find distance along complicated geometric surface
in [Matlab]
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From: Bruno Luong on 18 May 2010 06:20 "Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> wrote in message <hsto03$f28$1(a)fred.mathworks.com>... > > Following those geodesics from various azimuths is not as one-dimnsional an affair as one would like it to be. For example, if two geodesics proceeding as you correctly describe, Bruno, and in nearly parallel paths, go short distances on opposite sides of a vertex joining three facets, then after they pass that vertex their paths may cross each other at very sizable angles on the other side. This means that choosing an azimuth for one geodesic just to the left of another geodesic is no guarantee that that geodesic will remain to the left. It can go far to the right instead. Therefore there can remain still much of a combinatorial nature about seeking a shortest path across a surface composed of numerous plane facets and therefore exceedingly difficult to determine. You are right Roger, but I believe for the surface with positive curvature (convex polytope in particular in the case here), the geodesic ode is locally Lipschitz and stable. We must also decide to stop the search when the length of the geodesic get too long to avoid wrap around. There is no explosion or bifurcation of the solution. That makes the problem somewhat nicer. However I also think minimizing the path length for all the paths that go through 2 points is an even better approach. It must be fun to code such thing, unfortunately I don't have spare time to do so. Bruno
From: Meagan on 18 May 2010 10:04 I have posted my code below. It is very long and not cleaned up at all...sorry. When the code is run, you should get an airplane. Now I have my shape and would like to find the distance from say one wing to the nose of the plane but the path needs to stay on the surface of the plane. The shape can change based on the input array p1 thru p7 and the other problem is that when the airplane is made, most of the shapes intersect so a lot of the vertices for a particular component are not necessarily on the outside of the plane. I am not required to make my shape this way but eventually, I will have to convert my code to C so the functions must be embedded matlab compatible. Any suggestions or comments are greatly appreciated. Thanks, Meagan p1=[1 1 3 1 1 5 0 90 0 0 0 1.01]; p2=[2 2 1 3 1 1 0 0 0 -4.5 0 1.01]; p3=[3 2 1 1 10 0.2 0 0 0 -2 0 1]; p4=[4 2 1 1.5 0.5 0.5 0 0 0 -2 3 1]; p5=[5 2 1 2 1 1 0 0 0 4.5 0 1.01]; p6=[6 2 1 1.5 0.5 0.5 0 0 0 -2 -3 1]; p7=[7 2 1 1 .2 2 0 30 0 5 0 2]; cube.vertices=[ 0 0 0; 1 0 0; 1 1 0; 0 1 0; 0 0 1; 1 0 1; 1 1 1; 0 1 1;] ; cube.faces=[ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8; ] ; cube.vertices = cube.vertices * 2 - 1; cylinder.vertices=[-1,0,-1;-1,0,0;-0.500000000000000,-0.856380903262898,-1;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,-1;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,-1;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,-1;-0.500000000000000,0.856380903262898,0;0,-1,-1;0,-1,0;0,1,-1;0,1,0;0.500000000000000,-0.856380903262898,-1;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,-1;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,-1;0.856380903262898,-0.500000000000000,0;1,0,-1;1,0,0;0.856380903262898,0.500000000000000,-1;0.856380903262898,0.500000000000000,0;-1,0,1;-0.500000000000000,-0.856380903262898,1;-0.856380903262898,-0.500000000000000,1;-0.856380903262898,0.500000000000000,1;-0.500000000000000,0.856380903262898,1;0,-1,1;0,1,1;0.5000000000000 00,-0.856380903262898,1;0.500000000000000,0.856380903262898,1;0.856380903262898,-0.500000000000000,1;1,0,1;0.856380903262898,0.500000000000000,1;]; cylinder.faces=[3,4,5;5,4,6;5,6,1;1,6,2;1,2,7;7,2,8;7,8,9;9,8,10;11,12,3;3,12,4;9,10,13;13,10,14;11,15,12;12,15,16;17,13,18;18,13,14;15,19,16;16,19,20;19,21,20;20,21,22;21,23,22;22,23,24;23,17,24;24,17,18;4,26,6;6,26,27;6,27,2;2,27,25;2,25,8;8,25,28;8,28,10;10,28,29;12,30,4;4,30,26;10,29,14;14,29,31;12,16,30;30,16,32;18,14,33;33,14,31;16,20,32;32,20,34;20,22,34;34,22,35;22,24,35;35,24,36;24,18,36;36,18,33;]; sphere.vertices=[0,0,-1;-0.500000000000000,-0.500000000000000,-0.686740068930804;-0.500000000000000,-0.686740068930804,-0.500000000000000;-0.686740068930804,-0.500000000000000,-0.500000000000000;-0.500000000000000,0,-0.856380903262898;-0.856380903262898,0,-0.500000000000000;-0.500000000000000,0.500000000000000,-0.686740068930804;-0.686740068930804,0.500000000000000,-0.500000000000000;-0.500000000000000,0.686740068930805,-0.500000000000000;0,-0.500000000000000,-0.856380903262898;0,-0.856380903262898,-0.500000000000000;0,0.500000000000000,-0.856380903262898;0,0.856380903262898,-0.500000000000000;0.500000000000000,-0.500000000000000,-0.686740068930804;0.500000000000000,-0.686740068930804,-0.500000000000000;0.500000000000000,0,-0.856380903262898;0.500000000000000,0.500000000000000,-0.686740068930804;0.500000000000000,0.686740068930805,-0.500000000000000;0.686740068930805,-0.500000000000000,- 