
% DINthreadtorque
%
% TL=DINfindinTab(M,Tab,[takelarg])
% === INPUT PARAMETERS ===
% M: Scalar to find in Tab
% Tab: Table with M as first col; Table name is important
% takelarg: if true nearest larger is selected; default is true
% === OUTPUT RESULTS ======
% TL: Table row
%
% EXAMPLE:
% DIN433=[ 1.0 1.1 2.5 0.3; 1.2 1.3 3.0 0.3];
% DINfindinTab(1.1,DIN433)
%
% See also: DIN13, DIN336, DIN464, DIN912, DIN913, DIN985, DINhelp,
% DINthreadtorque
%
%
% Copyright 2020 Tim C. Lueth

SGManipulator05Link(LL)- Link and Link extender for Manipulator Design # 5

% SGManipulator05Link(LL) - Link and Link extender for Manipulator Design # 5
% (by Tim Lueth, VLFL-Lib, 2020-JUL-14 as class: KINEMATICS AND FRAMES)
%
% Those parts can be assembled using screws, spacer, and nut of DIN DIN
% 912, DIN 985, DIN 433 using Diameter 2.5mm and 8mm length and a ball
% bearing S692-X-2Z (2.50 Euro /Stück) with inside 2.5mm, outside 7mm and
% width 3.5mm
%
%
% (Status of: 2020-07-14)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdimensioning4, SGManipulator04Base, SGManipulator04Link,
% SGManipulator05Base
%
% [SL,SL2]=SGManipulator05Link([LL])
% === INPUT PARAMETERS ===
% LL: Axis Distance; default is 40
% === OUTPUT RESULTS ======
% SL: Link 2.5mm screw and 2.5mm Nut
% SL2: Link 2.5mm screw nut and 2.5mm screw nut
%
% EXAMPLE:
% [A,B,C,H,EF]=SGManipulator05Base
% [D]=SGManipulator05Link % Link and link extender
% SGTchain({A,B,C,D,H,B,H,EF},[pi pi 0 pi 0 pi 0]); SGn=ans; SGfigure; SGplotalpha(SGn,'w'); view(-30,30); fullview(0.5)
% SGfigure; view(-30,30); SGplotalpha(SGn);
%
%
% See also: SGdimensioning4, SGManipulator04Base, SGManipulator04Link,
% SGManipulator05Base
%
%
% Copyright 2020 Tim C. Lueth

SGManipulator05Base(LS)- Plate, Base, and Hand for Manipulator Design # 5

% SGManipulator05Base(LS) - Plate, Base, and Hand for Manipulator Design # 5
% (by Tim Lueth, VLFL-Lib, 2020-JUL-14 as class: KINEMATICS AND FRAMES)
%
% Those parts can be assembled using screws, spacer, and nut of DIN DIN
% 912, DIN 985, DIN 433 using Diameter 2.5mm and 8mm length and a ball
% bearing S692-X-2Z (2.50 Euro /Stück) with inside 2.5mm, outside 7mm and
% width 3.5mm
% (Status of: 2020-07-15)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdimensioning4, SGManipulator04Base, SGManipulator04Link,
% SGManipulator05Link
%
% [A,B,K,U,EF]=SGManipulator05Base([LS])
% === INPUT PARAMETERS ===
% LS: Length of Base and Hand; default is 40
% === OUTPUT RESULTS ======
% A: Base PLate
% B: Base
% K: 7 DoF
% U: Hand
% EF: Effektor
%
% EXAMPLE:
% [A,B,C,H,EF]=SGManipulator05Base
% [D]=SGManipulator05Link % Link and link extender
% SGTchain({A,B,C,D,H,B,H,EF},[pi pi 0 pi 0 pi 0]); SGn=ans; SGfigure; SGplotalpha(SGn,'w'); view(-30,30); fullview(0.5)
% SGfigure; view(-30,30); SGplotalpha(SGn)
%
% See also: SGdimensioning4, SGManipulator04Base, SGManipulator04Link,
% SGManipulator05Link
%
%
% Copyright 2020 Tim C. Lueth

SGdimensioning4(SG,pt)- Creates a simple 4 quadrant dimensioning view for a solid Geometry

% SGdimensioning4(SG,pt) - Creates a simple 4 quadrant dimensioning view for a solid Geometry
% (by Tim Lueth, VLFL-Lib, 2020-JUL-14 as class: VISUALIZATION)
%
% Very similar to SGTdimenionsing, which does not allow to change the
% font size but is programmed better (Status of: 2020-07-14)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioningTop, SGdimensioningSide,
% SGdimensioningFront
%
% hf=SGdimensioning4(SG,[pt])
% === INPUT PARAMETERS ===
% SG: Solid geometry
% pt: crossing point
% === OUTPUT RESULTS ======
% hf: heandle to figure
%
% EXAMPLE:
% SGsample(27); SG=ans;
% SGdimensioning4(SG);
% SGTdimensioning(SG);
%
% See also: SGTdimensioning, viewdimensioning, PLdimensioning,
% CVLdimclassifier, SGdimensioningTop, SGdimensioningSide,
% SGdimensioningFront
%
%
% Copyright 2020 Tim C. Lueth

exp_2020_07_02_subtractjoint- Sucvessfull experiment to create a universal revolute joint subtraction part

% exp_2020_07_02_subtractjoint - Sucvessfull experiment to create a universal revolute joint subtraction part
% (by Tim Lueth, VLFL-Lib, 2020-JUL-03 as class: KINEMATICS AND FRAMES)
%
% This part creates a revolute joint in each solid if subtracted (Status
% of: 2020-07-03)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGcutTa, exp_2018_08_04_jointsubstraction
%
% C=exp_2020_07_02_subtractjoint
% === OUTPUT RESULTS ======
% C: universal revolute joint subtraction part
%
% EXAMPLE:
% exp_2020_07_02_subtractjoint
%
% See also: SGcutTa, exp_2018_08_04_jointsubstraction
%
%
% Copyright 2020 Tim C. Lueth

SGManipulator04Link(LL)- Link and Link extender for Manipulator Design # 4

% SGManipulator04Link(LL) - Link and Link extender for Manipulator Design # 4
% (by Tim Lueth, VLFL-Lib, 2020-JUN-29 as class: KINEMATICS AND FRAMES)
%
% Those parts can be assembled using screws, spacer, and nut of DIN DIN
% 912, DIN 985, DIN 9021 using Diameter 2.5mm and 8mm length (Status of:
% 2020-06-29)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGManipulator04Base
%
% [SL,SL2]=SGManipulator04Link([LL])
% === INPUT PARAMETERS ===
% LL: Axis Distance; default is 40
% === OUTPUT RESULTS ======
% SL: Link 2.5mm screw and 2.5mm Nut
% SL2: Link 2.5mm screw nut and 2.5mm screw nut
%
% EXAMPLE:
% [A,B,C,H,EF]=SGManipulator04Base
% [D]=SGManipulator04Link % Link and link extender
% SGTchain({A,B,C,D,H,B,H,EF},[pi pi 0 pi 0 pi 0]); SGn=ans; SGfigure; SGplotalpha(SGn,'w'); view(-30,30); fullview(0.5)
% SGfigure; view(-30,30); SGplotalpha(SGn);
%
%
% See also: SGManipulator04Base
%
%
% Copyright 2020 Tim C. Lueth

SGmotorSolExpert(mn,d,n,h)- return the simplified solid Geometry of a 50:1 Gearbox Motor 6 V of www.sol-expert-group.de

% SGmotorSolExpert(mn,d,n,h) - return the simplified solid Geometry of a 50:1 Gearbox Motor 6 V of www.sol-expert-group.de
% (by Tim Lueth, VLFL-Lib, 2020-JUN-29 as class: MODELING PROCEDURES)
%
% The Motor has an Axle with motor shaft of 3mm/2.5mm and a an axis
% length of
% (Status of: 2020-07-08)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGdimensioning, SGmotorhousing
%
% [SG,SGG]=SGmotorSolExpert([mn,d,n,h])
% === INPUT PARAMETERS ===
% mn: option Name such as G50V6
% d: Diameter of the gear wheel; default is 10
% n: Number of teeth of the gear wheel; default is 21
% h: Height of the gear wheel; default is 7
% === OUTPUT RESULTS ======
% SG: Solid Geometry including Frames
% SGG: Gear 2mm, 15 Teethm
%
% EXAMPLE:
% SGmotorSolExpert('G50V6',10,15,3)
%
% See also: SGdimensioning, SGmotorhousing
%
%
% Copyright 2020 Tim C. Lueth

SGManipulator04Base(LS)- Plate, Base, and Hand for Manipulator Design # 4

% SGManipulator04Base(LS) - Plate, Base, and Hand for Manipulator Design # 4
% (by Tim Lueth, VLFL-Lib, 2020-JUN-27 as class: KINEMATICS AND FRAMES)
%
% Those parts can be assembled using screws, spacer, and nut of DIN DIN
% 912, DIN 985, DIN 9021 using Diameter 2.5mm and 8mm length (Status of:
% 2020-06-29)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGManipulator04Link
%
% [A,B,K,U,EF]=SGManipulator04Base([LS])
% === INPUT PARAMETERS ===
% LS: Length of Base and Hand; default is 40
% === OUTPUT RESULTS ======
% A: Base PLate
% B: Base
% K: 7 DoF
% U: Hand
% EF: Effektor
%
% EXAMPLE:
% [A,B,C,H,EF]=SGManipulator04Base
% [D]=SGManipulator04Link % Link and link extender
% SGTchain({A,B,C,D,H,B,H,EF},[pi pi 0 pi 0 pi 0]); SGn=ans; SGfigure; SGplotalpha(SGn,'w'); view(-30,30); fullview(0.5)
% SGfigure; view(-30,30); SGplotalpha(SGn);
%
%
% See also: SGManipulator04Link
%
%
% Copyright 2020 Tim C. Lueth

SGManipulator03Base(LS)- Base, and Hand for Manipulator Design # 3

% SGManipulator03Base(LS) - Base, and Hand for Manipulator Design # 3
% (by Tim Lueth, VLFL-Lib, 2020-JUN-23 as class: KINEMATICS AND FRAMES)
%
% Those parts can be assembled using screws, spacer, and nut of DIN DIN
% 912, DIN 985, DIN 9021 using Diameter 2.5mm and 8mm length (Status of:
% 2020-06-23)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGManipulator03Link
%
% [A,B,U,EF]=SGManipulator03Base([LS])
% === INPUT PARAMETERS ===
% LS: Length of Base and Hand; default is 40
% === OUTPUT RESULTS ======
% A: Base PLate
% B: Base
% U: Hand
% EF: Effektor
%
% EXAMPLE:
% [A,B,H,E]=SGManipulator03Base(20)
% [C,D]=SGManipulator03Link % Link and link extender
% SGn=SGTchain({A,B,C,H,B,H,E},[pi pi pi 0 pi 0 pi],0,SGTframeChain(1:7));
% SGfigure; view(-30,30); SGplotalpha(SGn);
%
%
% See also: SGManipulator03Link
%
%
% Copyright 2020 Tim C. Lueth

SGManipulator03Link(LL)- Link and Link extender for Manipulator Design # 3

% SGManipulator03Link(LL) - Link and Link extender for Manipulator Design # 3
% (by Tim Lueth, VLFL-Lib, 2020-JUN-23 as class: KINEMATICS AND FRAMES)
%
% Those parts can be assembled using screws, spacer, and nut of DIN DIN
% 912, DIN 985, DIN 9021 using Diameter 2.5mm and 8mm length (Status of:
% 2020-06-23)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGManipulator03Base
%
% [SL,SL2]=SGManipulator03Link([LL])
% === INPUT PARAMETERS ===
% LL: Axis Distance; default is 40
% === OUTPUT RESULTS ======
% SL: Link 2.5mm screw and 2.5mm Nut
% SL2: Link 2.5mm screw nut and 2.5mm screw nut
%
% EXAMPLE:
% [A,B,H,E]=SGManipulator03Base(20)
% [C,D]=SGManipulator03Link % Link and link extender
% SGn=SGTchain({A,B,C,H,B,H,E},[pi pi pi 0 pi 0 pi],0,SGTframeChain(1:7));
% SGfigure; view(-30,30); SGplotalpha(SGn);
%
%
% See also: SGManipulator03Base
%
%
% Copyright 2020 Tim C. Lueth

SGplotmultiple(SGc,frame);- creates a figure and simply plots all solids in a cell aray

% SGplotmultiple(SGc,frame); - creates a figure and simply plots all solids in a cell aray
% (by Tim Lueth, VLFL-Lib, 2020-JUN-21 as class: VISUALIZATION)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGwriteMultipleSTL, SGplotalpha, SGTplotalpha
%
% SGplotmultiple(SGc,[frame]);
% === INPUT PARAMETERS ===
% SGc: Cell array of Solids
% frame: if true; frames are plotted also; default is false
%
% EXAMPLE:
% loadweb JACO_robot.mat; whos JACO
% SGplotmultiple(JACO); % plot solids
% SGplotmultiple(JACO,true); % including frames
%
% See also: SGwriteMultipleSTL, SGplotalpha, SGTplotalpha
%
%
% Copyright 2020-2022 Tim C. Lueth

SGplotcellmultiple(SGc,,"scale","frames")- Creates a SGfigure and plots all cell elements in different subplots

% SGplotcellmultiple(SGc,,"scale","frames") - Creates a SGfigure and plots all cell elements in different subplots
% (by Tim Lueth, VLFL-Lib, 2020-JUN-21 as class: VISUALIZATION)
%
% It also plots the frames (Status of: 2022-03-29)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGplot, SGplotcell, SGwriteMultipleSTL, view4all, axisscale
%
% h=SGplotcellmultiple(SGc,[,"scale","frames"])
% === INPUT PARAMETERS ===
% SGc: Cell list of Solids that should be printed
% "scale": if used, all figures show the frames too
% "frames":
% === OUTPUT RESULTS ======
% h: handle to graphics objects
%
% EXAMPLE:
% A=SGsample(20)
% SGplotcellmultiple(A); % plot all with maximum size
% SGplotcellmultiple(A,'scale'); % Plot all in the same scale
%
% See also: SGplot, SGplotcell, SGwriteMultipleSTL, view4all, axisscale
%
%
% Copyright 2020-2022 Tim C. Lueth

SGofCPLzseparated(CPL,hl)- creates for each closed contour of a CPL an individual solid with an individual height

% SGofCPLzseparated(CPL,hl) - creates for each closed contour of a CPL an individual solid with an individual height
% (by Tim Lueth, VLFL-Lib, 2020-JUN-17 as class: SURFACES)
%
% creates never holes; required for some editor fnctns (Status of:
% 2020-06-17)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGofCPLz
%
% SG=SGofCPLzseparated(CPL,hl)
% === INPUT PARAMETERS ===
% CPL: CPL
% hl: sorted list for height in CPL
% === OUTPUT RESULTS ======
% SG: Solid Geoemtry
%
% EXAMPLE:
% SGofCPLzseparated(CPLsample(11),[7 8 3 9])
%
% See also: SGofCPLz
%
%
% Copyright 2020 Tim C. Lueth

SGsculpturepedestal(SG,Otext,ht,ov,ez)- create a pedestal for a sculpture

% SGsculpturepedestal(SG,Otext,ht,ov,ez) - create a pedestal for a sculpture
% (by Tim Lueth, VLFL-Lib, 2020-JUN-14 as class: AUTOMATIC DESIGN)
%
% Currently there are many STL for greek and roman sculptures available
% for download.
% It is a way of adding a standard pedestal, which has a height of 12.5%
% of the height of the sculpture and about 80% of the width and depth of
% the figure. (Status of: 2020-06-14)
%
% Introduced first in SolidGeometry 4.9
%
% See also: webdownload, https://www.yeggi.com/q/greek+statue/,
% https://www.myminifactory.com/search/?cat=112&query=venus
%
% [SG,SGB,SGT]=SGsculpturepedestal(SG,[Otext,ht,ov,ez])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% Otext: Text to add on sculpture; Lines separated by '\n'
% ht: desired height in z; default is 130; 0 for original size
% ov: overlap of hte pedestral; default is -1mm
% ez: orientation of text; default is [0 -1 0]; (Backside)
% === OUTPUT RESULTS ======
% SG: SG of complete Figure including pedestral and text
% SGB: SG of pedestral
% SGT: SG of text
%
% EXAMPLE:
% fname=webdownload('https://www.myminifactory.com/download/37471');
% SGreadSTL(fn); SG=ans;
% SGsculpturepedestal(SG,'Venus Italica\nAntonio Canova (1823)\n',0,-4);
% view(-150,6);shg;
%
% See also: webdownload, https://www.yeggi.com/q/greek+statue/,
% https://www.myminifactory.com/search/?cat=112&query=venus
%
%
% Copyright 2020 Tim C. Lueth

google()- just searches a string at google.com

% google() - just searches a string at google.com
% (by Tim Lueth, VLFL-Lib, 2020-APR-01 as class: USER INTERFACE)
%
% for lazy people like me .......
% (Status of: 2020-04-01)
%
% Introduced first in SolidGeometry 4.9
%
% See also: web
%
% google([])
%
% EXAMPLE:
% google servomotor
% google wiki servomotor
%
% See also: web
%
%
% Copyright 2020 Tim C. Lueth

filenameinc(fname,step,fchk,srch,dchn)- increases a file name and check it's existance by option

% filenameinc(fname,step,fchk,srch,dchn) - increases a file name and check it's existance by option
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-30 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: strcounter
%
% fni=filenameinc(fname,[step,fchk,srch,dchn])
% === INPUT PARAMETERS ===
% fname: file name
% step: step size; default is +1
% fchk: check if file or folder; default is true
% srch: default is false; try to increase the file name
% dchn: increase also all file names in folder names; default is true;
% === OUTPUT RESULTS ======
% fni:
%
% See also: strcounter
%
%
% Copyright 2020 Tim C. Lueth

strcounter(fn,step)- detects an integer number at the end of a string and increments it

% strcounter(fn,step) - detects an integer number at the end of a string and increments it
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-30 as class: AUXILIARY PROCEDURES)
%
% Auxiliary fnctn to manage file sequences for example (Status of:
% 2020-03-30)
%
% Introduced first in SolidGeometry 4.9
%
% See also: filenameinc
%
% [fni,ostr,cstr]=strcounter(fn,[step])
% === INPUT PARAMETERS ===
% fn: original string
% step: step size
% === OUTPUT RESULTS ======
% fni: new string name
% ostr: replaced chain
% cstr:
%
% EXAMPLE:
% [a,b,c]=strcounter('AIM_LEC_02_SLIDE_05 INCL SOUND.avi')
% strcounter('X345X123 ist ein TestA-100',-1)
% strcounter('X345X123 ist ein TestA-99')
% strcounter('X345X123 ist ein TestA-0099')
% strcounter('X345X123 ist ein TestA-0000',-1)
% strcounter('X345X123 ist ein TestA-100',-4)
%
%
% See also: filenameinc
%
%
% Copyright 2020 Tim C. Lueth

audiorecorderTLautostop(DV,FS,damp,SH)- records an audio sample from a specified device

% audiorecorderTLautostop(DV,FS,damp,SH) - records an audio sample from a specified device
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-28 as class: VIDEO/AUDIO/PDF)
%
% simplifies the use of different input devices (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences
%
% [y,FS]=audiorecorderTLautostop([DV,FS,damp,SH])
% === INPUT PARAMETERS ===
% DV: device string' default is webcam
% FS: Sampe rate; default is 16000
% damp: damping for stopping recorning; default is 0.1
% SH: if true; a time scale is displayed; default is true
% === OUTPUT RESULTS ======
% y: Signal
% FS: Sample rate
%
% EXAMPLE:
% audiorecorderTL('HELP',16000,2); % returns the existing input devices
% audiorecorderTL('pro X',16000,2); y=ans; soundTL(y,16000,'Pro X')
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences
%
%
% Copyright 2020 Tim C. Lueth

audioeditspokentext(Y,FS)- this keyboardbased fnct is to edit spoken text

% audioeditspokentext(Y,FS) - this keyboardbased fnct is to edit spoken text
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-28 as class: VIDEO/AUDIO/PDF)
%
% This is Tim's main editor fnctn to create digital video lecture during
% the CORONA-COVID-19 virus crisis! It is a powerful audio editor to
% record sentence by sentence to describe the content of an static image
% and to create an AVI video (1 fps) including audio. (Status of:
% 2020-03-30)
%
% Introduced first in SolidGeometry 4.9
%
% See also: audiotrim, audioseparatebreaks, audiorecordspokentext
%
% Y=audioeditspokentext(Y,FS)
% === INPUT PARAMETERS ===
% Y: Original Signal
% FS: Sample Rate
% === OUTPUT RESULTS ======
% Y: Final Text
%
% See also: audiotrim, audioseparatebreaks, audiorecordspokentext
%
%
% Copyright 2020 Tim C. Lueth

audioseparatebreaks(y,FS,damp,brkdur,minvoic)- separates an audio sequence of spoken text into breaks

% audioseparatebreaks(y,FS,damp,brkdur,minvoic) - separates an audio sequence of spoken text into breaks
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-28 as class: VIDEO/AUDIO/PDF)
%
% Introduced first in SolidGeometry 4.9
%
% See also: audiotrim
%
% [Voice,VLen]=audioseparatebreaks(y,[FS,damp,brkdur,minvoic])
% === INPUT PARAMETERS ===
% y: Audio Signal
% FS: Sample Rate; default is 16000
% damp: damping for break detection; linear = ; defalt 0.01 = -40dB
% brkdur: minimum break durance default is 0.3 seconds
% minvoic: minimal voice length; default is 1 second
% === OUTPUT RESULTS ======
% Voice: List of [start and end] samples for the voice segments
% VLen: length of the individual segments
%
% EXAMPLE:
% [Y,FS]=audioreadTL('/Users/lueth/Desktop/Ohne Titel.mp4'); [Y,FS]=audioresample(Y,FS,16000); FS
% soundTL(Y,FS)
% audioseparatebreaks(Y);
%
%
% See also: audiotrim
%
%
% Copyright 2020 Tim C. Lueth

audioresample(OSig,FSo,FSn)- resamples the audiosignal with a different sample rate

% audioresample(OSig,FSo,FSn) - resamples the audiosignal with a different sample rate
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-28 as class: VIDEO/AUDIO/PDF)
%
% For writing audiofiles, typically 44100 Hz are used. For voice
% recording, and processing 16000 is sufficient.
% The resample process does not use any windowing. (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: stretchAudio, audiotrim
%
% [NSig,FSn]=audioresample(OSig,[FSo,FSn])
% === INPUT PARAMETERS ===
% OSig: Original Signal
% FSo: Original Sample rate; default is 44100
% FSn: NEw Sample ratel default is 16000
% === OUTPUT RESULTS ======
% NSig: New Signal
% FSn: New Sample rate
%
% EXAMPLE:
% load handel.mat; filename = desktopdir('handel.wav'); audiowrite(filename,y,Fs); clear y Fs
% [y,FS]=audioreadTL;
% audioresample(y,FS,16000);
%
% See also: stretchAudio, audiotrim
%
%
% Copyright 2020 Tim C. Lueth

imageaudio2video(IName,isize,AName)- creates video clips from an image and an audio file with the same name

% imageaudio2video(IName,isize,AName) - creates video clips from an image and an audio file with the same name
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-28)
%
% Audiofile by default is same name as image; The default video time
% without sound is 45 seconds
% The clip is scaled and the image written with frame rate 1 fps in an
% AVI file. While the fnctn image2video is able to adapt the frame rate,
% the fram erate here is always 1 fps.
% (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: audiorecordsentences, image2video
%
% WName=imageaudio2video([IName,isize,AName])
% === INPUT PARAMETERS ===
% IName: Image file full name
% isize: number of rows or [c r]; default is 1080
% AName: Audiofilename or number of default time seconds (45 Sec)
% === OUTPUT RESULTS ======
% WName: Name of AVI file with audio track
%
% EXAMPLE:
% imfile=desktopdir('peppers.png'), copyfile(which('peppers.png'),imfile)
% imageaudio2video(imfile)
%
%
% See also: audiorecordsentences, image2video
%
%
% Copyright 2020 Tim C. Lueth

imageFolderContent(DirName)- finds all image files within a folder

% imageFolderContent(DirName) - finds all image files within a folder
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-27 as class: IMAGES)
%
% very slow fnctn since it really tries to open all files as image
% without considering the extensions (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: isfolder, isfile
%
% ImFileList=imageFolderContent([DirName])
% === INPUT PARAMETERS ===
% DirName: folder name
% === OUTPUT RESULTS ======
% ImFileList: cell list of image files
%
% EXAMPLE:
% imageFolderContent(desktopdir)
%
% See also: isfolder, isfile
%
%
% Copyright 2020 Tim C. Lueth

ftouch(fname)- file touch on mac - use carefully - does not support wildcards but only single files

% ftouch(fname) - file touch on mac - use carefully - does not support wildcards but only single files
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-27 as class: FILE HANDLING)
%
% only full filenames are allowed for this fnctn
% the wildcard touch fails in the batch fnctn if there are too many files
% such in the SG Library (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: isfile, touchfiles, pcodeTL
%
% ftouch(fname)
% === INPUT PARAMETERS ===
% fname: exact filename
%
% EXAMPLE:
% ftouch('pcodeTL.m')
%
% See also: isfile, touchfiles, pcodeTL
%
%
% Copyright 2020-2022 Tim C. Lueth

audioreadTL(AName,nFS)- similar to audioread but with sound output after readin

% audioreadTL(AName,nFS) - similar to audioread but with sound output after readin
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-27 as class: VIDEO/AUDIO/PDF)
%
% similar to audioread but allows interactive use and returns information
% during plays (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences, audiowriteTL
%
% [y,FS]=audioreadTL([AName,nFS])
% === INPUT PARAMETERS ===
% AName: Filename; User interaction required if empty
% nFS: desired sample frequency
% === OUTPUT RESULTS ======
% y: Signal
% FS: Sample Frequency
%
% EXAMPLE:
% audioreadTL('/Users/lueth/Desktop/IMG_9776.mp4');
% audioreadTL;
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences, audiowriteTL
%
%
% Copyright 2020 Tim C. Lueth

audiowriteTL(OSig,FS,FName)- writes an audio sequence with fixed frequency of 44100 Hz

% audiowriteTL(OSig,FS,FName) - writes an audio sequence with fixed frequency of 44100 Hz
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-27 as class: VIDEO/AUDIO/PDF)
%
% Since Windows supports only a few frequences, the signal is adjusted
% and written (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences
%
% Aname=audiowriteTL(OSig,[FS,FName])
% === INPUT PARAMETERS ===
% OSig: Original Audio
% FS: Original Audio Frequency; writing rate is always fixed to 44100 Hz
% FName: Filenamep; default is EXP-YYYY-MM-DD
% === OUTPUT RESULTS ======
% Aname: Full filename of written file
%
% EXAMPLE:
% [Y,FS]=audiorecorderTL;
% audiowriteTL(Y,FS); % It is not written in sample rate FS but using 44100 Hz
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences
%
%
% Copyright 2020 Tim C. Lueth

audiovocoder(OSig,acc)- changes the pitch of the signal without changing the length

% audiovocoder(OSig,acc) - changes the pitch of the signal without changing the length
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-27 as class: VIDEO/AUDIO/PDF)
%
% Uses stretchAudio (2019b)
% Acc Values > 1 make the voices deeper and slower in same time period
% (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: soundTL, audiorecorderTL, audiotrim, audiorecordsentences
%
% [NSig,NSR]=audiovocoder(OSig,[acc])
% === INPUT PARAMETERS ===
% OSig: Original signal
% acc: pitch; default is 1.03
% === OUTPUT RESULTS ======
% NSig: New Signal
% NSR: New Sample rate; not used yet
%
% EXAMPLE: Compare 3% voice vocoder
% y=audiorecorderTL('PRO X',16000,5); % record 5 seconds
% soundTL(audiovocoder(y,1),16000,'PRO X'); pause(5); soundTL(audiovocoder(y,1.03),16000,'PRO X')
%
%
% See also: soundTL, audiorecorderTL, audiotrim, audiorecordsentences
%
%
% Copyright 2020 Tim C. Lueth

audiorecordspokentext(org,FS,DV,def)- records a list of sentences an compiles it to a longer text

% audiorecordspokentext(org,FS,DV,def) - records a list of sentences an compiles it to a longer text
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-26 as class: VIDEO/AUDIO/PDF)
%
% Helps to record sentences for a slide (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audioeditspokentext
%
% B=audiorecordspokentext([org,FS,DV,def])
% === INPUT PARAMETERS ===
% org: Signal to append; default is empty
% FS: Sample rate default is 16000
% DV: device default is 'pro x'
% def: sentence length; default is 10 seconds
% === OUTPUT RESULTS ======
% B: Final Sequqnce
%
% EXAMPLE:
% audiorecordspokentext
%
% See also: soundTL, audiorecorderTL, audiotrim, audiovocoder,
% audioeditspokentext
%
%
% Copyright 2020 Tim C. Lueth

audiotrim(y,FS,n,thr)- trims an audio signal and adds a short break

% audiotrim(y,FS,n,thr) - trims an audio signal and adds a short break
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-26 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: soundTL, audiorecorderTL, audiovocoder, audiorecordsentences
%
% y=audiotrim(y,FS,[n,thr])
% === INPUT PARAMETERS ===
% y: samples
% FS: Sample rate
% n: seconds to add silence; default is 0.2
% thr: threshold for silence; default is 0.01
% === OUTPUT RESULTS ======
% y: sample signal
%
% EXAMPLE:
% y=audiorecorderTL('PRO X',16000,5); audiotrim(y,16000); y=ans; soundTL(y,16000,'pro x');
%
% See also: soundTL, audiorecorderTL, audiovocoder, audiorecordsentences
%
%
% Copyright 2020 Tim C. Lueth

audiorecorderTL(DV,FS,tim,SH)- records an audio sample from a specified device

% audiorecorderTL(DV,FS,tim,SH) - records an audio sample from a specified device
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-26 as class: VIDEO/AUDIO/PDF)
%
% simplifies the use of different input devices
% for autostop use audiorecorderTLautostop (Status of: 2020-03-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: soundTL, audiotrim, audiovocoder, audiorecordsentences,
% audiorecorderTLautostop
%
% [y,FS]=audiorecorderTL([DV,FS,tim,SH])
% === INPUT PARAMETERS ===
% DV: device string' default is webcam
% FS: Sampe rate; default is 16000
% tim: time to samplel default is 1 sec
% SH: if true; a time scale is displayed; default is true
% === OUTPUT RESULTS ======
% y: Signal
% FS: Sample rate
%
% EXAMPLE:
% audiorecorderTL('HELP',16000,2); % returns the existing input devices
% audiorecorderTL('pro X',16000,2); y=ans; soundTL(y,16000,'Pro X')
%
% See also: soundTL, audiotrim, audiovocoder, audiorecordsentences,
% audiorecorderTLautostop
%
%
% Copyright 2020 Tim C. Lueth

soundTL(y,FS,DV,SH)- same as sound by support audio output devices

% soundTL(y,FS,DV,SH) - same as sound by support audio output devices
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-26 as class: USER INTERFACE)
%
% Since an audioplayer is erased at the same time the fnctn returns, but
% the sound is not played, this fnctn is required to support different
% output devices similar to the sound fnctn (Status of: 2020-03-27)
%
% Introduced first in SolidGeometry 4.9
%
% See also: sound, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences
%
% soundTL(y,FS,[DV,SH])
% === INPUT PARAMETERS ===
% y: Samples
% FS: Sample rate
% DV: Device Name string to use
% SH: if true; a time scale is displayed; default is true
%
% EXAMPLE:
% audiorecorderTL('pro X',16000,5); y=ans; soundTL(y,16000,'Pro X')
%
% See also: sound, audiorecorderTL, audiotrim, audiovocoder,
% audiorecordsentences
%
%
% Copyright 2020 Tim C. Lueth

SGshrinktofit(SG,dim)- reduces the size that the solid fits into a bounding box

% SGshrinktofit(SG,dim) - reduces the size that the solid fits into a bounding box
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-22 as class: SURFACES)
%
% Simplified version of SGscale2dim
% Shrinks only if it does not fit (Status of: 2020-08-09)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGgrowoutsideFS, SGgrow, SGmagnifyVL, SGscale2dim
%
% [SGN,k]=SGshrinktofit(SG,[dim])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% dim: Maximum dimensions
% === OUTPUT RESULTS ======
% SGN: Shrinked Solid
% k: shrinking factor
%
% EXAMPLE:
% SGbox(1000*rand(1,3)); SG=ans;
% SGshrinktofit(SG,150)
% SGshrinktofit(SG,[150, 150 , 150])
%
% See also: SGgrowoutsideFS, SGgrow, SGmagnifyVL, SGscale2dim
%
%
% Copyright 2020 Tim C. Lueth

sprintfvec(f,s,X)- prints vectors in a way that it can used in code generation

% sprintfvec(f,s,X) - prints vectors in a way that it can used in code generation
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-21 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: fprintfvec, fprintfvec2, str2codelines
%
% ostr=sprintfvec([f,s,X])
% === INPUT PARAMETERS ===
% f: file pointer; default is ''
% s: format string
% X: number
% === OUTPUT RESULTS ======
% ostr: output string
%
% EXAMPLE:
% sprintfvec('%.3f',[1 2 3; 4 5 6])
% sprintfvec('%d',[1 2 3; 4 5 6])
%
% See also: fprintfvec, fprintfvec2, str2codelines
%
%
% Copyright 2020 Tim C. Lueth

FLselect3Dginput(VL,FL,singlef)- selects a point in the gca and finds the facets in a surface

% FLselect3Dginput(VL,FL,singlef) - selects a point in the gca and finds the facets in a surface
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-21 as class: USER INTERFACE)
%
% Introduced first in SolidGeometry 4.9
%
% See also: select3d, ginput
%
% fi=FLselect3Dginput(VL,FL,[singlef])
% === INPUT PARAMETERS ===
% VL: Vertex List
% FL: Facet list
% singlef: if true; only one facet is returned instead of all; default is
% true
% === OUTPUT RESULTS ======
% fi: list of facets that belong to the mouse click
%
% See also: select3d, ginput
%
%
% Copyright 2020 Tim C. Lueth

video2video(fname,WName,sizecr,cutt,frames,accel)- creates an AVI in different size and speed from a video file

% video2video(fname,WName,sizecr,cutt,frames,accel) - creates an AVI in different size and speed from a video file
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-11 as class: VISUALIZATION)
%
% This fnctn is manly the same as video2anim.
% The AVi file can be converted by many programs on PC or MAc to movie
% files. (Status of: 2020-03-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: image2video, videoCopyCutMovies, video2animatedGIF
%
% WName=video2video([fname,WName,sizecr,cutt,frames,accel])
% === INPUT PARAMETERS ===
% fname: Video file; default is ''=> selection by browser
% WName: Name for animated GIF file; default is same as Video file name
% sizecr: size columns by rows; default is unchanged; if scalar<10 =>
% ratio if scalar>10 =>rows
% cutt: [start time end time]; default is [0 inf]
% frames: fps; default is unchanged; 10 is a useful value;
% accel: integer acceleration factor > 1; default is 1
% === OUTPUT RESULTS ======
% WName: Name of written File
%
% EXAMPLE: Just try
% video2video('','',[1024 768],[2 3]) % select any video and cut between 2 and 3 seconds
% video2video('','',0.5,[2 3]) % scaling ration 0.5
% video2video('','',720 lines,[2 3]) % use 720 lines
% video2video('','',720 lines,[2 3],10) % use 720 lines and 10 fps
%
% See also: image2video, videoCopyCutMovies, video2animatedGIF
%
%
% Copyright 2020 Tim C. Lueth

strbreaklines(InpStr,numc)- Breaks a text string into paragraphs of a maximum number of chars per line