0.500000000000000;0.856380903262898,0,-0.500000000000000;0.686740068930805,0.500000000000000,-0.500000000000000;-1,0,0;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,0;0,-1,0;0,1,0;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,0;1,0,0;0.856380903262898,0.500000000000000,0;-0.500000000000000,-0.686740068930804,0.500000000000000;-0.686740068930804,-0.500000000000000,0.500000000000000;-0.856380903262898,0,0.500000000000000;-0.686740068930804,0.500000000000000,0.500000000000000;-0.500000000000000,0.686740068930805,0.500000000000000;0,-0.856380903262898,0.500000000000000;0,0.856380903262898,0.500000000000000;0.500000000000000,-0.686740068930804,0.500000000000000;0.500000000000000,0.686740068930805,0.500000000000000;0.6 86740068930805,-0.500000000000000,0.500000000000000;0.856380903262898,0,0.500000000000000;0.686740068930805,0.500000000000000,0.500000000000000;-0.500000000000000,-0.500000000000000,0.686740068930805;-0.500000000000000,0,0.856380903262898;-0.500000000000000,0.500000000000000,0.686740068930805;0,-0.500000000000000,0.856380903262898;0,0,1;0,0.500000000000000,0.856380903262898;0.500000000000000,-0.500000000000000,0.686740068930805;0.500000000000000,0,0.856380903262898;0.500000000000000,0.500000000000000,0.686740068930805;]; sphere.faces=[2,3,4;2,4,5;5,4,6;5,6,7;7,6,8;7,8,9;2,10,3;3,10,11;1,10,2;1,2,5;1,5,7;1,7,12;7,9,12;12,9,13;10,14,11;11,14,15;10,1,16;10,16,14;16,1,12;16,12,17;12,13,17;17,13,18;14,19,15;14,16,19;19,16,20;16,17,20;20,17,21;17,18,21;3,23,4;4,23,24;4,24,6;6,24,22;6,22,8;8,22,25;8,25,9;9,25,26;11,27,3;3,27,23;13,9,28;28,9,26;15,29,11;11,29,27;18,13,30;30,13,28;15,19,29;29,19,31;19,20,31;31,20,32;20,21,32;32,21,33;21,18,33;33,18,30;23,34,24;24,34,35;24,35,22;22,35,36;25,22,36;25,36,37;25,37,26;26,37,38;23,27,39;23,39,34;26,38,28;28,38,40;27,29,41;27,41,39;30,28,42;42,28,40;29,31,41;41,31,43;31,32,43;43,32,44;32,33,45;32,45,44;33,30,45;45,30,42;34,46,35;35,46,36;36,46,47;36,47,37;37,47,48;37,48,38;39,49,34;34,49,46;46,49,47;47,49,50;47,50,48;48,50,51;40,38,51;51,38,48;41,52,39;39,52,49;49,52,50;50,52,53;53,54,50;50,54,51;42,40,54;54,40,51;41,43,52;43,44,52;52,44,53;44,45,53;53,45,54;45,42,54;]; if (p1(2)==1) %part ID 1=UnitCylinder res=p1(3); %resolution scalex=p1(4); %diameter of cylinder in x direction scaley=p1(5); %diameter of cylinder in y direction scalez=p1(6); %length of cylinder rotx=p1(7); %rotation about x axis roty=p1(8); %rotation about y axis rotz=p1(9); %rotation about z axis transx=p1(10); %translation in x direction transy=p1(11); %translation in y direction transz=p1(12); %translation in z direction V1=cylinder.vertices; V1=[V1(:,1)*scalex, V1(:,2)*scaley, V1(:,3)*scalez]; cylinder.vertices=V1; a=rotz/57.29; %degrees to radians V1=cylinder.vertices; V1=[cos(a)*V1(:,1)-sin(a)*V1(:,2),sin(a)*V1(:,1)+cos(a)*V1(:,2),V1(:,3)]; cylinder.vertices=V1; a=roty/57.29; %degrees to radians V1=cylinder.vertices; V1=[cos(a)*V1(:,1)+sin(a)*V1(:,3), V1(:,2), -sin(a)*V1(:,1)+cos(a)*V1(:,3)]; cylinder.vertices=V1; a=rotx/57.29; %degrees to radians V1=cylinder.vertices; V1=[V1(:,1), cos(a)*V1(:,2)-sin(a)*V1(:,3), sin(a)*V1(:,2)+cos(a)*V1(:,3)]; cylinder.vertices=V1; V1=cylinder.vertices; V1=[V1(:,1)+transx, V1(:,2)+transy, V1(:,3)+transz]; cylinder.vertices=V1; part1=cylinder; elseif (p1(2)==2) %part ID 2=UnitSphere res=p1(3); %resolution scalex=p1(4); %diameter of sphere in x direction scaley=p1(5); %diameter of sphere in y direction scalez=p1(6); %diameter of sphere in z direction rotx=p1(7); %rotation about x axis roty=p1(8); %rotation about y axis rotz=p1(9); %rotation about z axis transx=p1(10); %translation in x direction transy=p1(11); %translation in y direction transz=p1(12); %translation in z direction M1=sphere.vertices; M1=[M1(:,1)*scalex, M1(:,2)*scaley, M1(:,3)*scalez]; sphere.vertices=M1; a=rotz/57.29; %degrees to radians M1=sphere.vertices; M1=[cos(a)*M1(:,1)-sin(a)*M1(:,2),sin(a)*M1(:,1)+cos(a)*M1(:,2), M1(:,3)]; sphere.vertices=M1; a=roty/57.29; %degrees to radians M1=sphere.vertices; M1=[cos(a)*M1(:,1)+sin(a)*M1(:,3), M1(:,2), -sin(a)*M1(:,1)+cos(a)*M1(:,3)]; sphere.vertices=M1; a=rotx/57.29; %degrees to radians M1=sphere.vertices; M1=[M1(:,1), cos(a)*M1(:,2)-sin(a)*M1(:,3), sin(a)*M1(:,2)+cos(a)*M1(:,3)]; sphere.vertices=M1; M1=sphere.vertices; M1=[M1(:,1)+transx, M1(:,2)+transy, M1(:,3)+transz]; sphere.vertices=M1; part1=sphere; elseif (p1(2)==3) %part ID 3=UnitCube res=p1(3); %resolution scalex=p1(4); %length in x direction scaley=p1(5); %length in y direction scalez=p1(6); %length in z direction rotx=p1(7); %rotation about x axis roty=p1(8); %rotation about y axis rotz=p1(9); %rotation about z axis transx=p1(10); %translation in x direction transy=p1(11); %translation in y direction transz=p1(12); %translation in z direction F1=cube.vertices; F1=[F1(:,1)*scalex, F1(:,2)*scaley, F1(:,3)*scalez]; cube.vertices=F1; a=rotz/57.29; %degrees to radians F1=cube.vertices; F1=[cos(a)*F1(:,1)-sin(a)*F1(:,2), sin(a)*F1(:,1)+cos(a)*F1(:,2), F1(:,3)]; cube.vertices=F1; a=roty/57.29; %degrees to radians F1=cube.vertices; F1=[cos(a)*F1(:,1)+sin(a)*F1(:,3),F1(:,2), -sin(a)*F1(:,1)+cos(a)*F1(:,3)]; cube.vertices=F1; a=rotx/57.29; %degrees to radians F1=cube.vertices; F1=[F(:,1),cos(a)*F1(:,2)-sin(a)*F1(:,3), sin(a)*F1(:,2)+cos(a)*F1(:,3)]; cube.vertices=F1; F1=cube.vertices; F1=[F1(:,1)+transx, F1(:,2)+transy, F1(:,3)+transz]; cube.vertices=F1; part1=cube; else p1(2)=0; end cube.vertices=[ 0 0 0; 1 0 0; 1 1 0; 0 1 0; 0 0 1; 1 0 1; 1 1 1; 0 1 1;] ; cube.faces=[ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8; ] ; cube.vertices = cube.vertices * 2 - 1; cylinder.vertices=[-1,0,-1;-1,0,0;-0.500000000000000,-0.856380903262898,-1;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,-1;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,-1;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,-1;-0.500000000000000,0.856380903262898,0;0,-1,-1;0,-1,0;0,1,-1;0,1,0;0.500000000000000,-0.856380903262898,-1;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,-1;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,-1;0.856380903262898,-0.500000000000000,0;1,0,-1;1,0,0;0.856380903262898,0.500000000000000,-1;0.856380903262898,0.500000000000000,0;-1,0,1;-0.500000000000000,-0.856380903262898,1;-0.856380903262898,-0.500000000000000,1;-0.856380903262898,0.500000000000000,1;-0.500000000000000,0.856380903262898,1;0,-1,1;0,1,1;0.5000000000000 00,-0.856380903262898,1;0.500000000000000,0.856380903262898,1;0.856380903262898,-0.500000000000000,1;1,0,1;0.856380903262898,0.500000000000000,1;]; cylinder.faces=[3,4,5;5,4,6;5,6,1;1,6,2;1,2,7;7,2,8;7,8,9;9,8,10;11,12,3;3,12,4;9,10,13;13,10,14;11,15,12;12,15,16;17,13,18;18,13,14;15,19,16;16,19,20;19,21,20;20,21,22;21,23,22;22,23,24;23,17,24;24,17,18;4,26,6;6,26,27;6,27,2;2,27,25;2,25,8;8,25,28;8,28,10;10,28,29;12,30,4;4,30,26;10,29,14;14,29,31;12,16,30;30,16,32;18,14,33;33,14,31;16,20,32;32,20,34;20,22,34;34,22,35;22,24,35;35,24,36;24,18,36;36,18,33;]; sphere.vertices=[0,0,-1;-0.500000000000000,-0.500000000000000,-0.686740068930804;-0.500000000000000,-0.686740068930804,-0.500000000000000;-0.686740068930804,-0.500000000000000,-0.500000000000000;-0.500000000000000,0,-0.856380903262898;-0.856380903262898,0,-0.500000000000000;-0.500000000000000,0.500000000000000,-0.686740068930804;-0.686740068930804,0.500000000000000,-0.500000000000000;-0.500000000000000,0.686740068930805,-0.500000000000000;0,-0.500000000000000,-0.856380903262898;0,-0.856380903262898,-0.500000000000000;0,0.500000000000000,-0.856380903262898;0,0.856380903262898,-0.500000000000000;0.500000000000000,-0.500000000000000,-0.686740068930804;0.500000000000000,-0.686740068930804,-0.500000000000000;0.500000000000000,0,-0.856380903262898;0.500000000000000,0.500000000000000,-0.686740068930804;0.500000000000000,0.686740068930805,-0.500000000000000;0.686740068930805,-0.500000000000000,- 0.500000000000000;0.856380903262898,0,-0.500000000000000;0.686740068930805,0.500000000000000,-0.500000000000000;-1,0,0;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,0;0,-1,0;0,1,0;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,0;1,0,0;0.856380903262898,0.500000000000000,0;-0.500000000000000,-0.686740068930804,0.500000000000000;-0.686740068930804,-0.500000000000000,0.500000000000000;-0.856380903262898,0,0.500000000000000;-0.686740068930804,0.500000000000000,0.500000000000000;-0.500000000000000,0.686740068930805,0.500000000000000;0,-0.856380903262898,0.500000000000000;0,0.856380903262898,0.500000000000000;0.500000000000000,-0.686740068930804,0.500000000000000;0.500000000000000,0.686740068930805,0.500000000000000;0.6 86740068930805,-0.500000000000000,0.500000000000000;0.856380903262898,0,0.500000000000000;0.686740068930805,0.500000000000000,0.500000000000000;-0.500000000000000,-0.500000000000000,0.686740068930805;-0.500000000000000,0,0.856380903262898;-0.500000000000000,0.500000000000000,0.686740068930805;0,-0.500000000000000,0.856380903262898;0,0,1;0,0.500000000000000,0.856380903262898;0.500000000000000,-0.500000000000000,0.686740068930805;0.500000000000000,0,0.856380903262898;0.500000000000000,0.500000000000000,0.686740068930805;]; sphere.faces=[2,3,4;2,4,5;5,4,6;5,6,7;7,6,8;7,8,9;2,10,3;3,10,11;1,10,2;1,2,5;1,5,7;1,7,12;7,9,12;12,9,13;10,14,11;11,14,15;10,1,16;10,16,14;16,1,12;16,12,17;12,13,17;17,13,18;14,19,15;14,16,19;19,16,20;16,17,20;20,17,21;17,18,21;3,23,4;4,23,24;4,24,6;6,24,22;6,22,8;8,22,25;8,25,9;9,25,26;11,27,3;3,27,23;13,9,28;28,9,26;15,29,11;11,29,27;18,13,30;30,13,28;15,19,29;29,19,31;19,20,31;31,20,32;20,21,32;32,21,33;21,18,33;33,18,30;23,34,24;24,34,35;24,35,22;22,35,36;25,22,36;25,36,37;25,37,26;26,37,38;23,27,39;23,39,34;26,38,28;28,38,40;27,29,41;27,41,39;30,28,42;42,28,40;29,31,41;41,31,43;31,32,43;43,32,44;32,33,45;32,45,44;33,30,45;45,30,42;34,46,35;35,46,36;36,46,47;36,47,37;37,47,48;37,48,38;39,49,34;34,49,46;46,49,47;47,49,50;47,50,48;48,50,51;40,38,51;51,38,48;41,52,39;39,52,49;49,52,50;50,52,53;53,54,50;50,54,51;42,40,54;54,40,51;41,43,52;43,44,52;52,44,53;44,45,53;53,45,54;45,42,54;]; if (p2(2)==1) %part ID 1=UnitCylinder res=p2(3); %resolution scalex=p2(4); %diameter of cylinder in x direction scaley=p2(5); %diameter of cylinder in y direction scalez=p2(6); %length of cylinder rotx=p2(7); %rotation about x axis roty=p2(8); %rotation about y axis rotz=p2(9); %rotation about z axis transx=p2(10); %translation in x direction transy=p2(11); %translation in y direction transz=p2(12); %translation in z direction V2=cylinder.vertices; V2=[V2(:,1)*scalex, V2(:,2)*scaley, V2(:,3)*scalez]; cylinder.vertices=V2; a=rotz/57.29; %degrees to radians V2=cylinder.vertices; V2=[cos(a)*V2(:,1)-sin(a)*V2(:,2), sin(a)*V(:,1)+cos(a)*V2(:,2), V2(:,3)]; cylinder.vertices=V2; a=roty/57.29; %degrees to radians V2=cylinder.vertices; V2=[cos(a)*V2(:,1)+sin(a)*V2(:,3), V2(:,2), -sin(a)*V2(:,1)+cos(a)*V2(:,3)]; cylinder.vertices=V2; a=rotx/57.29; %degrees to radians V2=cylinder.vertices; V2=[V(:,1), cos(a)*V2(:,2)-sin(a)*V2(:,3), sin(a)*V2(:,2)+cos(a)*V2(:,3)]; cylinder.vertices=V2; V2=cylinder.vertices; V2=[V2(:,1)+transx, V2(:,2)+transy, V2(:,3)+transz]; cylinder.vertices=V2; part2=cylinder; elseif (p2(2)==2) %part ID 2=UnitSphere res=p2(3); %resolution scalex=p2(4); %diameter of sphere in x direction scaley=p2(5); %diameter of sphere in y direction scalez=p2(6); %diameter of sphere in z direction rotx=p2(7); %rotation about x axis roty=p2(8); %rotation about y axis rotz=p2(9); %rotation about z axis transx=p2(10); %translation in x direction transy=p2(11); %translation in y direction transz=p2(12); %translation in z direction M2=sphere.vertices; M2=[M2(:,1)*scalex, M2(:,2)*scaley, M2(:,3)*scalez]; sphere.vertices=M2; a=rotz/57.29; %degrees to radians M2=sphere.vertices; M2=[cos(a)*M2(:,1)-sin(a)*M2(:,2), sin(a)*M2(:,1)+cos(a)*M2(:,2), M2(:,3)]; sphere.vertices=M2; a=roty/57.29; %degrees to radians M2=sphere.vertices; M2=[cos(a)*M2(:,1)+sin(a)*M2(:,3), M2(:,2), -sin(a)*M2(:,1)+cos(a)*M2(:,3)]; sphere.vertices=M2; a=rotx/57.29; %degrees to radians M2=sphere.vertices; M2=[M2(:,1), cos(a)*M2(:,2)-sin(a)*M2(:,3), sin(a)*M2(:,2)+cos(a)*M2(:,3)]; sphere.vertices=M2; M2=sphere.vertices; M2=[M2(:,1)+transx, M2(:,2)+transy, M2(:,3)+transz]; sphere.vertices=M2; part2=sphere; elseif (p2(2)==3) %part ID 3=UnitCube res=p2(3); %resolution scalex=p2(4); %length in x direction scaley=p2(5); %length in y direction scalez=p2(6); %length in z direction rotx=p2(7); %rotation about x axis roty=p2(8); %rotation about y axis rotz=p2(9); %rotation about z axis transx=p2(10); %translation in x direction transy=p2(11); %translation in y direction transz=p2(12); %translation in z direction F2=cube.vertices; F2=[F2(:,1)*scalex, F2(:,2)*scaley, F2(:,3)*scalez]; cube.vertices=F2; a=rotz/57.29; %degrees to radians F2=cube.vertices; F2=[cos(a)*F2(:,1)-sin(a)*F2(:,2), sin(a)*F2(:,1)+cos(a)*F2(:,2), F2(:,3)]; cube.vertices=F2; a=roty/57.29; %degrees to radians F2=cube.vertices; F2=[cos(a)*F2(:,1)+sin(a)*F2(:,3), F2(:,2), -sin(a)*F2(:,1)+cos(a)*F2(:,3)]; cube.vertices=F2; a=rotx/57.29; %degrees to radians F2=cube.vertices; F2=[F(:,1), cos(a)*F2(:,2)-sin(a)*F2(:,3),sin(a)*F2(:,2)+cos(a)*F2(:,3)]; cube.vertices=F2; F2=cube.vertices; F2=[F2(:,1)+transx, F2(:,2)+transy, F2(:,3)+transz]; cube.vertices=F2; part2=cube; else p2(2)=0; end cube.vertices=[ 0 0 0; 1 0 0; 1 1 0; 0 1 0; 0 0 1; 1 0 1; 1 1 1; 0 1 1;] ; cube.faces=[ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8; ] ; cube.vertices = cube.vertices * 2 - 1; cylinder.vertices=[-1,0,-1;-1,0,0;-0.500000000000000,-0.856380903262898,-1;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,-1;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,-1;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,-1;-0.500000000000000,0.856380903262898,0;0,-1,-1;0,-1,0;0,1,-1;0,1,0;0.500000000000000,-0.856380903262898,-1;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,-1;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,-1;0.856380903262898,-0.500000000000000,0;1,0,-1;1,0,0;0.856380903262898,0.500000000000000,-1;0.856380903262898,0.500000000000000,0;-1,0,1;-0.500000000000000,-0.856380903262898,1;-0.856380903262898,-0.500000000000000,1;-0.856380903262898,0.500000000000000,1;-0.500000000000000,0.856380903262898,1;0,-1,1;0,1,1;0.5000000000000 00,-0.856380903262898,1;0.500000000000000,0.856380903262898,1;0.856380903262898,-0.500000000000000,1;1,0,1;0.856380903262898,0.500000000000000,1;]; cylinder.faces=[3,4,5;5,4,6;5,6,1;1,6,2;1,2,7;7,2,8;7,8,9;9,8,10;11,12,3;3,12,4;9,10,13;13,10,14;11,15,12;12,15,16;17,13,18;18,13,14;15,19,16;16,19,20;19,21,20;20,21,22;21,23,22;22,23,24;23,17,24;24,17,18;4,26,6;6,26,27;6,27,2;2,27,25;2,25,8;8,25,28;8,28,10;10,28,29;12,30,4;4,30,26;10,29,14;14,29,31;12,16,30;30,16,32;18,14,33;33,14,31;16,20,32;32,20,34;20,22,34;34,22,35;22,24,35;35,24,36;24,18,36;36,18,33;]; sphere.vertices=[0,0,-1;-0.500000000000000,-0.500000000000000,-0.686740068930804;-0.500000000000000,-0.686740068930804,-0.500000000000000;-0.686740068930804,-0.500000000000000,-0.500000000000000;-0.500000000000000,0,-0.856380903262898;-0.856380903262898,0,-0.500000000000000;-0.500000000000000,0.500000000000000,-0.686740068930804;-0.686740068930804,0.500000000000000,-0.500000000000000;-0.500000000000000,0.686740068930805,-0.500000000000000;0,-0.500000000000000,-0.856380903262898;0,-0.856380903262898,-0.500000000000000;0,0.500000000000000,-0.856380903262898;0,0.856380903262898,-0.500000000000000;0.500000000000000,-0.500000000000000,-0.686740068930804;0.500000000000000,-0.686740068930804,-0.500000000000000;0.500000000000000,0,-0.856380903262898;0.500000000000000,0.500000000000000,-0.686740068930804;0.500000000000000,0.686740068930805,-0.500000000000000;0.686740068930805,-0.500000000000000,- 