% strbreaklines(InpStr,numc) - Breaks a text string into paragraphs of a maximum number of chars per line
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-07 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: splitlines, ismemberincell, cell2strlines, strsplit
%
% OutStr=strbreaklines(InpStr,[numc])
% === INPUT PARAMETERS ===
% InpStr: Input String
% numc: number of chars per line
% === OUTPUT RESULTS ======
% OutStr: Output String
%
% EXAMPLE:
% a='The quick brown fox jumps over the lazy dog. '
% a=repmat(a,1,20);
% strbreaklines(a,15)
% strbreaklines(a,40)
% strbreaklines(a,2)
%
% See also: splitlines, ismemberincell, cell2strlines, strsplit
%
%
% Copyright 2020-2022 Tim C. Lueth

PLcircumcenterofCPL(CPL,lim)- returns the points that create the circumcenters of a CPL

% PLcircumcenterofCPL(CPL,lim) - returns the points that create the circumcenters of a CPL
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-05 as class: CLOSED POLYGON LISTS)
%
% This fnctn can be used to understand the addition of points before the
% delaunay traingulation to avoid extreme triangle angles. (Status of:
% 2020-03-05)
%
% Introduced first in SolidGeometry 4.9
%
% See also: delaunayTriangulation
%
% PL=PLcircumcenterofCPL(CPL,[lim])
% === INPUT PARAMETERS ===
% CPL: CPL
% lim: minimum distance between the additional points; default is 0
% === OUTPUT RESULTS ======
% PL: Point list of circumcenterpoints of CPL
%
% EXAMPLE:
% PLcircumcenterofCPL(CPLsample(29),.1);
% PLcircumcenterofCPL(CPLsample(29),1);
% PLcircumcenterofCPL(CPLsample(29),2);
%
% See also: delaunayTriangulation
%
%
% Copyright 2020 Tim C. Lueth

SGstentVeitPhillipMohamadAbdelhafez(L,D,w,halfring)- SG of a silikon stent using the deisng rules of Veit Phillip and Mohamed Abdelhafez

% SGstentVeitPhillipMohamadAbdelhafez(L,D,w,halfring) - SG of a silikon stent using the deisng rules of Veit Phillip and Mohamed Abdelhafez
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-04 as class: SURFACES)
%
% This fnctn replaces the first SGofCPLstring by Tim Lueth of 2020-02-28.
% Michaell Kruttschnitt also designed a Stent Design fnctn using the
% SG-Lib. (Status of: 2020-03-05)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGstentPeterEwert01, SGstentradsym, SGstent
%
% SG=SGstentVeitPhillipMohamadAbdelhafez([L,D,w,halfring])
% === INPUT PARAMETERS ===
% L: Length (full length, upper opening, lower opening]
% D: Diameter (Stent, uper opening, lower opening]
% w: wall thicknes [wall upper ring radius, lower ring radius]
% halfring: false=fullring true=halfring; default is true;
% === OUTPUT RESULTS ======
% SG: Solid Geometry
%
% EXAMPLE:
% SGstentVeitPhillipMohamadAbdelhafez
% SGstentVeitPhillipMohamadAbdelhafez([140 20 30], [18 22 24], [1 2 2])
% SGstentVeitPhillipMohamadAbdelhafez([140 20 30], [18 22 24], [1 2 2],false)
%
% See also: SGstentPeterEwert01, SGstentradsym, SGstent
%
%
% Copyright 2020 Tim C. Lueth

SGexplain(name,parm,fname)- returs help texts similar to a wiki system

% SGexplain(name,parm,fname) - returs help texts similar to a wiki system
% (by Tim Lueth, VLFL-Lib, 2020-MÄR-01 as class: USER INTERFACE)
%
% Support Hyperlinks
% [[http://link | Text]]
% [[@goggle | Text]]
% [[@wiki | Text]]
% (Status of: 2020-10-18)
%
% Introduced first in SolidGeometry 4.9
%
% See also: strhyperlink, sprintfhyperlinktab, evalhyperlinktab, explain,
% notiz
%
% SGexplain([name,parm,fname])
% === INPUT PARAMETERS ===
% name: name of a search text
% parm: additional parameter such as 'edit'
% fname: File name for database; default is 'SGexplainDocumentation.txt'
%
% EXAMPLE:
% SGexplain
% SGexplain Alibaba
%
%
% See also: strhyperlink, sprintfhyperlinktab, evalhyperlinktab, explain,
% notiz
%
%
% Copyright 2020 Tim C. Lueth

triangleheight(v1,v2,v3)- returns the heights of a triangle - slow but correct

% triangleheight(v1,v2,v3) - returns the heights of a triangle - slow but correct
% (by Tim Lueth, Video-Lib, 2020-FEB-28 as class: ANALYTICAL GEOMETRY)
%
% Introduced first in SolidGeometry 4.9
%
% See also: mirroringatline3D, triangleheight
%
%
% h=triangleheight(v1,v2,v3)
% === INPUT PARAMETERS ===
% v1: vertex 1 or Vertex list
% v2: vertex 2
% v3: vertex 3
% === OUTPUT RESULTS ======
% h: [h1 h2 h3]
%
% EXAMPLE:
% VLsampletriangles(25); VL=ans;
% triangleheight(VL); view(-10,0)
%
% See also: mirroringatline3D, triangleheight
%
%
%
% Copyright 2020 Tim C. Lueth

SGchecktrianglegeometry(SG)- returns the extreme values for angle, edge length and area

% SGchecktrianglegeometry(SG) - returns the extreme values for angle, edge length and area
% (by Tim Lueth, VLFL-Lib, 2020-FEB-27 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGcheckmeshlab
%
% [wmin,emin,Amin,ai]=SGchecktrianglegeometry(SG)
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% === OUTPUT RESULTS ======
% wmin: Minimal angle
% emin: Minimal edge length
% Amin: Minimul area
% ai: index of areas with minial area
%
% EXAMPLE:
% [A,B]=CSGsample(13); SGfigure(B);
% SGchecktrianglegeometry(B)
%
% See also: SGcheckmeshlab
%
%
% Copyright 2020 Tim C. Lueth

VLFLshortopti(VL,FL,otyp)- returns the vertex list with optimal number of loss less reduced vertices

% VLFLshortopti(VL,FL,otyp) - returns the vertex list with optimal number of loss less reduced vertices
% (by Tim Lueth, VLFL-Lib, 2020-FEB-27 as class: AUXILIARY PROCEDURES)
%
% Some CAD Systems creates STL files that have different vertex
% coordinates for the same vertices because of inaccuracies. This fnctn
% uses VLcheckvertexaccuracy to find the optimal grid for loss less
% optimization
% This fnctn should be used after the first readin of an exported STL
% file. Afterwards it makes sense to check the file using SGcheckmeshlab
% (Status of: 2020-03-05)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLcheckvertexaccuracy, SGshortopti, SGshort,
% VLcheckboundaryaccuracy, SGcheckmeshlab
%
% [NVL,NFL]=VLFLshortopti(VL,FL,[otyp])
% === INPUT PARAMETERS ===
% VL: Vertex List
% FL: Facet List
% otyp: optimization type: 'vertex' or 'boundary'
% === OUTPUT RESULTS ======
% NVL: SG.VL, SG.FL with optimal number of loss less reduced vertices
% NFL: New Facet List
%
% EXAMPLE:
% load JACO_robot.mat
% VLFLshortopti(JC2.VL,JC2.FL)
% VLFLshortopti(JC2.VL,JC2.FL,'vertex')
% VLFLshortopti(JC2.VL,JC2.FL,'boundary')
%
%
% See also: VLcheckvertexaccuracy, SGshortopti, SGshort,
% VLcheckboundaryaccuracy, SGcheckmeshlab
%
%
% Copyright 2020 Tim C. Lueth

VLFLchecktrianglegeometry(VL,FL)- returns the extreme values for angle, edge length and area

% VLFLchecktrianglegeometry(VL,FL) - returns the extreme values for angle, edge length and area
% (by Tim Lueth, VLFL-Lib, 2020-FEB-25 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLFLcheckmeshlab
%
% [wmin,emin,Amin,ai]=VLFLchecktrianglegeometry(VL,FL)
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% === OUTPUT RESULTS ======
% wmin: Minimal angle
% emin: Minimal edge length
% Amin: Minimul area
% ai: index of areas of minal area
%
% EXAMPLE:
% [A,B]=CSGsample(13); SGfigure(B);
% VLFLchecktrianglegeometry(B.VL,B.FL);
%
% See also: VLFLcheckmeshlab
%
%
% Copyright 2020 Tim C. Lueth

PLtriangle(a1,a2,h)- returns a triangle from an agle

% PLtriangle(a1,a2,h) - returns a triangle from an agle
% (by Tim Lueth, VLFL-Lib, 2020-FEB-24 as class: CLOSED POLYGON LISTS)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLsample
%
% PL=PLtriangle([a1,a2,h])
% === INPUT PARAMETERS ===
% a1: angle; default 1e-2
% a2: angle; default is 0
% h: height of the triangle
% === OUTPUT RESULTS ======
% PL: Point list of a single triangle
%
% EXAMPLE:
% PLtriangle(1e-1,2e-1)
% PLtriangle(1e-)
%
% See also: PLsample
%
%
% Copyright 2020 Tim C. Lueth

EXP_2020_02_21_PLFLofPLFLequidelaunay (PL,FL)-

% EXP_2020_02_21_PLFLofPLFLequidelaunay (PL,FL) -
% (by Tim Lueth, VLFL-Lib, 2020-FEB-22 as class: EXPERIMENTS)
%
% Introduced first in SolidGeometry 4.9
%
% EXP_2020_02_21_PLFLofPLFLequidelaunay(PL,FL)
% === INPUT PARAMETERS ===
% PL:
% FL:
%
%
% Copyright 2020 Tim C. Lueth

PLtetragrid(d,bb,w)- returns a tetra grid point list for a bounding box or CPL

% PLtetragrid(d,bb,w) - returns a tetra grid point list for a bounding box or CPL
% (by Tim Lueth, VLFL-Lib, 2020-FEB-22 as class: CLOSED POLYGON LISTS)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLtetragridofCPL
%
% PL=PLtetragrid([d,bb,w])
% === INPUT PARAMETERS ===
% d: distance of
% bb: length, b h, bounding box or CPL
% w: wall distance/ default is d/3
% === OUTPUT RESULTS ======
% PL: Point list
%
% EXAMPLE:
% PLtetragrid(1,[5 3]);
% PLtetragrid(1,CPLsample(30),2); % Grid 1 , wall 2
% PLtetragrid(0,CPLsample(30)); % Grid automatic
% PLtetragrid(0,CPLsample(29));
%
% See also: PLtetragridofCPL
%
%
% Copyright 2020 Tim C. Lueth

PLaddTetragridofCPL(CPL,d,w)- returns a tetra grid point list for a bounding box or CPL

% PLaddTetragridofCPL(CPL,d,w) - returns a tetra grid point list for a bounding box or CPL
% (by Tim Lueth, VLFL-Lib, 2020-FEB-22 as class: CLOSED POLYGON LISTS)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLtetragrid, PLaddTricircumcentersofCPL,
% PLaddTrisplitpointsofCPL
%
% PL=PLaddTetragridofCPL([CPL,d,w])
% === INPUT PARAMETERS ===
% CPL: CPL
% d: distance of triangle grid points
% w: wall distance/ default is d/3
% === OUTPUT RESULTS ======
% PL: Point list
%
% EXAMPLE:
% PLaddTetragridofCPL(CPLsample(29),1); % Fixed Grid size of 1
% PLaddTetragridofCPL(CPLsample(29)); % Automatic adjustment
%
%
% See also: PLtetragrid, PLaddTricircumcentersofCPL,
% PLaddTrisplitpointsofCPL
%
%
% Copyright 2020 Tim C. Lueth

lplots(P1L,P2L,c,w,ts,ss,str,fs)- plots a straight lines between 2 point lists

% lplots(P1L,P2L,c,w,ts,ss,str,fs) - plots a straight lines between 2 point lists
% (by Tim Lueth, HT-Lib, 2020-FEB-21 as class: VISUALIZATION)
%
% plots a straight line between 2 point pairs (Status of: 2020-02-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: lplot, pplot, tfplot, aplot, tlplot, slplot, plotTP, plotL,
% plotT, T2Plot
%
% h=lplots(P1L,P2L,[c,w,ts,ss,str,fs])
% === INPUT PARAMETERS ===
% P1L: Starting point
% P2L: End point
% c: Color and symbol default is "r*-"
% w: line width; default is 1
% ts: tip size; 0==auto
% ss: start block size; 0==auto
% str: Text string at tip
% fs: font size of text
% === OUTPUT RESULTS ======
% h: handle to all line elements
%
% EXAMPLE:
% SGfigure; lplots(rand(10,2),rand(10,2),'r-',2,0,0)
%
% See also: lplot, pplot, tfplot, aplot, tlplot, slplot, plotTP, plotL,
% plotT, T2Plot
%
%
% Copyright 2020 Tim C. Lueth

PLsampletriangles(z,n)- creates extreme triangle geometries

% PLsampletriangles(z,n) - creates extreme triangle geometries
% (by Tim Lueth, VLFL-Lib, 2020-FEB-18 as class: ANALYTICAL GEOMETRY)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLFLsamplecircles, VLsampletriangles, PLtriangle
%
% PLsampletriangles([z,n])
% === INPUT PARAMETERS ===
% z: extreme dimension; default is 1e-15
% n: number of additional random point around the triangle
%
% EXAMPLE:
% PLsampletriangles
%
% See also: VLFLsamplecircles, VLsampletriangles, PLtriangle
%
%
% Copyright 2020 Tim C. Lueth

EXP_2020_02_17_accuracy(bary,z)- This experiment was used to detect error in coplanar and barycentric transformations

% EXP_2020_02_17_accuracy(bary,z) - This experiment was used to detect error in coplanar and barycentric transformations
% (by Tim Lueth, VLFL-Lib, 2020-FEB-17 as class: EXPERIMENTS)
%
% Testing PLofVLcoplanar with an extremely sharpedged triangle (EDUCATION
% FNCTN)
% Using this fnctn it became clear that the most accuracte method to
% achieve coplanar cartesion coordates is a simple rotation using a
% triangle and for barycentric coordinates
% AFTERWARDS the triangulation class must be used for barycentric
% coordinats.
% The fnctn carttobaryVL of 2012 will be modified appropriately to
% achieve the same accuracy.
%
% (Status of: 2020-02-18)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLofVLcoplanar, carttobaryVL
%
% EXP_2020_02_17_accuracy([bary,z])
% === INPUT PARAMETERS ===
% bary: false = cartesian, true = barycentric
% z: accuracy; default is 1e-15 (lowest limit! for PLofVLcoplanar)
%
% EXAMPLE:
% EXP_2020_02_17_accurcay(true,1e-17)
%
% See also: PLofVLcoplanar, carttobaryVL
%
%
% Copyright 2020 Tim C. Lueth

VLFLdeleteFLofvi(VL,FL,vi)- removes the faces that belongs to a specific vertex

% VLFLdeleteFLofvi(VL,FL,vi) - removes the faces that belongs to a specific vertex
% (by Tim Lueth, VLFL-Lib, 2020-FEB-15 as class: SURFACES)
%
% more or less for education, understanding and testing
% ri=sum(ismember(FL,vi),2)>0; FLN=FL(~ri,:);
% (Status of: 2020-02-15)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLFLremoveVertex
%
% [FLN,EL,CIL,CVL]=VLFLdeleteFLofvi(VL,FL,[vi])
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% vi: index of vertices to remove frome the facet list
% === OUTPUT RESULTS ======
% FLN: New facet list
% EL: Open edge list
% CIL: CIL of open Edge list
% CVL: CVL of open edge list
%
% EXAMPLE:
% A=SGbox
% X=A; VLFLdeleteFLofvi(A.VL,A.FL,6); X.FL=ans % connectable edges
% VLFLfreeboundary(X)
% SGsample(43); A=ans;
% X=A; VLFLdeleteFLofvi(A.VL,A.FL,55); X.FL=ans % unconnectable edges
%
%
% See also: VLFLremoveVertex
%
%
% Copyright 2020 Tim C. Lueth

VLFLcircFLedges(VL,FL)- modifies the Facet list by circulating rows to minimize the distance P2-P3.

% VLFLcircFLedges(VL,FL) - modifies the Facet list by circulating rows to minimize the distance P2-P3.
% (by Tim Lueth, VLFL-Lib, 2020-FEB-15 as class: SURFACES)
%
% Time consuming fnctn:
% An FL consists of the sequence of three vertex indices [P1 P2 P3]. In
% principle, each row of the FL can rotate its entries without any change
% happening: [1 2 3] = [2 3 1] = [ 3 1 2].
% In many calculations, however, the cross product at point P1 is always
% calculated using the equation
% cross(P2-P1,P3-P1). This calculation is the more accurate the longer
% the two legs P2P1 and P3P1 are. For very acute-angled triangles, it can
% be useful to circulate rows of the facet list so that the distance
% P3-P2 is shorter than the other two, i.e. the apex angle is in P1. This
% would also allow the accuracy limit of the triangle to be reliably
% determined by the angle in P1:
% For small angles the following applies: a = tan(a) but it is necessary
% to use cos instead of tan, since tan is the upper border of cos
% (Status of: 2020-02-19)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLDLBBofVLFL
%
% [FL,cosa]=VLFLcircFLedges(VL,FL)
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% === OUTPUT RESULTS ======
% FL: Facet list with circulated rows to minimize distance |P2P3|
% cosa: resulting cos alpha of angle at P1
%
% EXAMPLE:
% [A,B]=CSGsample(13); SGfigure(B)
% SGsample(27); B=ans;
% VLFLcircFLedges(B.VL,B.FL);
% B.FL=VLFLcircFLedges(B.VL,B.FL);
%
% See also: VLDLBBofVLFL
%
%
% Copyright 2020 Tim C. Lueth

delaunayTriangulationONE2D(PLO,CL,thr)- creates a delaunayTriangulation of a single triangle avoiding inaccuracy problems

% delaunayTriangulationONE2D(PLO,CL,thr) - creates a delaunayTriangulation of a single triangle avoiding inaccuracy problems
% (by Tim Lueth, VLFL-Lib, 2020-FEB-10 as class: SURFACES)
%
% ATTENTION THE 2D delaunayTriangulation of a coplanar 3D set cannot
% guarantee the normal vector
% The first three points have to be the outer triangle in the point order
% [1 2 3].
% Similar fnctn to VLFLinsertFacetPoints.
% The use of barycentric coordinates as introduced in
% VLFLinsertFacetPoints is still the most accurate solution.
% There are two main rules:
% 1) If a point is outside of the triangle; the point is corrected to the
% point of the line
% 2) If a point is inside of a triangle but near, it is moved to the line
% (Status of: 2020-02-10)
%
% Introduced first in SolidGeometry 4.9
%
% See also: delaunayTriangulation2D, VLFLinsertFacetPoints
%
% [FLN,CLN,outside,nearside]=delaunayTriangulationONE2D(PLO,CL,[thr])
% === INPUT PARAMETERS ===
% PLO: 2D Point list in order [p1; p2; p3; .....]
% CL: Constraintlist
% thr: threshold for testing; default is 1e-7
% === OUTPUT RESULTS ======
% FLN: Facet List = Connectivity List
% CLN: Edge List - Constraint List
% outside: points of PLO that are outside of edges of the triangle
% nearside: points of PLO that are inside near the edges of the triangle
%
% EXAMPLE:
% delaunayTriangulationONE2D([0 0; 2 2; 2 0; 1 1],[1 2;2 3;3 1])
% delaunayTriangulationONE2D([0 0; 2 2; 2 0; 1 1+.1],[1 2;2 3;3 1]) % Distortion
% delaunayTriangulationONE2D([0 0; 2 2; 2 0; 1 1+.1],[1 2;2 3;3 1;3 4]) % Condition
%
% See also: delaunayTriangulation2D, VLFLinsertFacetPoints
%
%
% Copyright 2020 Tim C. Lueth

finduniqueVL(NVL,VL,tol,warn)- similar to unique but more reliable

% finduniqueVL(NVL,VL,tol,warn) - similar to unique but more reliable
% (by Tim Lueth, VLFL-Lib, 2020-FEB-08 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: unique, uniquetol
%
% [ic,err,ia]=finduniqueVL(NVL,VL,[tol,warn])
% === INPUT PARAMETERS ===
% NVL: vector row list to search in
% VL: vector row list to search for
% tol: tolerance for warning; default is 1e-12
% warn: if true; warnings are shown; default is true
% === OUTPUT RESULTS ======
% ic: list of index entries; 3rd result of unique
% err: deviation between VL and best fit in NVL
% ia: list of index entries; 2nd result of unique
%
% EXAMPLE:
% finduniqueVL(rand(10,3),rand(6,3))
% X=rand(10,3); X=[X(1:5,:);X(3,:); X(1,:);X(6:end,:)]
% [ic,err,ia]=finduniqueVL(X,X) % identical mapping
% [ic,err,ia]=finduniqueVL(X,X+1e-3) % warning since thr= 1e-12
% [ic,err,ia]=finduniqueVL(X,X+1e-3,0.01) % No warning since thr= 0.01
%
%
% See also: unique, uniquetol
%
%
% Copyright 2020 Tim C. Lueth

ELremovedoubledconstraints(CL)- removes doubles from a constraint edge list

% ELremovedoubledconstraints(CL) - removes doubles from a constraint edge list
% (by Tim Lueth, VLFL-Lib, 2020-FEB-08 as class: EDGE LISTS)
%
% There is a bug in delaunayTriangulation
% (Status of: 2020-02-10)
%
% Introduced first in SolidGeometry 4.9
%
% See also: BUGREPORT_delaunayTriangulation, delaunayTriangulation
%
% CL=ELremovedoubledconstraints(CL)
% === INPUT PARAMETERS ===
% CL: Constraint edge list
% === OUTPUT RESULTS ======
% CL: Constraint edge list with no doubles
%
% EXAMPLE:
% ELremovedoubledconstraints([1 2; 1 2; 3 4;3 4; 4 3])
%
% See also: BUGREPORT_delaunayTriangulation, delaunayTriangulation
%
%
% Copyright 2020 Tim C. Lueth

BUGREPORT_delaunayTriangulation- this simple fnct shows an triangulation bug in delaunayTriangulation 2019a

% BUGREPORT_delaunayTriangulation - this simple fnct shows an triangulation bug in delaunayTriangulation 2019a
% (by Tim Lueth, VLFL-Lib, 2020-FEB-08 as class: EXPERIMENTS)
%
% Introduced first in SolidGeometry 4.9
%
% BUGREPORT_delaunayTriangulation
%
%
% Copyright 2020 Tim C. Lueth

viewVLinspect (VL,vi)- inspects one by one points of the vertex list

% viewVLinspect (VL,vi) - inspects one by one points of the vertex list
% (by Tim Lueth, VLFL-Lib, 2020-FEB-04 as class: USER INTERFACE)
%
% Introduced first in SolidGeometry 4.9
%
% See also: camset
%
% viewVLinspect(VL,[vi])
% === INPUT PARAMETERS ===
% VL: Vertex list
% vi: optional index list to VL
%
% EXAMPLE:
% SGbox; A=ans; viewVLinspect(A.VL,5:8)
%
% See also: camset
%
%
% Copyright 2020 Tim C. Lueth

ELofcrosspoints2F(XL,PA,PB,PinA,PinB)- returns the Edge Constraint List from a crosspoint List

% ELofcrosspoints2F(XL,PA,PB,PinA,PinB) - returns the Edge Constraint List from a crosspoint List
% (by Tim Lueth, VLFL-Lib, 2020-FEB-02 as class: SURFACES)
%
% This fnctn is an auxiliary fnctn that will finally be part of
% crosspoint2F.
% The challenge is NOT only to find the cross points, but to find the
% edge constraints which can be different for triangle A and triangle B
% if some points of A are inside B and vice versa. Fortunately, the
% intersection points of cross2F or crosspoints2F are already generated
% in the correct order. It is only possible that sometimes two lines have
% to be swapped! Afterwards, the points are already available in the
% correct order. Now, at the end, the points that are located within the
% intersected triangle must be added. Here the list of the triangle A and
% B differs. After that the intersection sequence in triangle A and
% triangle B is fixed. Now you only have to create an edge list using
% circshift and afterwards edges with identical start and end points can
% be deleted.
% (Status of: 2020-02-03)
%
% Introduced first in SolidGeometry 4.9
%
% See also: crosspoints2F
%
% ELofcrosspoints2F(XL,PA,PB,PinA,PinB)
% === INPUT PARAMETERS ===
% XL: List of cross points of triangle A and triangle B (may include PA
% and PB)
% PA: Three points of triangle A
% PB: Three points of triangle B
% PinA: index list which points of B are inside A
% PinB: index list which points of A are inside B
%
% See also: crosspoints2F
%
%
% Copyright 2020 Tim C. Lueth

plothatch(h,col,w,dist,angle);- creates a hatch for a graphics object

% plothatch(h,col,w,dist,angle); - creates a hatch for a graphics object
% (by Iram Weinstein, Kirill Pankratov, Tim Lueth, VLFL-Lib, 2020-JAN-29
% as class: USER INTERFACE)
%
% =======================================================================
% OBSOLETE (2022-05-22) - USE 'CPLplothatched' INSTEAD
% =======================================================================
%
% Not Bug free - removed!! (Status of: 2022-05-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: [ CPLplothatched ] ; CPLhatch, CPLplothatched,
% CVLzplothatched, hatch
%
% hh=plothatch(h,[col,w,dist,angle]);
% === INPUT PARAMETERS ===
% h: hadle to graphics object
% col: color; default is 'r--'
% w: line width; default is 1
% dist: distance in steps of 100*sofgca
% angle: angle in multiples of 30 degree
% === OUTPUT RESULTS ======
% hh: handle to hatch
%
% EXAMPLE:
% SGfigure; h=CPLplot(PLstar(10)); plothatch(h,'g-',2,0);
%
% See also: [ CPLplothatched ] ; CPLhatch, CPLplothatched,
% CVLzplothatched, hatch
%
%
% Copyright 2020-2022 Tim C. Lueth

crosspoints2F(p1,p2,p3,pa,pb,pc,SHW)- This Fnct designed for SGbool6 returns all crossing points of 2 triangles

% crosspoints2F(p1,p2,p3,pa,pb,pc,SHW) - This Fnct designed for SGbool6 returns all crossing points of 2 triangles
% (by Tim Lueth, VLFL-Lib, 2020-JAN-28 as class: SURFACES)
%
% In contrast to fnctn cross2F of 2012 and cross2Fplanar, which are the
% origin and a step inbetween of this fnctn, crosspoints2F is able to
% handle the following cases:
% A) Two triangles are not in-plane or in-parallel as in cross2F of 2012
% B) Two triangles are in-parallel but not in-plane and have no crossings
% C) Two triangles are in-plane and have a lot of
% Furthermore, the consideration for the inplane-case is not only the
% cross-points but also which point is inside of another triangle.
% Furthermore, the constraint edge list for a delaunay triangulation is
% also returned (Status of: 2020-02-07)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLsampletriangles, cross2F, cross2Fplanar
%
% [XP,PinA,PinB,EL1,EL2]=crosspoints2F(p1,p2,p3,pa,pb,pc,[SHW])
% === INPUT PARAMETERS ===
% p1: Vertex 1 of A; or a VL=[p1;p2;p3;pa;pb;pc]
% p2: Vertex 2 of A
% p3: Vertex 3 of A
% pa: Vertex 1 of B
% pb: Vertex 2 of B
% pc: Vertex 3 of B
% SHW: show additional information if true
% === OUTPUT RESULTS ======
% XP: Crosspoints of Edges [edgeA edgeB X Y Z dir] similar to cross2F but
% handles also co-planar points
% PinA: Additional Points in A if both traingles co-planar (may be not in
% XP)
% PinB: Additional Points in B if both traingles co-planar (may be not in
% XP)
% EL1: Edges between additional points in A (MAGENTA)
% EL2: Edges between additional points in B (CYAN)
%
% EXAMPLE:
% VLsampletriangles(3); VL=ans; crosspoints2F(VL(1,:),VL(2,:),VL(3,:),VL(4,:),VL(5,:),VL(6,:))
% crosspoints2F([-10 -5 -5],[10 -5 5],[-1 -5 5],[-5 -5 0],[5 -5 0],[5 -5 20]);
%
% See also: VLsampletriangles, cross2F, cross2Fplanar
%
%
% Copyright 2020 Tim C. Lueth

exp_2020_01_27_speedtest(Nr,n)- EXperiment zum Vergleich der VErfahren zur Separierung planarer Dreiecke

% exp_2020_01_27_speedtest(Nr,n) - EXperiment zum Vergleich der VErfahren zur Separierung planarer Dreiecke
% (by Tim Lueth, VLFL-Lib, 2020-JAN-27 as class: EXPERIMENTS)
%
% Using VLcross2Lines3D nine times is between 1.5 and 100 times faster
% than calling delaunayTriangulation2D
% No crossings: 100 time
% 6 crossings: 1.5 times
% In case of cross2F the speed of crossF is just between 4 and 1.5 times
% faster than calling delaunayTriangulation2D (Status of: 2020-01-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLcross2Lines3D, delaunayTriangulation2D, cross2F
%
% exp_2020_01_27_speedtest([Nr,n])
% === INPUT PARAMETERS ===
% Nr: Testnr. of VLsampletriangles
% n: number of tests; default is 10000
%
% EXAMPLE:
% exp_2020_01_27_speedtest(1);% No crossing
% exp_2020_01_27_speedtest(9); % 6 crossing
% exp_2020_01_27_speedtest(11); % 6 crossing
%
% See also: VLcross2Lines3D, delaunayTriangulation2D, cross2F
%
%
% Copyright 2020 Tim C. Lueth

delaunayTriangulation2D(VL,CL)- returns a 2D delaunay triangulation for planar surfaces in 3D

% delaunayTriangulation2D(VL,CL) - returns a 2D delaunay triangulation for planar surfaces in 3D
% (by Tim Lueth, VLFL-Lib, 2020-JAN-26 as class: SURFACES)
%
% Not speed optimzed at the moment.
% A Delaunay Triangulation in 2D consists of a point cloud, an area
% decomposition into triangles and a list of constraints, i.e. an edge
% list containing forced exceptions to the optimal Delaunay
% Triangulation.
% The Matlab delaunayTriangulation fnctn generates either a rejection or
% a convex hull for planar surfaces in 3D, without this being detectable
% in advance.
% My fnctn creates a planar Delaunay triangulation in 3D and returns the
% constraint list separately as an Edge List.
% It is based on a rotation of all points into a plane based on the first
% 4 points of the vertex list, the delaunay triangulation in 2D wrt to
% the Constraint-Edge List, and the transformation of a new crossing
% points into 3D as the original points and rounding to 12 significant
% digits. (Status of: 2020-01-28)
%
% Introduced first in SolidGeometry 4.9
%
% See also: delaunayTriangulation, triangulation
%
% [TR3,CL,NVL,chng,FL,isInter]=delaunayTriangulation2D(VL,[CL])
% === INPUT PARAMETERS ===
% VL: Vertex list, Point list in 3D
% CL: Edge List, Constraints
% === OUTPUT RESULTS ======
% TR3: triangulation
% CL: Edge List, constraints
% NVL: true if points list is extended or consolidated (doubled vertex
% removal)
% chng: Full Triangulation
% FL: inInteriorflag
% isInter:
%
% EXAMPLE:
% n=1 % Test number
% [A,B]=VLsampletriangles(n); VL=[A;B]*rot(1,2,3); SGfigure; VLELplots(VL,[1 2;2 3; 3 1; 4 5;5 6;6 4]);
% delaunayTriangulation2D([A;B],[1 2;2 3;3 1])
% delaunayTriangulation2D(VL,[1 2;2 3;3 1;4 5;5 6;6 4])
% delaunayTriangulation2D(VL,[1 2;2 3; 3 1; 4 5;5 6;6 4])
% delaunayTriangulation2D(VLsampletriangles(11),[1 2;2 3;3 1; 4 6; 6 5; 5 4]), view(0,0)
% delaunayTriangulation2D(VLsampletriangles(11),[1 2;2 3;3 1; 6 4; 5 6; 4 5]), view(0,0)
% delaunayTriangulation2D([0 0 0;0 1 0;3 0 0; 1 0 0; 2 0 0],[1 2;2 3;3 1; 4 5;5 4])
%
% See also: delaunayTriangulation, triangulation
%
%
% Copyright 2020 Tim C. Lueth

VLsampletriangles(Nr,cmd)- returns pairs of vertex lists for triangle tests

% VLsampletriangles(Nr,cmd) - returns pairs of vertex lists for triangle tests
% (by Tim Lueth, VLFL-Lib, 2020-JAN-24 as class: VERTICES / CLOUDS)
%
% This fnctn creates pairs of triangles and in addition is a test for
% cross2F and crosspoints2F and ELofcrosspoints2F in case of planar and
% non planar surfaces.
% (Status of: 2020-02-05)
%
% Introduced first in SolidGeometry 4.9
%
% See also: cross2F, CPLsample, SGsample, VLsample, PLsample, VLFLsample,
% CSGsample, SGerrorsample, SGfischertechniksample, SGcmdsample,
% CVLzsample
%
% [VLA,VLB,cp,cpa,cpb,EL1]=VLsampletriangles([Nr,cmd])
% === INPUT PARAMETERS ===
% Nr: Number of traingle test
% cmd: such as 'last','flipA','Acirc1','Acirc2','rand','swapAB','rot'
% === OUTPUT RESULTS ======
% VLA: 3 Points of VLA or if nargout==1, [VLA;VLB]
% VLB: 3 Points of VLB if nargout>=2
% cp: List of unique cross points if nargout>=3
% cpa: points in A
% cpb: points in B
% EL1: Edge list of crossing constraints
%
% EXAMPLE:
% VLsampletriangles; % show all
% VLsampletriangles(9); % Sample Pair Nr 9
% VLsampletriangles('','rand')
% VLsampletriangles(10)
% VLsampletriangles(10,'rand')
% VLsampletriangles(10,'flipA, Acirc1')
%
% See also: cross2F, CPLsample, SGsample, VLsample, PLsample, VLFLsample,
% CSGsample, SGerrorsample, SGfischertechniksample, SGcmdsample,
% CVLzsample
%
%
% Copyright 2020-2021 Tim C. Lueth

VLcrossstraightnline3D(A,B,C,D)- returns the crossing point of 2 lines in [x y z]

% VLcrossstraightnline3D(A,B,C,D) - returns the crossing point of 2 lines in [x y z]
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: ANALYTICAL GEOMETRY)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLcross2Lines, PLcrossstraightnline, VLcross2Lines3D
%
% [CP,ka,kb,kc]=VLcrossstraightnline3D(A,B,C,D)
% === INPUT PARAMETERS ===
% A: starting point A [x y z] or PL[4 x 2
% B: ending point A [x y z]
% C: starting point B [x y z]
% D: Direction from C to [x y z]
% === OUTPUT RESULTS ======
% CP: Crossing Point
% ka: factor from A to B
% kb: factor from C into direction D; always > 0
% kc: reason for removal
%
% EXAMPLE:
% VLcrossstraightnline3D([[0 -4 0 ];[0 10 0];[-3 -3 0]; [1 1 0]])
% VLcrossstraightnline3D([[0 -4 0 ];[0 10 0];[-3 -3 0]; [1 1 1]])
%
% See also: PLcross2Lines, PLcrossstraightnline, VLcross2Lines3D
%
%
% Copyright 2020 Tim C. Lueth

VLcross2Lines3D(A,B,C,D)- returns the crossing point of 2 lines in [x y z]