0.500000000000000;0.856380903262898,0,-0.500000000000000;0.686740068930805,0.500000000000000,-0.500000000000000;-1,0,0;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,0;0,-1,0;0,1,0;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,0;1,0,0;0.856380903262898,0.500000000000000,0;-0.500000000000000,-0.686740068930804,0.500000000000000;-0.686740068930804,-0.500000000000000,0.500000000000000;-0.856380903262898,0,0.500000000000000;-0.686740068930804,0.500000000000000,0.500000000000000;-0.500000000000000,0.686740068930805,0.500000000000000;0,-0.856380903262898,0.500000000000000;0,0.856380903262898,0.500000000000000;0.500000000000000,-0.686740068930804,0.500000000000000;0.500000000000000,0.686740068930805,0.500000000000000;0.6 86740068930805,-0.500000000000000,0.500000000000000;0.856380903262898,0,0.500000000000000;0.686740068930805,0.500000000000000,0.500000000000000;-0.500000000000000,-0.500000000000000,0.686740068930805;-0.500000000000000,0,0.856380903262898;-0.500000000000000,0.500000000000000,0.686740068930805;0,-0.500000000000000,0.856380903262898;0,0,1;0,0.500000000000000,0.856380903262898;0.500000000000000,-0.500000000000000,0.686740068930805;0.500000000000000,0,0.856380903262898;0.500000000000000,0.500000000000000,0.686740068930805;]; sphere.faces=[2,3,4;2,4,5;5,4,6;5,6,7;7,6,8;7,8,9;2,10,3;3,10,11;1,10,2;1,2,5;1,5,7;1,7,12;7,9,12;12,9,13;10,14,11;11,14,15;10,1,16;10,16,14;16,1,12;16,12,17;12,13,17;17,13,18;14,19,15;14,16,19;19,16,20;16,17,20;20,17,21;17,18,21;3,23,4;4,23,24;4,24,6;6,24,22;6,22,8;8,22,25;8,25,9;9,25,26;11,27,3;3,27,23;13,9,28;28,9,26;15,29,11;11,29,27;18,13,30;30,13,28;15,19,29;29,19,31;19,20,31;31,20,32;20,21,32;32,21,33;21,18,33;33,18,30;23,34,24;24,34,35;24,35,22;22,35,36;25,22,36;25,36,37;25,37,26;26,37,38;23,27,39;23,39,34;26,38,28;28,38,40;27,29,41;27,41,39;30,28,42;42,28,40;29,31,41;41,31,43;31,32,43;43,32,44;32,33,45;32,45,44;33,30,45;45,30,42;34,46,35;35,46,36;36,46,47;36,47,37;37,47,48;37,48,38;39,49,34;34,49,46;46,49,47;47,49,50;47,50,48;48,50,51;40,38,51;51,38,48;41,52,39;39,52,49;49,52,50;50,52,53;53,54,50;50,54,51;42,40,54;54,40,51;41,43,52;43,44,52;52,44,53;44,45,53;53,45,54;45,42,54;]; if (p3(2)==1) %part ID 1=UnitCylinder res=p3(3); %resolution scalex=p3(4); %diameter of cylinder in x direction scaley=p3(5); %diameter of cylinder in y direction scalez=p3(6); %length of cylinder rotx=p3(7); %rotation about x axis roty=p3(8); %rotation about y axis rotz=p3(9); %rotation about z axis transx=p3(10); %translation in x direction transy=p3(11); %translation in y direction transz=p3(12); %translation in z direction V3=cylinder.vertices; V3=[V3(:,1)*scalex, V3(:,2)*scaley, V3(:,3)*scalez]; cylinder.vertices=V3; a=rotz/57.29; %degrees to radians V3=cylinder.vertices; V3=[cos(a)*V3(:,1)-sin(a)*V3(:,2), sin(a)*V3(:,1)+cos(a)*V3(:,2),V3(:,3)]; cylinder.vertices=V3; a=roty/57.29; %degrees to radians V3=cylinder.vertices; V3=[cos(a)*V3(:,1)+sin(a)*V3(:,3),V3(:,2), -sin(a)*V3(:,1)+cos(a)*V3(:,3)]; cylinder.vertices=V3; a=rotx/57.29; %degrees to radians V3=cylinder.vertices; V3=[V3(:,1), cos(a)*V3(:,2)-sin(a)*V3(:,3), sin(a)*V3(:,2)+cos(a)*V3(:,3)]; cylinder.vertices=V3; V3=cylinder.vertices; V3=[V3(:,1)+transx, V3(:,2)+transy, V3(:,3)+transz]; cylinder.vertices=V3; part3=cylinder; elseif (p3(2)==2) %part ID 2=UnitSphere res=p3(3); %resolution scalex=p3(4); %diameter of sphere in x direction scaley=p3(5); %diameter of sphere in y direction scalez=p3(6); %diameter of sphere in z direction rotx=p3(7); %rotation about x axis roty=p3(8); %rotation about y axis rotz=p3(9); %rotation about z axis transx=p3(10); %translation in x direction transy=p3(11); %translation in y direction transz=p3(12); %translation in z direction M3=sphere.vertices; M3=[M3(:,1)*scalex, M3(:,2)*scaley, M3(:,3)*scalez]; sphere.vertices=M3; a=rotz/57.29; %degrees to radians M3=sphere.vertices; M3=[cos(a)*M3(:,1)-sin(a)*M3(:,2),sin(a)*M3(:,1)+cos(a)*M3(:,2),M3(:,3)]; sphere.vertices=M3; a=roty/57.29; %degrees to radians M3=sphere.vertices; M3=[cos(a)*M3(:,1)+sin(a)*M3(:,3),M3(:,2),-sin(a)*M3(:,1)+cos(a)*M3(:,3)]; sphere.vertices=M3; a=rotx/57.29; %degrees to radians M3=sphere.vertices; M3=[M3(:,1), cos(a)*M3(:,2)-sin(a)*M3(:,3),sin(a)*M3(:,2)+cos(a)*M3(:,3)]; sphere.vertices=M3; M3=sphere.vertices; M3=[M3(:,1)+transx, M3(:,2)+transy, M3(:,3)+transz]; sphere.vertices=M3; part3=sphere; elseif (p3(2)==3) %part ID 