% VLcross2Lines3D(A,B,C,D) - returns the crossing point of 2 lines in [x y z]
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: ANALYTICAL GEOMETRY)
%
% Accelerated version by previous checks. still uses rref in case of
% crossings
% Renamed to PLcross2Lines from originally cross4PN
% (Status of: 2020-01-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLcross2Lines, PLcrossstraightnline, VLcrossstraightnline3D
%
% [CP,ka,kb,kc]=VLcross2Lines3D(A,B,C,D)
% === INPUT PARAMETERS ===
% A: starting point A [x y] or PL[4 x 2
% B: ending point A [x y]
% C: starting point B [x y]
% D: ending point B [x y]
% === OUTPUT RESULTS ======
% CP: Crossing Point
% ka: factor from A to B
% kb: factor from C into direction D; always > 0
% kc: reason for removal
%
% EXAMPLE:
% VLcross2Lines3D([[0 -4 0];[0 10 0];[-3 -3 0]; [+5 1 0]])
% VLcross2Lines3D([[0 -4 0];[0 10 0];[-3 -3 0]; [+5 1 1]])
% VLcross2Lines3D([[0 -4 0];[0 10 0];[-3 -3 1]; [+5 1 1]])
%
% See also: PLcross2Lines, PLcrossstraightnline, VLcrossstraightnline3D
%
%
% Copyright 2020 Tim C. Lueth

PLcrossstraightnline(A,B,C,D)- returns the crossing point of 2 lines in [x y]

% PLcrossstraightnline(A,B,C,D) - returns the crossing point of 2 lines in [x y]
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: ANALYTICAL GEOMETRY)
%
% Accelerated version by previous checks. still uses rref in case of
% crossings
% Renamed to PLcross2Lines from originally cross4PN
% PLcross2Lines (Status of: 2020-01-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLcross2Lines, VLcross2Lines3D, VLcrossstraightnline3D
%
% [CP,ka,kb,kc]=PLcrossstraightnline(A,B,C,D)
% === INPUT PARAMETERS ===
% A: starting point A [x y] or PL[4 x 2
% B: ending point A [x y]
% C: starting point B [x y]
% D: Direction from B to [x y]
% === OUTPUT RESULTS ======
% CP: Crossing Point
% ka: factor from A to B
% kb: factor from C into direction D; always > 0
% kc: reason for removal
%
% EXAMPLE:
% PLcrossstraightnline([[0 -4];[0 10];[-3 -3]; [+1 +1]])
% PLcrossstraightnline([[0 -4];[0 10];[-3 -3]; [-1 -1]])
% PLcrossstraightnline([[0 -4];[0 10];[-3 -3]; [+4 +4]])
%
% See also: PLcross2Lines, VLcross2Lines3D, VLcrossstraightnline3D
%
%
% Copyright 2020 Tim C. Lueth

FLofVLPLofVLplaneprojection(VL,EL)- returns a FL for 2D could also be FLofVLELplanarDelaunay

% FLofVLPLofVLplaneprojection(VL,EL) - returns a FL for 2D could also be FLofVLELplanarDelaunay
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: SURFACES)
%
% In contrast to a transformation relative to the normal vector of the
% plane, this fnctn estimates the normal vector (VLeigenvect) based on
% the eigenvalues of the covariance matrix insteead of simply three
% vaertices. The smallest eigenvalue/eigenvector is then used to create a
% normal vector. This normal vector is used in combination with
% PLofVLplaneprojection to map the surface to 2D coordinates.
% Fast version for large vertex lists (Status of: 2020-01-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: FLofDelaunay, FLofPLEL, VLFLofVLELdelaunay3D,
% FLofVLDelaunay2Dprojection
%
% [FL,PL]=FLofVLPLofVLplaneprojection(VL,[EL])
% === INPUT PARAMETERS ===
% VL: Vertex List of a 2D Surface inb 3D Space
% EL: Optional Edge list
% === OUTPUT RESULTS ======
% FL: Facet List
% PL: Projection Point list; Not a real Transofmation
%
% EXAMPLE:
% AVL=[0 0 0; 20 0 0; 20 0 10; 0 0 10]; BVL=VLtransR(AVL,rot(pi/10,pi/4,pi/9))
% FLofVLPLofVLplaneprojection(BVL)
% FLofVLPLofVLplaneprojection(BVL,[1 3])
%
% See also: FLofDelaunay, FLofPLEL, VLFLofVLELdelaunay3D,
% FLofVLDelaunay2Dprojection
%
%
% Copyright 2020 Tim C. Lueth

VLeigenvect(VL)- Calculates Eigenvectors and Eigenvalues of Vertex list

% VLeigenvect(VL) - Calculates Eigenvectors and Eigenvalues of Vertex list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: VERTICES / CLOUDS)
%
% Similar to TofVL
% IN SG-LIB 5.0 we have to following concepts:
% - (2010) - T3P: T - right hand system from 3 Point. Origin is p1
% - (2012) - TofVL: T - Eigenvalues and Center of convexhull of VL
% - (2015) - PLofVL: T - ex is the longest distance of mean(VL)
% - (2016) - TofPez: T - ey has no x dimension or ex=[0 0 1]
% - (2019) - TofVLFL:T - ez is calucated from the face normals, o=mean(VL)
% - (2020) - VLeigenvect - same as TofVL but no convex hull and faster
% - (2020) - TofCVL: T - ez is calucated from the edge normals, o=mean(VL)
% (Status of: 2020-09-14)
%
% Introduced first in SolidGeometry 4.9
%
% See also: TofVLFL, TofVL, T3P, TofPez, PLofVL, TofCVL
%
% [EVL,EWL,T]=VLeigenvect(VL)
% === INPUT PARAMETERS ===
% VL: Vertex List
% === OUTPUT RESULTS ======
% EVL: row list of eigenvecors ordered in norm of eigenvalue
% EWL: row of Eigenvalue
% T: Transformation matrix
%
% EXAMPLE:
% VLeigenvect(VLtransR(rand(30,3),rot(pi/10,pi/4,pi/9)));
% A.VL=[0 0 0; 20 0 0; 20 0 10; 0 0 10]; VLeigenvect(VLtransR(A.VL,rot(pi/10,pi/4,pi/9)));
%
% See also: TofVLFL, TofVL, T3P, TofPez, PLofVL, TofCVL
%
%
% Copyright 2020 Tim C. Lueth

zoomVL(VL,gwfac)- simply zooms into a bounding box of the vertex list

% zoomVL(VL,gwfac) - simply zooms into a bounding box of the vertex list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: USER INTERFACE)
%
% Introduced first in SolidGeometry 4.9
%
% See also: zoom, zoompatch
%
% ax=zoomVL(VL,[gwfac])
% === INPUT PARAMETERS ===
% VL: Vertex List
% gwfac: growing factor; default is 1.1
% === OUTPUT RESULTS ======
% ax: axis
%
% EXAMPLE:
% SGbox(randminv(20,3,[1 15]),8,'pack'); zoomVL(VLFLofSG(ans))
%
% See also: zoom, zoompatch
%
%
% Copyright 2020 Tim C. Lueth

viVLFLnearestneighborVL(VLA,FLA,VL)- returns the vertex indices of the nearest neighbors of a Vertex list

% viVLFLnearestneighborVL(VLA,FLA,VL) - returns the vertex indices of the nearest neighbors of a Vertex list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: SURFACES)
%
% TR=triangulation(FLA,VLA); vi=nearestNeighbor(TR,VL); (Status of:
% 2020-01-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: FLofVLFLfi, FLofVLFLnearestneighborVL, FLofVLFLvi
%
% vi=viVLFLnearestneighborVL(VLA,FLA,VL)
% === INPUT PARAMETERS ===
% VLA: Vertex List of Solid
% FLA: Facet List of Solid
% VL: Vertex list to check
% === OUTPUT RESULTS ======
% vi: neares neighbor index to VLA
%
% EXAMPLE:
% SG=SGbox; viVLFLnearestneighborVL(SG.VL,SG.FL,rand(1,3)*10)
%
% See also: FLofVLFLfi, FLofVLFLnearestneighborVL, FLofVLFLvi
%
%
% Copyright 2020 Tim C. Lueth

isInteriorofCPL(CPL,PL);- tests whether a point is inside of a closed contour in 2D!

% isInteriorofCPL(CPL,PL); - tests whether a point is inside of a closed contour in 2D!
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: ANALYZING PROCEDURES)
%
% for simple CPL; this fnctn is faster than insideCPL
% +1 means point is inside or on contour
% 0 means point is outside (Status of: 2020-10-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: crosstest, insideCPL, insideCPS, insideC, CPLselectbyP
%
% ii=isInteriorofCPL(CPL,PL);
% === INPUT PARAMETERS ===
% CPL: Vertex list of the contour
% PL: Point to check
% === OUTPUT RESULTS ======
% ii: +1==inside or on, 0==outside
%
% EXAMPLE:
% isInteriorofCPL(CPLsample(8)/10,rand(1000000,2));
% isInteriorofCPL(PLcircle(1),rand(1000000,2));
%
%
% See also: crosstest, insideCPL, insideCPS, insideC, CPLselectbyP
%
%
% Copyright 2020-2021 Tim C. Lueth

insideCPL(VL,PL);- tests whether a point is inside of a closed contour in 2D!

% insideCPL(VL,PL); - tests whether a point is inside of a closed contour in 2D!
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: ANALYZING PROCEDURES)
%
% ONLY FOR SINGLE CLOSED CONTOURS
% for simple CPL; this fnctn is faster than
% +1 means point is inside
% -1 means point is outside
% 0 means point is on the contour (Status of: 2020-10-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: crosstest, insideCPS, isInteriorofCPL, insideC, CPLselectbyP
%
% tp=insideCPL(VL,PL);
% === INPUT PARAMETERS ===
% VL: Vertex list of the contour! MUST BE CLOSED OTHERWISE START/END
% POINTS ARE NOT DETECTED
% PL: Point to check
% === OUTPUT RESULTS ======
% tp: +1==inside, -1==outside, 0== on the contour
%
% EXAMPLE:
% insideCPL([0 0; 1 0; 1 1; 0 0],rand(1000000,2));
%
% See also: crosstest, insideCPS, isInteriorofCPL, insideC, CPLselectbyP
%
%
% Copyright 2020 Tim C. Lueth

SGboolDEBUG(cmd)- reads in in the STL Geometries that created problems during SGboolh

% SGboolDEBUG(cmd) - reads in in the STL Geometries that created problems during SGboolh
% (by Tim Lueth, VLFL-Lib, 2020-JAN-22 as class: SURFACES)
%
% SGboolDEBUG: Starting with SG-Lib. 4.9, the fnctn "SGboolh" writes the
% STL-Files for corrupted Arguments or corrupted Results to the
% desktopdir:
% SG-Lib_Debug_Boolh_FAIL_A.STL is Operand/Parameter A if SGBoolh failed!
% SG-Lib_Debug_Boolh_FAIL_B.STL is Operand/Parameter B if SGBoolh failed!
% Always both Parameters are written to file by SGboolh (Status of:
% 2020-01-22)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGboolh, SGboolanalyze, SGcheckmeshlab
%
% [SGs,erra,errb]=SGboolDEBUG([cmd])
% === INPUT PARAMETERS ===
% cmd: optional command for checking in further versions
% === OUTPUT RESULTS ======
% SGs: Cell list of 2 Solids {A,B}
% erra: errors of A of SGcheckmeshlab
% errb: errors of B of SGcheckmeshlab
%
% EXAMPLE:
% SGdumbbell('bool'); SG=ans; view(90,0); err=SGcheckmeshlab(SG);
% SGboolDEBUG; SG=ans; A=SG{1}; B=SG{2}; % Ready to make further testing
%
% See also: SGboolh, SGboolanalyze, SGcheckmeshlab
%
%
% Copyright 2020 Tim C. Lueth

SGsortcollVLFL(SGc)- returns a collision index list of all SG in the SG cell list and considers all VLFL

% SGsortcollVLFL(SGc) - returns a collision index list of all SG in the SG cell list and considers all VLFL
% (by Tim Lueth, VLFL-Lib, 2020-JAN-21 as class: SURFACES)
%
% In contrast to SGsortcollVLFLBB, which considers the Bounding Boxes of
% all Facets of two solids, this fnctn checks afterwards real
% intersections of all facets if necessary. It includes the code of
% SGsortcollBB and SGsortcollVLFL to save time. (Status of: 2020-01-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsortfitinBB, SGsortcollBB, SGsortisinsideBB,
% SGsortcollVLFLBB
%
% [ELcoll,CIL,SG]=SGsortcollVLFL(SGc)
% === INPUT PARAMETERS ===
% SGc: Bounding Box List or Solid Geometry cell list with n entries
% === OUTPUT RESULTS ======
% ELcoll: Collision pair list | It is an undirected graph
% CIL: logical collision index list, size n
% SG: Solid Geometry list
%
% EXAMPLE:
% A=SGbox; B=SGsphere(4); SGfigure; C={A,B}; SGsurfaces(C); SGsortcollVLFL(C)
% BB=rounddiv(randminv(20,3,[1 10]),2) % Create 10 Bounding boxes
% SGbox(BB,30,'randxy'); SG=ans % Create 10 Boxes in random distance
% SGsortcollVLFL(SG) % Collision pair list
% [a,b]=SGsortcollBB(SG)
% SG=SGsurfaces(SGdumbbell), SGsortcollVLFLBB(SG)
% SG=SGsurfaces(SGdumbbell), SGsortcollVLFL(SG)
% SG=SGsurfaces(SGdumbbell); SGsortisinsideBB(SG)
%
%
% See also: SGsortfitinBB, SGsortcollBB, SGsortisinsideBB,
% SGsortcollVLFLBB
%
%
% Copyright 2020 Tim C. Lueth

SGdumbbell(type)- returns the shape of a dumbbell

% SGdumbbell(type) - returns the shape of a dumbbell
% (by Tim Lueth, VLFL-Lib, 2020-JAN-21 as class: SURFACES)
%
% more a less a testing fnctn for specific surface geometries such as
% SGbox, SGboxsphere etc. (Status of: 2020-01-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGboxsphere, SGBox
%
% SG=SGdumbbell([type])
% === INPUT PARAMETERS ===
% type: design method such as 'bool' or 'rot'
% === OUTPUT RESULTS ======
% SG: Solid Geometry
%
% EXAMPLE:
% SGdumbbell
% SGdumbbell('bool')
% SGdumbbell('rot')
%
%
% See also: SGboxsphere, SGBox
%
%
% Copyright 2020 Tim C. Lueth

SGbendcone(SG,R1,R2,L,Rz1,Rz2)- bends a solid geometry around a conic segment with defined geometry

% SGbendcone(SG,R1,R2,L,Rz1,Rz2) - bends a solid geometry around a conic segment with defined geometry
% (by Nicholas Moser, VLFL-Lib, 2020-JAN-21 as class: SURFACES)
%
% SGbendcone takes in a solid geometry and parameters defining the
% geometry of a cone centered along the y-axis. It returns the deformed
% solid so that it is wrapped around the virtual cone, with the xy-plane
% being transferred to the surface of this cone (Status of: 2020-02-03)
%
% See also: SGbending, SGbendedCPL, SGcone
%
% SG=SGbendcone(SG,R1,[R2,L,Rz1,Rz2])
% === INPUT PARAMETERS ===
% SG: Solid geometry to be bent
% R1: Radius of the cone at the xz-plane
% R2: Radius of the cone at a distance L along the +y-axis. Defaults to R1
% L: Distance between R1 and R2. Defaults to furthest distance of solid
% geometry along +y-axis
% Rz1: radius in the z-direction. Together with R1, defines an elliptical
% cross-section
% Rz2: radius in the z-direction. Together with R2, defines an elliptical
% cross-section
% === OUTPUT RESULTS ======
% SG: deformed solid geometry. Positioned as if the cone was centered on
% the y-axis
%
% EXAMPLE:
% SGofCPLzdelaunayGrid(CPLoftext('test'),2,.5); SGT=ans
% SGbendcone(SGT,10,20)
%
%
% See also: SGbending, SGbendedCPL, SGcone
%

SGsortcollVLFLBB(BBL)- returns a collision index list of all SG in the SG cell list but considers the BB of VLFL

% SGsortcollVLFLBB(BBL) - returns a collision index list of all SG in the SG cell list but considers the BB of VLFL
% (by Tim Lueth, VLFL-Lib, 2020-JAN-21 as class: SURFACES)
%
% In contrast to SGsortcollBB, which consideres only the Bounding Box of
% the Solids, this fnctn checks in case of a potential collision also the
% Bounding Boxes of all Facets of two solids. I includes the code of
% SGsortcollBB to save time. Next step would be SGintersectFacetPoints.
% (Status of: 2020-01-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsortfitinBB, SGsortcollBB, SGsortisinsideBB,
% SGintersectFacetPoints
%
% [ELcoll,CIL,SG]=SGsortcollVLFLBB(BBL)
% === INPUT PARAMETERS ===
% BBL: Bounding Box List or Solid Geometry cell list with n entries
% === OUTPUT RESULTS ======
% ELcoll: Collision pair list | It is an undirected graph
% CIL: logical collision index list, size n
% SG: Solid Geometry list
%
% EXAMPLE:
% A=SGbox; B=SGsphere(4); SGfigure; C={A,B}; SGsurfaces(C); SGsortcollVLFLBB(C)
% BB=rounddiv(randminv(20,3,[1 10]),2) % Create 10 Bounding boxes
% SGbox(BB,30,'randxy'); SG=ans % Create 10 Boxes in random distance
% SGsortcollBB(SG) % Collision pair list
% [a,b]=SGsortcollBB(SG)
%
% See also: SGsortfitinBB, SGsortcollBB, SGsortisinsideBB,
% SGintersectFacetPoints
%
%
% Copyright 2020 Tim C. Lueth

SGsortisinsideBB(BBL)- returns a fits-in index list of all SG in the SG cell list