3=UnitCube res=p3(3); %resolution scalex=p3(4); %length in x direction scaley=p3(5); %length in y direction scalez=p3(6); %length in z direction rotx=p3(7); %rotation about x axis roty=p3(8); %rotation about y axis rotz=p3(9); %rotation about z axis transx=p3(10); %translation in x direction transy=p3(11); %translation in y direction transz=p3(12); %translation in z direction F3=cube.vertices; F3=[F3(:,1)*scalex, F3(:,2)*scaley, F3(:,3)*scalez]; cube.vertices=F3; a=rotz/57.29; %degrees to radians F3=cube.vertices; F3=[cos(a)*F3(:,1)-sin(a)*F3(:,2),sin(a)*F3(:,1)+cos(a)*F3(:,2),F3(:,3)]; cube.vertices=F3; a=roty/57.29; %degrees to radians F3=cube.vertices; F3=[cos(a)*F3(:,1)+sin(a)*F3(:,3),F3(:,2), -sin(a)*F3(:,1)+cos(a)*F3(:,3)]; cube.vertices=F3; a=rotx/57.29; %degrees to radians F3=cube.vertices; F3=[F3(:,1),cos(a)*F3(:,2)-sin(a)*F3(:,3),sin(a)*F3(:,2)+cos(a)*F3(:,3)]; cube.vertices=F3; F3=cube.vertices; F3=[F3(:,1)+transx, F3(:,2)+transy, F3(:,3)+transz]; cube.vertices=F3; part3=cube; else p3(2)=0; end cube.vertices=[ 0 0 0; 1 0 0; 1 1 0; 0 1 0;0 0 1; 1 0 1; 1 1 1; 0 1 1;] ; cube.faces=[ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8; ] ; cube.vertices = cube.vertices * 2 - 1; cylinder.vertices=[-1,0,-1;-1,0,0;-0.500000000000000,-0.856380903262898,-1;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,-1;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,-1;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,-1;-0.500000000000000,0.856380903262898,0;0,-1,-1;0,-1,0;0,1,-1;0,1,0;0.500000000000000,-0.856380903262898,-1;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,-1;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,-1;0.856380903262898,-0.500000000000000,0;1,0,-1;1,0,0;0.856380903262898,0.500000000000000,-1;0.856380903262898,0.500000000000000,0;-1,0,1;-0.500000000000000,-0.856380903262898,1;-0.856380903262898,-0.500000000000000,1;-0.856380903262898,0.500000000000000,1;-0.500000000000000,0.856380903262898,1;0,-1,1;0,1,1;0.5000000000000 00,-0.856380903262898,1;0.500000000000000,0.856380903262898,1;0.856380903262898,-0.500000000000000,1;1,0,1;0.856380903262898,0.500000000000000,1;]; cylinder.faces=[3,4,5;5,4,6;5,6,1;1,6,2;1,2,7;7,2,8;7,8,9;9,8,10;11,12,3;3,12,4;9,10,13;13,10,14;11,15,12;12,15,16;17,13,18;18,13,14;15,19,16;16,19,20;19,21,20;20,21,22;21,23,22;22,23,24;23,17,24;24,17,18;4,26,6;6,26,27;6,27,2;2,27,25;2,25,8;8,25,28;8,28,10;10,28,29;12,30,4;4,30,26;10,29,14;14,29,31;12,16,30;30,16,32;18,14,33;33,14,31;16,20,32;32,20,34;20,22,34;34,22,35;22,24,35;35,24,36;24,18,36;36,18,33;]; sphere.vertices=[0,0,-1;-0.500000000000000,-0.500000000000000,-0.686740068930804;-0.500000000000000,-0.686740068930804,-0.500000000000000;-0.686740068930804,-0.500000000000000,-0.500000000000000;-0.500000000000000,0,-0.856380903262898;-0.856380903262898,0,-0.500000000000000;-0.500000000000000,0.500000000000000,-0.686740068930804;-0.686740068930804,0.500000000000000,-0.500000000000000;-0.500000000000000,0.686740068930805,-0.500000000000000;0,-0.500000000000000,-0.856380903262898;0,-0.856380903262898,-0.500000000000000;0,0.500000000000000,-0.856380903262898;0,0.856380903262898,-0.500000000000000;0.500000000000000,-0.500000000000000,-0.686740068930804;0.500000000000000,-0.686740068930804,-0.500000000000000;0.500000000000000,0,-0.856380903262898;0.500000000000000,0.500000000000000,-0.686740068930804;0.500000000000000,0.686740068930805,-0.500000000000000;0.686740068930805,-0.500000000000000,- 0.500000000000000;0.856380903262898,0,-0.500000000000000;0.686740068930805,0.500000000000000,-0.500000000000000;-1,0,0;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,0;0,-1,0;0,1,0;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,0;1,0,0;0.856380903262898,0.500000000000000,0;-0.500000000000000,-0.686740068930804,0.500000000000000;-0.686740068930804,-0.500000000000000,0.500000000000000;-0.856380903262898,0,0.500000000000000;-0.686740068930804,0.500000000000000,0.500000000000000;-0.500000000000000,0.686740068930805,0.500000000000000;0,-0.856380903262898,0.500000000000000;0,0.856380903262898,0.500000000000000;0.500000000000000,-0.686740068930804,0.500000000000000;0.500000000000000,0.686740068930805,0.500000000000000;0.6 86740068930805,-0.500000000000000,0.500000000000000;0.856380903262898,0,0.500000000000000;0.686740068930805,0.500000000000000,0.500000000000000;-0.500000000000000,-0.500000000000000,0.686740068930805;-0.500000000000000,0,0.856380903262898;-0.500000000000000,0.500000000000000,0.686740068930805;0,-0.500000000000000,0.856380903262898;0,0,1;0,0.500000000000000,0.856380903262898;0.500000000000000,-0.500000000000000,0.686740068930805;0.500000000000000,0,0.856380903262898;0.500000000000000,0.500000000000000,0.686740068930805;]; sphere.faces=[2,3,4;2,4,5;5,4,6;5,6,7;7,6,8;7,8,9;2,10,3;3,10,11;1,10,2;1,2,5;1,5,7;1,7,12;7,9,12;12,9,13;10,14,11;11,14,15;10,1,16;10,16,14;16,1,12;16,12,17;12,13,17;17,13,18;14,19,15;14,16,19;19,16,20;16,17,20;20,17,21;17,18,21;3,23,4;4,23,24;4,24,6;6,24,22;6,22,8;8,22,25;8,25,9;9,25,26;11,27,3;3,27,23;13,9,28;28,9,26;15,29,11;11,29,27;18,13,30;30,13,28;15,19,29;29,19,31;19,20,31;31,20,32;20,21,32;32,21,33;21,18,33;33,18,30;23,34,24;24,34,35;24,35,22;22,35,36;25,22,36;25,36,37;25,37,26;26,37,38;23,27,39;23,39,34;26,38,28;28,38,40;27,29,41;27,41,39;30,28,42;42,28,40;29,31,41;41,31,43;31,32,43;43,32,44;32,33,45;32,45,44;33,30,45;45,30,42;34,46,35;35,46,36;36,46,47;36,47,37;37,47,48;37,48,38;39,49,34;34,49,46;46,49,47;47,49,50;47,50,48;48,50,51;40,38,51;51,38,48;41,52,39;39,52,49;49,52,50;50,52,53;53,54,50;50,54,51;42,40,54;54,40,51;41,43,52;43,44,52;52,44,53;44,45,53;53,45,54;45,42,54;]; if (p4(2)==1) %part ID 1=UnitCylinder res=p4(3); %resolution scalex=p4(4); %diameter of cylinder in x direction scaley=p4(5); %diameter of cylinder in y direction scalez=p4(6); %length of cylinder rotx=p4(7); %rotation about x axis roty=p4(8); %rotation about y axis rotz=p4(9); %rotation about z axis transx=p4(10); %translation in x direction transy=p4(11); %translation in y direction transz=p4(12); %translation in z direction V4=cylinder.vertices; V4=[V4(:,1)*scalex, V4(:,2)*scaley, V4(:,3)*scalez]; cylinder.vertices=V4; a=rotz/57.29; %degrees to radians V4=cylinder.vertices; V4=[cos(a)*V4(:,1)-sin(a)*V4(:,2),sin(a)*V4(:,1)+cos(a)*V4(:,2),V4(:,3)]; cylinder.vertices=V4; a=roty/57.29; %degrees to radians V4=cylinder.vertices; V4=[cos(a)*V4(:,1)+sin(a)*V4(:,3),V4(:,2), -sin(a)*V4(:,1)+cos(a)*V4(:,3)]; cylinder.vertices=V4; a=rotx/57.29; %degrees to radians V4=cylinder.vertices; V4=[V4(:,1), cos(a)*V4(:,2)-sin(a)*V4(:,3), sin(a)*V4(:,2)+cos(a)*V4(:,3)]; cylinder.vertices=V4; V4=cylinder.vertices; V4=[V4(:,1)+transx, V4(:,2)+transy, V4(:,3)+transz]; cylinder.vertices=V4; part4=cylinder; elseif (p4(2)==2) %part ID 2=UnitSphere res=p4(3); %resolution scalex=p4(4); %diameter of sphere in x direction scaley=p4(5); %diameter of sphere in y direction scalez=p4(6); %diameter of sphere in z direction rotx=p4(7); %rotation about x axis roty=p4(8); %rotation about y axis rotz=p4(9); %rotation about z axis transx=p4(10); %translation in x direction transy=p4(11); %translation in y direction transz=p4(12); %translation in z direction M4=sphere.vertices; M4=[M4(:,1)*scalex, M4(:,2)*scaley, M4(:,3)*scalez]; sphere.vertices=M4; a=rotz/57.29; %degrees to radians M4=sphere.vertices; M4=[cos(a)*M4(:,1)-sin(a)*M4(:,2),sin(a)*M4(:,1)+cos(a)*M4(:,2),M4(:,3)]; sphere.vertices=M4; a=roty/57.29; %degrees to radians M4=sphere.vertices; M4=[cos(a)*M4(:,1)+sin(a)*M4(:,3), M4(:,2),-sin(a)*M4(:,1)+cos(a)*M4(:,3)]; sphere.vertices=M4; a=rotx/57.29; %degrees to radians M4=sphere.vertices; M4=[M4(:,1), cos(a)*M4(:,2)-sin(a)*M4(:,3),sin(a)*M4(:,2)+cos(a)*M4(:,3)]; sphere.vertices=M4; M4=sphere.vertices; M4=[M4(:,1)+transx, M4(:,2)+transy, M4(:,3)+transz]; sphere.vertices=M4; part4=sphere; elseif (p4(2)==3) %part ID 3=UnitCube res=p4(3); %resolution scalex=p4(4); %length in x direction scaley=p4(5); %length in y direction scalez=p4(6); %length in z direction rotx=p4(7); %rotation about x axis roty=p4(8); %rotation about y axis rotz=p4(9); %rotation about z axis transx=p4(10); %translation in x direction transy=p4(11); %translation in y direction transz=p4(12); %translation in z direction F4=cube.vertices; F4=[F4(:,1)*scalex, F4(:,2)*scaley, F4(:,3)*scalez]; cube.vertices=F4; a=rotz/57.29; %degrees to radians F4=cube.vertices; F4=[cos(a)*F4(:,1)-sin(a)*F4(:,2), sin(a)*F4(:,1)+cos(a)*F4(:,2),F4(:,3)]; cube.vertices=F4; a=roty/57.29; %degrees to radians F4=cube.vertices; F4=[cos(a)*F4(:,1)+sin(a)*F4(:,3), F4(:,2), -sin(a)*F4(:,1)+cos(a)*F4(:,3)]; cube.vertices=F4; a=rotx/57.29; %degrees to radians F4=cube.vertices; F4=[F4(:,1), cos(a)*F4(:,2)-sin(a)*F4(:,3), sin(a)*F4(:,2)+cos(a)*F4(:,3)]; cube.vertices=F4; F4=cube.vertices; F4=[F4(:,1)+transx, F4(:,2)+transy, F4(:,3)+transz]; cube.vertices=F4; part4=cube; else p4(2)=0; end cube.vertices=[ 0 0 0; 1 0 0; 1 1 0; 0 1 0; 0 0 1; 1 0 1; 1 1 1; 0 1 1;] ; cube.faces=[ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8; ] ; cube.vertices = cube.vertices * 2 - 1; cylinder.vertices=[-1,0,-1;-1,0,0;-0.500000000000000,-0.856380903262898,-1;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,-1;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,-1;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,-1;-0.500000000000000,0.856380903262898,0;0,-1,-1;0,-1,0;0,1,-1;0,1,0;0.500000000000000,-0.856380903262898,-1;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,-1;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,-1;0.856380903262898,-0.500000000000000,0;1,0,-1;1,0,0;0.856380903262898,0.500000000000000,-1;0.856380903262898,0.500000000000000,0;-1,0,1;-0.500000000000000,-0.856380903262898,1;-0.856380903262898,-0.500000000000000,1;-0.856380903262898,0.500000000000000,1;-0.500000000000000,0.856380903262898,1;0,-1,1;0,1,1;0.5000000000000 