% SGsortisinsideBB(BBL) - returns a fits-in index list of all SG in the SG cell list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-21 as class: SURFACES)
%
% In contrast to fnctn SGsortfitinBB, which takes only into account the
% size of the boxes, this fnctn really considers size and position of the
% Bounding boxes.
% The next step would be to check the collisions of all the faces if a
% box is crossing or inside by SGsortcollVLFLBB or
% [~,~,~,~,~,~,bba]=VLDLBBofVLFL(VLA,FLA);
% [~,~,~,~,~,~,bbb]=VLDLBBofVLFL(VLB,FLB);
% CL=collofBBs(bba,bbb); (Status of: 2020-01-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsortcollBB, SGsortfitinBB, SGsortcollVLFLBB, VLDLBBofVLFL,
% collofBBs
%
% [ELins,iso,xsi,bsi,isi]=SGsortisinsideBB(BBL)
% === INPUT PARAMETERS ===
% BBL: Bounding Box List or Solid Geometry cell list with n entries
% === OUTPUT RESULTS ======
% ELins: Is enclosed-in pair list | It is a directed graph
% iso: Neither inside nor encapsulation
% xsi: inbetween , i.e. encapuslation and enclosing
% bsi: encapsulating but not enclosed
% isi: nothing inside
%
% EXAMPLE:
% BB=rounddiv(randminv(20,3,[1 30]),2) % Create 20 Bounding boxes
% SGbox(BB); SG=ans % Create 20 Boxes centered
% SGsortisinsideBB(SG) % Collision pair list
% [a,iso,xsi,bsi,isi]=SGsortisinsideBB(SG)
%
% See also: SGsortcollBB, SGsortfitinBB, SGsortcollVLFLBB, VLDLBBofVLFL,
% collofBBs
%
%
% Copyright 2020 Tim C. Lueth

SGsortfitinBB(BBL)- returns a fits-in index list of all SG in the SG cell list

% SGsortfitinBB(BBL) - returns a fits-in index list of all SG in the SG cell list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-20 as class: SURFACES)
%
% In contrast to fnctn SGsortisinsideBB, this fnctn takes only into
% account the size of the bounding boxes and not the position.
% The next step would be to check the collisions of all the faces if a
% box is crossing or inside by SGsortcollVLFLBB or
% [~,~,~,~,~,~,bba]=VLDLBBofVLFL(VLA,FLA);
% [~,~,~,~,~,~,bbb]=VLDLBBofVLFL(VLB,FLB);
% CL=collofBBs(bba,bbb); (Status of: 2020-01-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsortcollBB, SGsortisinsideBB, SGsortcollVLFLBB,
% VLDLBBofVLFL, collofBBs
%
% [ELfit,iso,xsi,bsi,isi]=SGsortfitinBB(BBL)
% === INPUT PARAMETERS ===
% BBL: Bounding Box List or Solid Geometry cell list with n entries
% === OUTPUT RESULTS ======
% ELfit: Fits in pair list | It is a directed graph
% iso: Neither inside nor encapsulation
% xsi: inbetween , i.e. encapuslation and enclosing
% bsi: encapsulating but not enclosed
% isi: nothing inside
%
% EXAMPLE:
% BB=rounddiv(randminv(20,3,[1 10]),2) % Create 10 Bounding boxes
% SGbox(BB,'','rand'); SG=ans % Create 10 Boxes in random distance
% SGsortfitinBB(SG) % Collision pair list
% [a,b]=SGsortfitinBB(SG)
%
% See also: SGsortcollBB, SGsortisinsideBB, SGsortcollVLFLBB,
% VLDLBBofVLFL, collofBBs
%
%
% Copyright 2020 Tim C. Lueth

SGsortcollBB(BBL)- returns a collision index list of all SG in the SG cell list

% SGsortcollBB(BBL) - returns a collision index list of all SG in the SG cell list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-20 as class: SURFACES)
%
% This fnctn returns if there is a collision between two bounding boxes
% of the solids in the cell list
% The next step would be to check the collisions of all the faces by
% SGsortcollVLFLBB or
% [~,~,~,~,~,~,bba]=VLDLBBofVLFL(VLA,FLA);
% [~,~,~,~,~,~,bbb]=VLDLBBofVLFL(VLB,FLB);
% CL=collofBBs(bba,bbb);
%
% (Status of: 2020-01-21)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGsortfitinBB, SGsortisinsideBB, SGsortcollVLFLBB,
% VLDLBBofVLFL, collofBBs
%
% [ELcoll,CIL,ss,SG]=SGsortcollBB(BBL)
% === INPUT PARAMETERS ===
% BBL: Bounding Box List or Solid Geometry cell list with n entries
% === OUTPUT RESULTS ======
% ELcoll: Collision pair list | It is an undirected graph
% CIL: logical collision index list, size n
% ss: bounding bo size list
% SG: Solid Geometry list
%
% EXAMPLE:
% A=SGbox; B=SGsphere(4); SGfigure; C={A,B}; SGsurfaces(C); SGsortcollBB(C)
% BB=rounddiv(randminv(20,3,[1 10]),2) % Create 10 Bounding boxes
% SGbox(BB,30,'randxy'); SG=ans % Create 10 Boxes in random distance
% SGsortcollBB(SG) % Collision pair list
% [a,b]=SGsortcollBB(SG)
%
% See also: SGsortfitinBB, SGsortisinsideBB, SGsortcollVLFLBB,
% VLDLBBofVLFL, collofBBs
%
%
% Copyright 2020 Tim C. Lueth

FLofoppositefacesofVLFL(VL,FL,dmax,redf)- returns the list of faces that have opposit facets within a bounding box

% FLofoppositefacesofVLFL(VL,FL,dmax,redf) - returns the list of faces that have opposit facets within a bounding box
% (by Tim Lueth, VLFL-Lib, 2020-JAN-20 as class: SURFACES)
%
% This heuristic fnctn uses VLFLoppositefaces on a facet reduced surface
% (SGreduceVLFL) to detect opposite faces, and uses later
% SGisInteriorofBB to detect all surfaces within this BB.
% This allows to analyze even larger bone surfaces or other surface
% scanned solids
%
% Current only ONE opposite face are is supported! The fnctn is still
% slow because of SGisInteriorofBB
%
% The fnctn should later cut the narrow bride between femur an patella
% (Status of: 2020-01-20)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGnearestpointsofSG, VLFLoppositefaces
%
% si=FLofoppositefacesofVLFL(VL,FL,[dmax,redf])
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% dmax: maximal distance
% redf: number of reduced facet for first opposit faces check. default is
% 1000
% === OUTPUT RESULTS ======
% si: logical index of facets
%
% EXAMPLE:
% SG=SGsample(25)
% FLofoppositefacesofVLFL(SG.VL,SG.FL);
% FLofoppositefacesofVLFL(SG.VL,SG.FL,[1 2]);
%
% See also: SGnearestpointsofSG, VLFLoppositefaces
%
%
% Copyright 2020 Tim C. Lueth

VLFLoppositefaces(VL,FL,dmax,slec)- returns the list of faces that have opposit facets in the same solid

% VLFLoppositefaces(VL,FL,dmax,slec) - returns the list of faces that have opposit facets in the same solid
% (by Tim Lueth, VLFL-Lib, 2020-JAN-19 as class: SURFACES)
%
% SLOW fnctn works up to 1000 facets within a second, 4 seconds for 2000
% facets etc.
% Use heuristic fnctn FLofoppositefacesofVLFL for larger face numbers
% such as bone surfaces or other surface scanned solids
% (Status of: 2020-01-20)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGnearestpointsofSG, FLofoppositefacesofVLFL
%
% [ofi,DL,SGB,FCL,FNL]=VLFLoppositefaces(VL,FL,[dmax,slec])
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% dmax: maximal distance
% slec: '&' or '|' '&' forces the faces to hit a surface of the same
% set; default is '&'
% === OUTPUT RESULTS ======
% ofi: logical index of facets
% DL: [si dist ei cp ]
% SGB: Solid Geometry of the Bounding Box
% FCL: Facet center list
% FNL: Facet Normal list
%
% EXAMPLE:
% SG=SGsample(25)
% VLFLoppositefaces(SG.VL,SG.FL);
% VLFLoppositefaces(SG.VL,SG.FL,[1 2]);
%
% See also: SGnearestpointsofSG, FLofoppositefacesofVLFL
%
%
% Copyright 2020 Tim C. Lueth

find2logical(ind,N)- converts a index list into a logical vector

% find2logical(ind,N) - converts a index list into a logical vector
% (by Tim Lueth, VLFL-Lib, 2020-JAN-19 as class: AUXILIARY PROCEDURES)
%
% exist most probably already in matlab (Status of: 2020-01-19)
%
% Introduced first in SolidGeometry 4.9
%
% See also: rcofind, indofrc
%
% l=find2logical(ind,N)
% === INPUT PARAMETERS ===
% ind: index list
% N: numel of logical row vector
% === OUTPUT RESULTS ======
% l: logical row vector
%
% EXAMPLE:
% find2logical([1 3 5],6)
% find2logical([1 3 5]',6)
%
% See also: rcofind, indofrc
%
%
% Copyright 2020 Tim C. Lueth

SGfindjointDoFofSG(A,B,slim,stol)- try to find the DoF between two solids

% SGfindjointDoFofSG(A,B,slim,stol) - try to find the DoF between two solids
% (by Tim Lueth, VLFL-Lib, 2020-JAN-18 as class: SURFACES)
%
% Very slow since 12 times collision detection
% Still required to test (Status of: 2020-01-18)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGnearestpointsofSG, SGintersectingtriangles,
% SGintersectFacetPoints
%
% [DOF,T]=SGfindjointDoFofSG(A,B,[slim,stol])
% === INPUT PARAMETERS ===
% A: Solid A
% B: Solid B
% slim: range limit for search; default is 10; inf works too.
% stol: tolerance wrt to minimal point; default is .1; 1 = 100 Percent
% of minimal distance is accepted
% === OUTPUT RESULTS ======
% DOF: List [Avi Bvi dist nvec] of minimal distance point pairs
% T: Facets a A with a least one point in DIL(:,1)
%
% EXAMPLE:
% A=SGbox; B=SGhollowsolid(A,1,4);; A=SGtransrelSG(A,B,'right',0.2); SGfindjointDoFofSG(A,B,inf)
% A=SGbox; B=SGhollowsolid(A,1,4);; A=SGtransrelSG(A,B,'ontop',0.2); SGfindjointDoFofSG(A,B,inf)
% A=SGsphere(5); B=SGhollowsolid(A,1,4); SGfindjointDoFofSG(A,B,inf)
%
% See also: SGnearestpointsofSG, SGintersectingtriangles,
% SGintersectFacetPoints
%
%
% Copyright 2020 Tim C. Lueth

FLofVLFLnearestneighborVL(VL,FL,VLR)- Facet List that contains vertices that are neighbors of a vertex list

% FLofVLFLnearestneighborVL(VL,FL,VLR) - Facet List that contains vertices that are neighbors of a vertex list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-18 as class: SURFACES)
%
% This fnctn calls FLofVLFLvi after using TR=triangulation(FL,VL);
% vi=nearestNeighbor(TR,VLR); (Status of: 2020-01-18)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisInteriorofBB, SGnearestpointsofSG, FLofVLFLvi,
% FLofVLFLfi, FSofSGfacet
%
% [NFL,fi3,fi2,fi1]=FLofVLFLnearestneighborVL(VL,FL,VLR)
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet List
% VLR: vertex list to find the nearest neighbor for
% === OUTPUT RESULTS ======
% NFL: FL(fi3,:); (GREEN)
% fi3: all faces that have three points of VL(vi,:)
% fi2: all faces that have 2 points of VL(vi,:)
% fi1: all faces that have 1 points of VL(vi,:)
%
% EXAMPLE:
% SG=SGboxsphere; FLofVLFLnearestneighborVL(SG.VL,SG.FL,rand(100,3)*2);
%
% See also: SGisInteriorofBB, SGnearestpointsofSG, FLofVLFLvi,
% FLofVLFLfi, FSofSGfacet
%
%
% Copyright 2020 Tim C. Lueth

SGnearestpointsofSG(A,B,slim,stol)- returns the nearest vertices and facets of two solid geometries

% SGnearestpointsofSG(A,B,slim,stol) - returns the nearest vertices and facets of two solid geometries
% (by Tim Lueth, VLFL-Lib, 2020-JAN-17 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGintersectingtriangles, SGintersectFacetPoints,
% SGfindjointDoFofSG
%
% [DILM,FLAi,FLBi,DIL]=SGnearestpointsofSG(A,B,[slim,stol])
% === INPUT PARAMETERS ===
% A: Solid A
% B: Solid B
% slim: range limit for search; default is 10; inf works too.
% stol: tolerance wrt to minimal point; default is .1; 1 = 100 Percent
% of minimal distance is accepted
% === OUTPUT RESULTS ======
% DILM: List [Avi Bvi dist nvec] of minimal distance point pairs
% FLAi: Facets a A with a least one point in DIL(:,1)
% FLBi: Facets a A with a least one point in DIL(:,2)
% DIL: Full List [Avi Bvi dist nvec] of minimal distance point pairs
%
% EXAMPLE:
% SG=SGsurfaces(SGsample(25));
% SGnearestpointsofSG(SG{1},SG{2}); M=ans; mean(M(:,4:6)), std(M(:,4:6))
% loadweb JACO_robot.mat; JC2=SGshortopti(JC2); JC3=SGshortopti(JC3);
% R=rot(pi/10,pi/5,pi/3); JC2=SGtransR(SGshortopti(JC2),R); JC3=SGtransR(SGshortopti(JC3),R);
% SGnearestpointsofSG(JC2,JC3);
% C=SGboxsphere; D=SGtransrelSG(SGbox,C,'ontop',+5);
% SGnearestpointsofSG(C,D); M=ans, mean(M(:,4:6)), std(M(:,4:6))
%
%
% See also: SGintersectingtriangles, SGintersectFacetPoints,
% SGfindjointDoFofSG
%
%
% Copyright 2020 Tim C. Lueth

SGisIntersectingBB(SG,bb,T)- returns all facets of a solid that are crossed/intersected by a bounding box

% SGisIntersectingBB(SG,bb,T) - returns all facets of a solid that are crossed/intersected by a bounding box
% (by Tim Lueth, VLFL-Lib, 2020-JAN-16 as class: SURFACES)
%
% The bounding box can also be a SGofBB Solid Geometry, and it is also
% possible to transfer the bounding box by a HT Frame like SGofBBui.
% (Status of: 2020-01-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisInteriorofBB, SGofBBui, FLofVLFLvi, FLofVLFLfi,
% VLFLselect, VLFLselectcrossingfacets
%
% [SGi,si,ci,SIL]=SGisIntersectingBB(SG,bb,[T])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% bb: bound bog or second solid
% T: Transformation matrix for bb
% === OUTPUT RESULTS ======
% SGi: Solid that has faces that are crossed/intersected by the BB
% si: facets of SG (not SGi) that are crossed/intersected by BB
% ci: facets of SG (not SGi) that belong to the same surfaces of si
% SIL: Sort Selection and Index list used to create SGi using VLFLselect
%
% EXAMPLE:
% SG=SGofCPLcommand('c 4, h 10 m 4, dupg 3 3 1 20');
% SGfigure; SGplotalpha(SG,'r',1); view(-30,30); SGofBBui; A=ans;
% SGisIntersectingBB(SG,A)
%
%
% See also: SGisInteriorofBB, SGofBBui, FLofVLFLvi, FLofVLFLfi,
% VLFLselect, VLFLselectcrossingfacets
%
%
% Copyright 2020 Tim C. Lueth

SGisInteriorofBB(SG,bb,T)- returns all facets of a solid that are within a bounding box

% SGisInteriorofBB(SG,bb,T) - returns all facets of a solid that are within a bounding box
% (by Tim Lueth, VLFL-Lib, 2020-JAN-16 as class: SURFACES)
%
% The bounding box can also be a SGofBB Solid Geometry, and it is also
% possible to transfer the bounding box by a HT Frame like SGofBBui.
% (Status of: 2020-01-16)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisIntersectingBB, SGofBBui, FLofVLFLvi, FLofVLFLfi,
% VLFLselect
%
% [SGi,si,ci,SIL]=SGisInteriorofBB(SG,bb,[T])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% bb: bound bog or second solid
% T: Transformation matrix for bb
% === OUTPUT RESULTS ======
% SGi: Solid that has vertices inside of the BB
% si: facets of SG (not SGi) with all vertices inside of BB
% ci: facets of SG (not SGi) that belong to the same surfaces of si
% SIL: Sort Selection and Index list used to create SGi using VLFLselect
%
% EXAMPLE:
% SG=SGofCPLcommand('c 4, h 10 m 4, dupg 3 3 1 20');
% SGfigure; SGplotalpha(SG,'r',1); view(-30,30); SGofBBui; A=ans;
% SGisInteriorofBB(SG,A)
%
%
% See also: SGisIntersectingBB, SGofBBui, FLofVLFLvi, FLofVLFLfi,
% VLFLselect
%
%
% Copyright 2020 Tim C. Lueth

FLofVLFLfi(VL,FL,fi)- returns the facets that are attached to the known facets

% FLofVLFLfi(VL,FL,fi) - returns the facets that are attached to the known facets
% (by Tim Lueth, VLFL-Lib, 2020-JAN-16 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisInteriorofBB, FLofVLFLvi, FSofSGfacet
%
% cfi=FLofVLFLfi(VL,FL,fi)
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% fi: facet indices that are know to belong to the surface
% === OUTPUT RESULTS ======
% cfi: connected facet index
%
% EXAMPLE:
% SG=SGofCPLcommand('c 4, h 10 m 4, dupg 3 3 1 20');
% FLofVLFLfi(SG.VL,SG.FL,500);
%
% See also: SGisInteriorofBB, FLofVLFLvi, FSofSGfacet
%
%
% Copyright 2020 Tim C. Lueth

FLofVLFLvi(VL,FL,vi)- Facet List that contains entries of a vertex list

% FLofVLFLvi(VL,FL,vi) - Facet List that contains entries of a vertex list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-16 as class: SURFACES)
%
% This fnctn can be used with vertex indices of the Solid given by VLFL
% in nearest neighbor mode for any vertex list
% Best is to call TR=triangulation(FL,VL); vi=nearestNeighbor(TR,vi); if
% vi ist a full vertex list
% (Status of: 2020-09-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisInteriorofBB, SGnearestpointsofSG, FLofVLFLfi, FSofSGfacet
%
% [FL,fi3,fi2,fi1,fi0]=FLofVLFLvi(VL,FL,vi)
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet List
% vi: vertex index list OR logical vi or vertex list for
% triangulation.nearestNeighbor
% === OUTPUT RESULTS ======
% FL: FL(fi3,:); (GREEN)
% fi3: all faces that have three points of VL(vi,:) - green
% fi2: all faces that have 2 points of VL(vi,:) - yellow
% fi1: all faces that have 1 points of VL(vi,:) - magenta
% fi0: all faces that have 0 points of VL(vi,:) - red
%
% EXAMPLE:
% SG=SGboxsphere; FLofVLFLvi(SG.VL,SG.FL,[1 2 3 4])
% SG=SGboxsphere; FLofVLFLvi(SG.VL,SG.FL,[1 2 3]);
% SG=SGboxsphere; FLofVLFLvi(SG.VL,SG.FL,[1 2 3]*1.00001);
%
% See also: SGisInteriorofBB, SGnearestpointsofSG, FLofVLFLfi, FSofSGfacet
%
%
% Copyright 2020 Tim C. Lueth

SGxor(A,B,relpos)- Boolean XOR of Solid Geometries

% SGxor(A,B,relpos) - Boolean XOR of Solid Geometries
% (by Tim Lueth, VLFL-Lib, 2020-JAN-14 as class: SURFACES)
%
% SGxor should not be used since it creates Solid that cannot be sliced!
% This fnctn belongs to a changed concept of polyshape versus the mapping
% toolbox since 2017b
% Therefor the fnctns SGintersect, SGsubtract, SGunion, SGxor were
% implemented (Status of: 2021-01-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbool, SGtransrelSG, SGboolh, SGintersect, SGsubtract,
% SGunion, SGconcat, SGsupplement
%
% SG=SGxor([A,B,relpos])
% === INPUT PARAMETERS ===
% A: Solid A
% B: Solid B
% relpos: list of relative positions for SGtransrelSG
% === OUTPUT RESULTS ======
% SG: Boolean Result of A+B
%
% EXAMPLE:
% SGxor(SGboxsphere([30,20,10],4,10))
% SGxor(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','left',-2)
% SGxor(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','infront',-2)
%
% See also: SGbool, SGtransrelSG, SGboolh, SGintersect, SGsubtract,
% SGunion, SGconcat, SGsupplement
%
%
% Copyright 2020-2021 Tim C. Lueth

SGintersect(A,B,relpos)- Boolean intersection of Solid Geometries

% SGintersect(A,B,relpos) - Boolean intersection of Solid Geometries
% (by Tim Lueth, VLFL-Lib, 2020-JAN-14 as class: SURFACES)
%
% more or less SGbool('&',A,SGtransrelSG(B,A))
% This fnctn belongs to a changed concept of polyshape versus the mapping
% toolbox since 2017b
% Therefor the fnctns SGintersect, SGsubtract, SGunion, SGxor were
% implemented (Status of: 2021-01-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGconvexofSGintersect, SGbool, SGtransrelSG, SGboolh,
% SGsubtract, SGunion, SGxor, SGconcat, SGsupplement
%
% SG=SGintersect([A,B,relpos])
% === INPUT PARAMETERS ===
% A: Solid A
% B: Solid B
% relpos: list of relative positions for SGtransrelSG
% === OUTPUT RESULTS ======
% SG: Boolean Result of A+B
%
% EXAMPLE:
% SGintersect(SGboxsphere([30,20,10],4,10))
% SGintersect(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','left',-2)
% SGintersect(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','infront',-2)
%
% See also: SGconvexofSGintersect, SGbool, SGtransrelSG, SGboolh,
% SGsubtract, SGunion, SGxor, SGconcat, SGsupplement
%
%
% Copyright 2020-2021 Tim C. Lueth

SGunion(AA,B,relpos)- Boolean Addition of Solid Geometries

% SGunion(AA,B,relpos) - Boolean Addition of Solid Geometries
% (by Tim Lueth, VLFL-Lib, 2020-JAN-14 as class: SURFACES)
%
% more or less SGbool('+',A,SGtransrelSG(B,A))
% This fnctn belongs to a changed concept of polyshape versus the mapping
% toolbox since 2017b
% Therefor the fnctns SGintersect, SGsubtract, SGunion, SGxor were
% implemented (Status of: 2021-01-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbool, SGtransrelSG, SGboolh, SGintersect, SGsubtract,
% SGxor, SGconcat, SGsupplement
%
% SG=SGunion([AA,B,relpos])
% === INPUT PARAMETERS ===
% AA: Solid A
% B: Solid B
% relpos: list of relative positions for SGtransrelSG
% === OUTPUT RESULTS ======
% SG: Boolean Result of A+B
%
% EXAMPLE:
% SGunion({SGbox(10),SGbox(20),SGbox(30)}) % Cell mode
% SGunion(SGboxsphere([30,20,10],4,10))
% SGunion(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','left',-2)
% SGunion(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','infront',-2)
%
% See also: SGbool, SGtransrelSG, SGboolh, SGintersect, SGsubtract,
% SGxor, SGconcat, SGsupplement
%
%
% Copyright 2020-2021 Tim C. Lueth

VLreadPLY(FName,mag)- reads in a Point Cloud in PLY Format

% VLreadPLY(FName,mag) - reads in a Point Cloud in PLY Format
% (by Tim Lueth, VLFL-Lib, 2020-JAN-13 as class: VERTICES / CLOUDS)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGreadPLY
%
% LITERATURE:
% http://graphics.stanford.edu/data/3Dscanrep/#bunny,
%
% [VL,ptCloud]=VLreadPLY([FName,mag])
% === INPUT PARAMETERS ===
% FName: File Name or Empty for interactive selection
% mag: magnification; default is 1000
% === OUTPUT RESULTS ======
% VL: Vertex List; double prec
% ptCloud: Point Cloud; single prec
%
% EXAMPLE:
% VLreadPLY('/Volumes/LUETH-WIN/WIN AIM Matlab Libraries/Point Clouds/bunny/reconstruction/bun_zipper.ply')
%
% See also: SGreadPLY
%
%
% Copyright 2020 Tim C. Lueth

SGofBBui(h,viewd,plong)- interactive mode to create a bounding box of the current camera view and 2 mouse clicks

% SGofBBui(h,viewd,plong) - interactive mode to create a bounding box of the current camera view and 2 mouse clicks
% (by Tim Lueth, VLFL-Lib, 2020-JAN-13 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: BBofSGcutT
%
% [SB,dd,T,bb]=SGofBBui([h,viewd,plong])
% === INPUT PARAMETERS ===
% h: handle to gca
% viewd: if true; the box depends on the view direction
% plong:
% === OUTPUT RESULTS ======
% SB: Solid of SGtransT(SGofBB(dd,0),T)
% dd: bounding box
% T: Camera View Transformation
% bb: smallest BB in view direction
%
% EXAMPLE:
% SG=SGofCPLcommand('c 4, h 10 m 4, dupg 3 3 1 20');
% SGfigure; SGplotalpha(SG,'r',1); view(-30,30);
% SGofBBui
%
% See also: BBofSGcutT
%
%
% Copyright 2020 Tim C. Lueth

rotate3dlight(tog)- Switches the automatic camera light conditions on and off

% rotate3dlight(tog) - Switches the automatic camera light conditions on and off
% (by Tim Lueth, VLFL-Lib, 2020-JAN-13 as class: VISUALIZATION)
%
% Up to Rel 4.8, SGfigure automatically installed view point cameras,
% which automatically adjusted the lighting conditions of a plot. This
% slowed down the rotation of large surfaces (detected by Alexandra
% Mercader). Therefor by default the SG-Lib ist not installing the
% rotating view point lights anymore, but it is possible to switch this
% feature on an off by this fnctn. (Status of: 2020-07-03)
%
% Introduced first in SolidGeometry 4.9
%
% See also: camlightTL, VLFLplotlight, SGshadelight, SGshowcolors
%
% rotate3dlight([tog])
% === INPUT PARAMETERS ===
% tog: 'on', 'off', or toggle by no parameter
%
% EXAMPLE:
% rotate3dlight
% rotate3dlight off
% rotate3dlight on
%
% See also: camlightTL, VLFLplotlight, SGshadelight, SGshowcolors
%
%
% Copyright 2020 Tim C. Lueth

PLofVLplaneprojection(VL,nv)- main axis projection of a vertex list along the largest dimension of a normal vector

% PLofVLplaneprojection(VL,nv) - main axis projection of a vertex list along the largest dimension of a normal vector
% (by Yilun Sun, VLFL-Lib, 2020-JAN-13 as class: VERTICES / CLOUDS)
%
% This fnctn was written by YILUN Sun on 2018-08-16. It uses the effect
% that the max fnctn returns the first occurance index of the largest
% value of the operand.
% This is not a true to scale fnctn since it is a axis projection !!!
% This fnctn can easily extented to more than 3 dimensions. (Status of:
% 2020-01-13)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLprojection, VLtransT, TofVL
%
% PL=PLofVLplaneprojection(VL,nv)
% === INPUT PARAMETERS ===
% VL: Vertex list
% nv: normal vector; default is [0 0 1] ==> xy projection
% === OUTPUT RESULTS ======
% PL: 2D Point list as main axis projection (not true to scale)
%
% EXAMPLE:
% PLofVLplaneprojection (rand(30,3));
% PLofVLplaneprojection (rand(30,3),[0 0 1]);
% PLofVLplaneprojection (rand(30,3),[0 1 0]);
% PLofVLplaneprojection (rand(30,3),[1 0 0]);
% PLofVLplaneprojection (rand(30,3),[1 1 1]);
% PLofVLplaneprojection (rand(30,3),[.9 0 1]);
%
% See also: VLprojection, VLtransT, TofVL
%

isonVLFLplanes(VLA,FLA,VL,tol)- returns wether a point is on a plane of a facet not necessarily inside of the facet

% isonVLFLplanes(VLA,FLA,VL,tol) - returns wether a point is on a plane of a facet not necessarily inside of the facet
% (by Tim Lueth, VLFL-Lib, 2020-JAN-12 as class: SURFACES)
%
% In contrast to isonVLFL/isonVLFLsurface this fnctn returns if a point
% is on a plane defined by the facets, i.e. distance to any point of the
% plane * normal vector (Status of: 2020-01-12)
%
% Introduced first in SolidGeometry 4.9
%
% See also: isonVLFL, isonVLFLsurface
%
% [vi,il]=isonVLFLplanes(VLA,FLA,VL,[tol])
% === INPUT PARAMETERS ===
% VLA: Vertex list
% FLA: Facet list
% VL: Vertex list to test
% tol: default is 1e-5
% === OUTPUT RESULTS ======
% vi: vertex index list true/false
% il: cell list of facets for each vertex
%
% EXAMPLE:
% A=SGbool('-',SGbox([30,20,10]),SGbox([26,16,6]));
% isonVLFLplanes(A.VL,A.FL,[0 0 5])
% isonVLFLplanes(A.VL,A.FL,[12 12 5])
% isonVLFLsurface(A.VL,A.FL,[12 12 5])
% isonVLFLplanes(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,1)))
%
% See also: isonVLFL, isonVLFLsurface
%
%
% Copyright 2020 Tim C. Lueth

BBaddtolerance(BB,tol)- increases the size of a Boundary Box

% BBaddtolerance(BB,tol) - increases the size of a Boundary Box
% (by Tim Lueth, VLFL-Lib, 2020-JAN-11 as class: AUXILIARY PROCEDURES)
%
% in contrast to BBgrow, this fnctn BBaddtolerance adds a tolerance and
% does not magnify the BB.
% this fnctn is able to handle lists of BBs (Status of: 2020-01-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: axis, BBofSG, BBgrow
%
% BBG=BBaddtolerance(BB,[tol])
% === INPUT PARAMETERS ===
% BB: bounding box or axis
% tol: growing size
% === OUTPUT RESULTS ======
% BBG: new bounding box
%
% EXAMPLE:
% BBaddtolerance(BBofCPL(PLcircle(4)),1)
% BBaddtolerance(BBofSG(SGbox),1)
%
% BBgrow(BBofCPL(PLcircle(4)),1)
% BBgrow(BBofSG(SGbox),1)
%
% See also: axis, BBofSG, BBgrow
%
%
% Copyright 2020 Tim C. Lueth

SGisOnsurface(SG,VL);- returns whether a point is on a surface

% SGisOnsurface(SG,VL); - returns whether a point is on a surface
% (by Tim Lueth, VLFL-Lib, 2020-JAN-11 as class: SURFACES)
%
% Based on isonVLFL
% (Status of: 2020-01-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisInterior, VLFLisInterior, isonVLFLsurface, isonVLFL,
% VLisInteriorofBBlist
%
% vi=SGisOnsurface(SG,VL);
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% VL: Vertex list to test
% === OUTPUT RESULTS ======
% vi: On Surface Index of VL
%
% EXAMPLE:
% A=SGbool('-',SGbox([30,20,10]),SGbox([26,16,6]));
% SGisOnsurface(A,0.5*(A.VL+circshift(A.VL,1)))
% isonVLFL(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,3)))
% isonVLFL(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,3)))
%
% See also: SGisInterior, VLFLisInterior, isonVLFLsurface, isonVLFL,
% VLisInteriorofBBlist
%
%
% Copyright 2020 Tim C. Lueth

VLisInteriorofBBlist(BBL,VP)- returns for a list of Bounding Boxes and a single vertex the BB that contain the vertex

% VLisInteriorofBBlist(BBL,VP) - returns for a list of Bounding Boxes and a single vertex the BB that contain the vertex
% (by Tim Lueth, VLFL-Lib, 2020-JAN-11 as class: SURFACES)
%
% After calculating the Bounding Boxes for a list of facets of a surface,
% there is an interst to find out whether a point is inside of such a
% box. This fnctn is used for detection vertices that are on surfaces by
% isonVLFL or isonVLFLsurface. (Status of: 2020-01-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: VLDLBBofVLFL, isonVLFLsurface, isonVLFL
%
% bi=VLisInteriorofBBlist(BBL,VP)
% === INPUT PARAMETERS ===
% BBL: List of Bounding Boxes
% VP: Single Vertex
% === OUTPUT RESULTS ======
% bi: bounding box index for is on bounding box or inside bounding box
%
% EXAMPLE:
% A=SGbox([30,20,10])
% [~,~,~,~,~,~,BBL]=VLDLBBofVLFL(A.VL,A.FL)
% VLisInteriorofBBlist(BBL,A.VL(1,:))
%
%
% See also: VLDLBBofVLFL, isonVLFLsurface, isonVLFL
%
%
% Copyright 2020 Tim C. Lueth

isonVLFL(VLA,FLA,VL)- returns whether a point is on a surface

% isonVLFL(VLA,FLA,VL) - returns whether a point is on a surface
% (by Tim Lueth, VLFL-Lib, 2020-JAN-11 as class: SURFACES)
%
% Developed on 2018-08-16 by Yilun Sun to improve the SGisInterior Fnctn
% Accelerated Version by Tim Lueth 2020-01-11
% For VLA:[40000×3 double] FLA:[79996×3 double] and VL:[40000×3 double]
% this fnctn takes instead of 40 seconds just 6.7 seconds (Status of:
% 2020-01-12)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisInterior, VLFLisInterior, isonVLFLsurface,
% isonVLFLplanes, VLisInteriorofBBlist, SGisOnsurface
%
% vi=isonVLFL(VLA,FLA,VL)
% === INPUT PARAMETERS ===
% VLA: Vertex list
% FLA: Facet list
% VL: Vertex list to test
% === OUTPUT RESULTS ======
% vi: On Surface Index of VL
%
% EXAMPLE:
% A=SGbox([30,20,10]);
% A=SGbool('-',SGbox([30,20,10]),SGbox([26,16,6]));
% isonVLFL(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,1)))
% isonVLFL(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,3)))
% isonVLFL(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,3)))
%
% See also: SGisInterior, VLFLisInterior, isonVLFLsurface,
% isonVLFLplanes, VLisInteriorofBBlist, SGisOnsurface
%
%
% Copyright 2020 Tim C. Lueth

VLFLplotalpha(VL,FL,c,a,e)- plots a solid support directly color and alpha value

% VLFLplotalpha(VL,FL,c,a,e) - plots a solid support directly color and alpha value
% (by Tim Lueth, VLFL-Lib, 2020-JAN-11 as class: USER INTERFACE)
%
% This fnctn was written 2019-06-12 in Tokyo visiting Hajime Asama's Lab
% at The University of Tokyo (Status of: 2020-01-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGplot, setplotlight, SGplotalpha
%
% h=VLFLplotalpha(VL,FL,[c,a,e])
% === INPUT PARAMETERS ===
% VL: Vertex List
% FL: Facet List
% c: color; default is [];
% a: alpha value; default is [];
% e: edge color; default is [];
% === OUTPUT RESULTS ======
% h: handle to graphics object patch
%
% EXAMPLE:
% A=SGbox([30,20,10])
% SGfigure; view(-30,30); VLFLplotalpha(A.VL,A.FL,'r',0.9)
% SGfigure; view(-30,30); VLFLplotalpha(A.VL,A.FL,'r',0.9,'k')
%
% See also: SGplot, setplotlight, SGplotalpha
%
%
% Copyright 2020 Tim C. Lueth

isonVLFLsurface(VL,FL,VLT)- returns whether a point is on a surface

% isonVLFLsurface(VL,FL,VLT) - returns whether a point is on a surface
% (by Yilun Sun, VLFL-Lib, 2020-JAN-11 as class: SURFACES)
%
% Developed on 2018-08-16 by Yilun Sun to improve the SGisInterior Fnctn
% (Status of: 2020-01-12)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGisInterior, VLFLisInterior, isonVLFL, isonVLFLplanes
%
% VILon=isonVLFLsurface(VL,FL,VLT)
% === INPUT PARAMETERS ===
% VL: Vertex list
% FL: Facet list
% VLT: Vertex list to test
% === OUTPUT RESULTS ======
% VILon: On Surface Index of VLT
%
% EXAMPLE:
% A=SGbox([30,20,10]);
% A=SGbool('-',SGbox([30,20,10]),SGbox([26,16,6]));
% isonVLFLsurface(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,1)))
% isonVLFLsurface(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,3)))
% isonVLFLsurface(A.VL,A.FL,0.5*(A.VL+circshift(A.VL,3)))
%
% See also: SGisInterior, VLFLisInterior, isonVLFL, isonVLFLplanes
%

SGsubtract(A,B,relpos)- Boolean Subtraction of Solid Geometries

% SGsubtract(A,B,relpos) - Boolean Subtraction of Solid Geometries
% (by Tim Lueth, VLFL-Lib, 2020-JAN-10 as class: SURFACES)
%
% more or less SGbool('-',A,SGtransrelSG(B,A))
% This fnctn belongs to a changed concept of polyshape versus the mapping
% toolbox since 2017b
% Therefor the fnctns SGintersect, SGsubtract, SGunion, SGxor were
% implemented (Status of: 2021-01-04)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbool, SGseparatebyPez, SGtransrelSG, SGboolh, SGintersect,
% SGunion, SGxor, SGconcat, SGsupplement
%
% SG=SGsubtract([A,B,relpos])
% === INPUT PARAMETERS ===
% A: Solid A
% B: Solid B
% relpos: list of relative positions for SGtransrelSG
% === OUTPUT RESULTS ======
% SG: Boolean Result of A-B
%
% EXAMPLE:
% SGsubtract(SGboxsphere([30,20,10],4,10))
% SGsubtract(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','left',-2)
% SGsubtract(SGboxsphere([30,20,10],4,10),SGbox([5,5,5]),'incenter','infront',-2)
%
% See also: SGbool, SGseparatebyPez, SGtransrelSG, SGboolh, SGintersect,
% SGunion, SGxor, SGconcat, SGsupplement
%
%
% Copyright 2020-2022 Tim C. Lueth

SGpunchTCPLthrough(SG,To,CPL)- punching: shoots a contour through a solid

% SGpunchTCPLthrough(SG,To,CPL) - punching: shoots a contour through a solid
% (by Tim Lueth, VLFL-Lib, 2020-JAN-09 as class: SURFACES)
%
% This fnctns works only for correct boolean merged solids! No open
% boundaries et al.
% This fnctn fails if tehre are hollow cavities inside of a solid
% This fnctn was developed 6.Nov.2018 as SGcutTCPL first (Status of:
% 2020-01-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: BBofSGcutT, SGcut, SGcut2, SGcutBB, SGcutTd,
% SGpunchTCPLfirstwall
%
% [C,Ts,succ]=SGpunchTCPLthrough([SG,To,CPL])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% To: Optional T frame
% CPL: Closed Polygon Line
% === OUTPUT RESULTS ======
% C: Resulting Solid
% Ts: HT MAtrix for cutting in z direction
% succ: flag for success
%
% EXAMPLE:
% SGpunchTCPLthrough(SGsample(25),TofP([-4 -6 0]),[PLcircle(1,8);nan nan;PLcircle(0.5)])
% SGpunchTCPLthrough(SGsample(25),'',[PLcircle(1,8);nan nan;PLcircle(0.5)])
% SGpunchTCPLthrough(SGboxsphere,'',[PLcircle(1,8);nan nan;PLcircle(0.5)])
%
%
% See also: BBofSGcutT, SGcut, SGcut2, SGcutBB, SGcutTd,
% SGpunchTCPLfirstwall
%
%
% Copyright 2020 Tim C. Lueth

SGboxsphere(S,n)- Solid of a box with an containing sphere, mainly used for testing

% SGboxsphere(S,n) - Solid of a box with an containing sphere, mainly used for testing
% (by Tim Lueth, VLFL-Lib, 2020-JAN-09 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGbox, SGcone, SGsphere, SGarrow, SGspherelink, SGtrapezoid
%
% SG=SGboxsphere([S,n])
% === INPUT PARAMETERS ===
% S: Diameter [x y z]
% n: number of edges in x y
% === OUTPUT RESULTS ======
% SG: Solid Geometry
%
% EXAMPLE:
% SGboxsphere([30,20,10],6)
%
% See also: SGbox, SGcone, SGsphere, SGarrow, SGspherelink, SGtrapezoid
%
%
% Copyright 2020 Tim C. Lueth

SGpunchTCPLfirstwall(SG,To,CPL,olap,plan)- punchs from a frame or from an outside poit a hole with a CPL into the first wall

% SGpunchTCPLfirstwall(SG,To,CPL,olap,plan) - punchs from a frame or from an outside poit a hole with a CPL into the first wall
% (by Tim Lueth, VLFL-Lib, 2020-JAN-09 as class: SURFACES)
%
% In case of wrong orientations (inside volumes, the SG bool fnctn fails)
% (Status of: 2020-01-11)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGcutT, CPLofSGcutT, SGcutTinsertpins, SGcutTCPL,
% SGpunchTCPLthrough
%
% [SG,p,ez]=SGpunchTCPLfirstwall([SG,To,CPL,olap,plan])
% === INPUT PARAMETERS ===
% SG: Solid Geometry
% To: Frame to punch; default is interactive Mode
% CPL: CPL or radius
% olap: overlap; default is radius or 1e-2
% plan: if true, the surface is used to punchl default is false
% === OUTPUT RESULTS ======
% SG: Solid Geometry
% p: punch point
% ez: punch direction
%
% EXAMPLE:
% SGpunchTCPLfirstwall(SGsample(13),'',.7,0,false)
% SGpunchTCPLfirstwall(SGsample(13),'',.7,0,true)
% SGpunchTCPLfirstwall(SGboxsphere,'',[PLcircle(2,4)])
% SGpunchTCPLfirstwall(SGboxsphere,'',[PLcircle(2,4)],'',true)
%
% See also: SGcutT, CPLofSGcutT, SGcutTinsertpins, SGcutTCPL,
% SGpunchTCPLthrough
%
%
% Copyright 2020 Tim C. Lueth

matrixofCPL(CPL,nrc)- simplified version of matrixdistanceofCPL

% matrixofCPL(CPL,nrc) - simplified version of matrixdistanceofCPL
% (by Tim Lueth, VLFL-Lib, 2020-JAN-09 as class: CLOSED POLYGON LISTS)
%
% Introduced first in SolidGeometry 4.9
%
% See also: matrixdistanceofCPL
%
% [M,GPL,ax]=matrixofCPL(CPL,[nrc])
% === INPUT PARAMETERS ===
% CPL: CPL
% nrc: [nx ny] or [dx dy] if [dx,dy]<10 mm
% === OUTPUT RESULTS ======
% M: Matrix
% GPL: Grid Point Coordinates
% ax: [xmin xmax ymin ymax]
%
% EXAMPLE:
% matrixofCPL(CPLsample(29));
%
% See also: matrixdistanceofCPL
%
%
% Copyright 2020 Tim C. Lueth

crosspointVLFL2(VL,FL,p,ez)- returns the surfacepoint of a solid hit by a beam

% crosspointVLFL2(VL,FL,p,ez) - returns the surfacepoint of a solid hit by a beam
% (by Tim Lueth, VLFL-Lib, 2020-JAN-08 as class: AUXILIARY PROCEDURES)
%
% In contrast to crosspointVLFL this fnctn supports different ez vectors
% Straight forward but fast procedure to calucate the surface point of a
% beam starting at point p in the direction of ez. (Status of: 2020-01-09)
%
% Introduced first in SolidGeometry 4.9
%
% See also: intersectstriangle, VLprojection, crosspointVLFL,
% crosspointsVLFLofT
%
% [cp,t,fi,a]=crosspointVLFL2(VL,FL,p,[ez])
% === INPUT PARAMETERS ===
% VL: Vertex list of a solid
% FL: Facet list of a solid
% p: beam starting point
% ez: beam direction vector; if empty the facet normal vectors are used
% === OUTPUT RESULTS ======
% cp: cross point on surface, empty if there is no crossing point
% t: distance (t * ez)
% fi: facet index of 1st crossed surface
% a: full list of facet index and distance [fi, d]
%
% EXAMPLE:
% SG=SGtransP(SGbox([80,80,5]),[0 0 40]); p=[5 0 0];
% crosspointVLFL2(SG.VL,SG.FL,p,[1 1 5])
% crosspointVLFL2(SG.VL,SG.FL,p,[1 0 1.2])
% crosspointVLFL2(SG.VL,SG.FL,p)
% SGsample(3);SG=ans;
% crosspointVLFL2(SG.VL,SG.FL,[0.1 .1 8])
%
% See also: intersectstriangle, VLprojection, crosspointVLFL,
% crosspointsVLFLofT
%
%
% Copyright 2020 Tim C. Lueth

dist2line(P1,ev,p)- mirrors a point at a straight line in 2D

% dist2line(P1,ev,p) - mirrors a point at a straight line in 2D
% (by Tim Lueth, VLFL-Lib, 2020-JAN-08 as class: ANALYTICAL GEOMETRY)
%
% Should be renamed into PLmirroratline (Status of: 2020-01-08)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLcross2Lines, PLcrossCPLline, mirroringatline3D,
% mirroringatline2D
%
% [mp,do,cp,ov]=dist2line(P1,ev,p)
% === INPUT PARAMETERS ===
% P1: Point on line
% ev: direction vector
% p: point to mirror
% === OUTPUT RESULTS ======
% mp: mirror point
% do: distance to straight line (wrt to ev)
% cp: crossing point on line
% ov: orthogonal vector to straight line from p to cp
%
% EXAMPLE:
% mirroringatline([0 0],+[-1 -6],[1 1])
%
% See also: PLcross2Lines, PLcrossCPLline, mirroringatline3D,
% mirroringatline2D
%
%
% Copyright 2020 Tim C. Lueth

matrixPLplot(M,PL)- plots a matrix and a point list

% matrixPLplot(M,PL) - plots a matrix and a point list
% (by Tim Lueth, VLFL-Lib, 2020-JAN-08 as class: AUXILIARY PROCEDURES)
%
% shows the result of path planning (Status of: 2020-01-08)
%
% Introduced first in SolidGeometry 4.9
%
% See also: matrixplot
%
% h=matrixPLplot(M,PL)
% === INPUT PARAMETERS ===
% M: Matrix entries
% PL: [r c] or [y x] list
% === OUTPUT RESULTS ======
% h: handle to graphics objects
%
% EXAMPLE:
% matrixdistancefield(M,[20 70;80 50]); M=ans; whos M
% SGfigure; matrixPLplot(M,[1 1; 100 50])
%
%
% See also: matrixplot
%
%
% Copyright 2020 Tim C. Lueth

SGselect3dPL(SG,p)- similar to select3d cals nearest point and vertices but for any fiven point

% SGselect3dPL(SG,p) - similar to select3d cals nearest point and vertices but for any fiven point
% (by Tim Lueth, VLFL-Lib, 2020-JAN-08 as class: SURFACES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: select3d, crosspointVLFL2, SGselect3d, SGselect3Dsurface
%
% [NL,FVL,fi]=SGselect3dPL(SG,[p])
% === INPUT PARAMETERS ===
% SG: Solid Geoemtry
% p: point to be checked
% === OUTPUT RESULTS ======
% NL: List of point with nearest distance to PL
% FVL: list of point on nearest vertex
% fi: index of nearest vertex
%
% EXAMPLE:
% SGselect3dPL(SGsample(3),[0 -6 80])
% SGselect3dPL(SGsample(3),[0 -6 8])
% SGselect3dPL(SGsample(3),[1 -6 8])
% [a,b,c]=SGselect3dPL(SGsample(3),[1 -6 8])
% [a,b,c]=SGselect3dPL(SGsample(3),[1 -6 80])
%
% See also: select3d, crosspointVLFL2, SGselect3d, SGselect3Dsurface
%
%
% Copyright 2020 Tim C. Lueth

matrixfillseedpoints(M,neighb,PLrc);- fills a matrix similiar as matrixdistanceofCPL but with discrete values

% matrixfillseedpoints(M,neighb,PLrc); - fills a matrix similiar as matrixdistanceofCPL but with discrete values
% (by Tim Lueth, VLFL-Lib, 2020-JAN-08 as class: AUXILIARY PROCEDURES)
%
% Introduced first in SolidGeometry 4.9
%
% See also: GPLofmatrix, matrixdistanceofCPL, ELofmatrixneigbors,
% ELofmatrixneigborweight, matrixlocalminmax, matrixskeleton,
% matrixfilldistance, matrixfillborder
%
% MM=matrixfillseedpoints(M,[neighb,PLrc]);
% === INPUT PARAMETERS ===
% M: Matrix with nan as untouchable regions
% neighb: '8' oder '4' as neighborhood; default is '8'
% PLrc: List of Start points using PLrc defining the
% === OUTPUT RESULTS ======
% MM: Matrix with discrete distance values
%
% EXAMPLE:
% matrixfillseedpoints(matrixdistanceofCPL(CPLsample(29),[100 100]),'',[50 50]);
% matrixfillseedpoints(matrixdistanceofCPL(CPLsample(29),[100 100]),'',[80 50]);
% matrixfillseedpoints(matrixdistanceofCPL(CPLsample(29),[100 100]),'',[10 70]);
%
% See also: GPLofmatrix, matrixdistanceofCPL, ELofmatrixneigbors,
% ELofmatrixneigborweight, matrixlocalminmax, matrixskeleton,
% matrixfilldistance, matrixfillborder
%
%
% Copyright 2020 Tim C. Lueth

matrixpath(M,GL,AP,ST)- searches a path in a potential field matrix from start point to matrix value = zeros

% matrixpath(M,GL,AP,ST) - searches a path in a potential field matrix from start point to matrix value = zeros
% (by Tim Lueth, RP-Lib, 2020-JAN-08 as class: AUXILIARY PROCEDURES)
%
% Use matrixfillseedpoints, matrixfilldistance, matrixfillborder,
% matrixdistanceofCPL, matrixdistancefield, first (Status of: 2020-01-09)
%
% Introduced first in SolidGeometry 4.9
%
% See also: PLshortestpathinCPL, matrixfillseedpoints,
% matrixfilldistance, matrixfillborder, ELofmatrixneigborweight,
% matrixdistancefield, matrixdistanceofCPL
%
%
% PL=matrixpath(M,[GL,AP,ST])
% === INPUT PARAMETERS ===
% M: Matrix as result of
% GL: Goal start tart search from
% AP: Attraction point; default is Matrix==0
% ST: Style of Line "push', 'pull' , 'dist'; default is pull
% === OUTPUT RESULTS ======
% PL: PLrc list from start to end
%
% EXAMPLE:
% matrixfillseedpoints(matrixdistanceofCPL(CPLsample(29),[100 100]),'8',[80 50]); M=ans; whos M
% matrixpath(M,[30 20],'','push') % select farest point to straight line
% matrixpath(M,[30 20],'','pull') % select nearest point to straight line
% matrixpath(M,[30 20],'','dist') % select nearest point to goal
%
% See also: PLshortestpathinCPL, matrixfillseedpoints,
% matrixfilldistance, matrixfillborder, ELofmatrixneigborweight,
% matrixdistancefield, matrixdistanceofCPL
%
%
%
% Copyright 2020 Tim C. Lueth

SGofVLFLz(VL,FL,z)- returns a fitting solid based on a surface, i.e. simplified version of SGofSurface

% SGofVLFLz(VL,FL,z) - returns a fitting solid based on a surface, i.e. simplified version of SGofSurface
% (by Tim Lueth, VLFL-Lib, 2020-JAN-07 as class: SURFACES)
%
% Fast and stable fnctn even for large data sets. (Status of: 2020-01-07)
%
% Introduced first in SolidGeometry 4.9
%
% See also: SGofSurface, VLFLofCPLdelaunayGrid, VLtransN, VLFLvertexNormal
%
% SG=SGofVLFLz(VL,FL,[z])
% === INPUT PARAMETERS ===
% VL: Vertex list of a surface (nx3)
% FL: Facet list of a surface (nx3)
% z: thickness of the solid; default is 0.5
% === OUTPUT RESULTS ======
% SG: resulting solid that can be attached to the surface
%
% EXAMPLE:
% [VL,FL]=VLFLsample(14); SGofVLFLz(VL,FL,1)
% [VL,FL]=VLFLsample(18); SGofVLFLz(VL,FL,1)
%
% See also: SGofSurface, VLFLofCPLdelaunayGrid, VLtransN, VLFLvertexNormal
%
%
% Copyright 2020 Tim C. Lueth

SGisInterior(SG,VL)- returns the isInside Flag for a SG and a VL

% SGisInterior(SG,VL) - returns the isInside Flag for a SG and a VL
% (by MATLAB-CENTRAL, VLFL-Lib, 2020-JAN-07 as class: SURFACES)
%
% It is still a fast checking fnctn for points that are on or not on the
% surface. Surface points belong to the inner points. Bugs appear if
% points are at the same position but different z axis. Could easily be
% solved. See mesh2mesh to learn how to improve VLFLinpolyhedron. (Status
% of: 2020-01-16)
%
% See also: VLisInteriorofBB, mesh2mesh, VLFLinpolyhedron, BBiscollofVL,
% outboundingbox, VLcrossingSG, crossingfacets2VLFL, SGisconvex
%
% [VIL,Vin,Von]=SGisInterior(SG,VL)
% === INPUT PARAMETERS ===
% SG: Solid Geoemtry or cell list
% VL: Vertex list to test or Frame T
% === OUTPUT RESULTS ======
% VIL: Vertex inside or surface
% Vin: Vertex inside not on surface
% Von: Vertex on surface not inside
%
% EXAMPLE:
% SGplatesofSGML(SGbox([60,40,20]),1.5,PLcircle(4)); SG=ans;
% [~,~,~,VL]=meshgridofBB(BBofSG(SG),50,50,50,0); SGisInterior(SG,VL);
% A=SGbool('-',SGbox([30,20,10]),SGbox([26,16,6])); B=SGsphere(10);
% SGisInterior(A,[A.VL;B.VL]);
%
% See also: VLisInteriorofBB, mesh2mesh, VLFLinpolyhedron, BBiscollofVL,
% outboundingbox, VLcrossingSG, crossingfacets2VLFL, SGisconvex
%

SG-Lib • Solid Geometry Library Toolbox for Generative AI

Solid Modelling • Finite Element based Optimization • Multi-Body Simulation