00,-0.856380903262898,1;0.500000000000000,0.856380903262898,1;0.856380903262898,-0.500000000000000,1;1,0,1;0.856380903262898,0.500000000000000,1;]; cylinder.faces=[3,4,5;5,4,6;5,6,1;1,6,2;1,2,7;7,2,8;7,8,9;9,8,10;11,12,3;3,12,4;9,10,13;13,10,14;11,15,12;12,15,16;17,13,18;18,13,14;15,19,16;16,19,20;19,21,20;20,21,22;21,23,22;22,23,24;23,17,24;24,17,18;4,26,6;6,26,27;6,27,2;2,27,25;2,25,8;8,25,28;8,28,10;10,28,29;12,30,4;4,30,26;10,29,14;14,29,31;12,16,30;30,16,32;18,14,33;33,14,31;16,20,32;32,20,34;20,22,34;34,22,35;22,24,35;35,24,36;24,18,36;36,18,33;]; sphere.vertices=[0,0,-1;-0.500000000000000,-0.500000000000000,-0.686740068930804;-0.500000000000000,-0.686740068930804,-0.500000000000000;-0.686740068930804,-0.500000000000000,-0.500000000000000;-0.500000000000000,0,-0.856380903262898;-0.856380903262898,0,-0.500000000000000;-0.500000000000000,0.500000000000000,-0.686740068930804;-0.686740068930804,0.500000000000000,-0.500000000000000;-0.500000000000000,0.686740068930805,-0.500000000000000;0,-0.500000000000000,-0.856380903262898;0,-0.856380903262898,-0.500000000000000;0,0.500000000000000,-0.856380903262898;0,0.856380903262898,-0.500000000000000;0.500000000000000,-0.500000000000000,-0.686740068930804;0.500000000000000,-0.686740068930804,-0.500000000000000;0.500000000000000,0,-0.856380903262898;0.500000000000000,0.500000000000000,-0.686740068930804;0.500000000000000,0.686740068930805,-0.500000000000000;0.686740068930805,-0.500000000000000,- 0.500000000000000;0.856380903262898,0,-0.500000000000000;0.686740068930805,0.500000000000000,-0.500000000000000;-1,0,0;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,0;0,-1,0;0,1,0;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,0;1,0,0;0.856380903262898,0.500000000000000,0;-0.500000000000000,-0.686740068930804,0.500000000000000;-0.686740068930804,-0.500000000000000,0.500000000000000;-0.856380903262898,0,0.500000000000000;-0.686740068930804,0.500000000000000,0.500000000000000;-0.500000000000000,0.686740068930805,0.500000000000000;0,-0.856380903262898,0.500000000000000;0,0.856380903262898,0.500000000000000;0.500000000000000,-0.686740068930804,0.500000000000000;0.500000000000000,0.686740068930805,0.500000000000000;0.6 86740068930805,-0.500000000000000,0.500000000000000;0.856380903262898,0,0.500000000000000;0.686740068930805,0.500000000000000,0.500000000000000;-0.500000000000000,-0.500000000000000,0.686740068930805;-0.500000000000000,0,0.856380903262898;-0.500000000000000,0.500000000000000,0.686740068930805;0,-0.500000000000000,0.856380903262898;0,0,1;0,0.500000000000000,0.856380903262898;0.500000000000000,-0.500000000000000,0.686740068930805;0.500000000000000,0,0.856380903262898;0.500000000000000,0.500000000000000,0.686740068930805;]; sphere.faces=[2,3,4;2,4,5;5,4,6;5,6,7;7,6,8;7,8,9;2,10,3;3,10,11;1,10,2;1,2,5;1,5,7;1,7,12;7,9,12;12,9,13;10,14,11;11,14,15;10,1,16;10,16,14;16,1,12;16,12,17;12,13,17;17,13,18;14,19,15;14,16,19;19,16,20;16,17,20;20,17,21;17,18,21;3,23,4;4,23,24;4,24,6;6,24,22;6,22,8;8,22,25;8,25,9;9,25,26;11,27,3;3,27,23;13,9,28;28,9,26;15,29,11;11,29,27;18,13,30;30,13,28;15,19,29;29,19,31;19,20,31;31,20,32;20,21,32;32,21,33;21,18,33;33,18,30;23,34,24;24,34,35;24,35,22;22,35,36;25,22,36;25,36,37;25,37,26;26,37,38;23,27,39;23,39,34;26,38,28;28,38,40;27,29,41;27,41,39;30,28,42;42,28,40;29,31,41;41,31,43;31,32,43;43,32,44;32,33,45;32,45,44;33,30,45;45,30,42;34,46,35;35,46,36;36,46,47;36,47,37;37,47,48;37,48,38;39,49,34;34,49,46;46,49,47;47,49,50;47,50,48;48,50,51;40,38,51;51,38,48;41,52,39;39,52,49;49,52,50;50,52,53;53,54,50;50,54,51;42,40,54;54,40,51;41,43,52;43,44,52;52,44,53;44,45,53;53,45,54;45,42,54;]; if (p5(2)==1) %part ID 1=UnitCylinder res=p5(3); %resolution scalex=p5(4); %diameter of cylinder in x direction scaley=p5(5); %diameter of cylinder in y direction scalez=p5(6); %length of cylinder rotx=p5(7); %rotation about x axis roty=p5(8); %rotation about y axis rotz=p5(9); %rotation about z axis transx=p5(10); %translation in x direction transy=p5(11); %translation in y direction transz=p5(12); %translation in z direction V5=cylinder.vertices; V5=[V5(:,1)*scalex, V5(:,2)*scaley, V5(:,3)*scalez]; cylinder.vertices=V5; a=rotz/57.29; %degrees to radians V5=cylinder.vertices; V5=[cos(a)*V5(:,1)-sin(a)*V5(:,2), sin(a)*V5(:,1)+cos(a)*V5(:,2),V5(:,3)]; cylinder.vertices=V5; a=roty/57.29; %degrees to radians V5=cylinder.vertices; V5=[cos(a)*V5(:,1)+sin(a)*V5(:,3), V5(:,2), -sin(a)*V5(:,1)+cos(a)*V5(:,3)]; cylinder.vertices=V5; a=rotx/57.29; %degrees to radians V5=cylinder.vertices; V5=[V5(:,1), cos(a)*V5(:,2)-sin(a)*V5(:,3), sin(a)*V5(:,2)+cos(a)*V5(:,3)]; cylinder.vertices=V5; V5=cylinder.vertices; V5=[V5(:,1)+transx, V5(:,2)+transy, V5(:,3)+transz]; cylinder.vertices=V5; part5=cylinder; elseif (p5(2)==2) %part ID 2=UnitSphere res=p5(3); %resolution scalex=p5(4); %diameter of sphere in x direction scaley=p5(5); %diameter of sphere in y direction scalez=p5(6); %diameter of sphere in z direction rotx=p5(7); %rotation about x axis roty=p5(8); %rotation about y axis rotz=p5(9); %rotation about z axis transx=p5(10); %translation in x direction transy=p5(11); %translation in y direction transz=p5(12); %translation in z direction M5=sphere.vertices; M5=[M5(:,1)*scalex, M5(:,2)*scaley, M5(:,3)*scalez]; sphere.vertices=M5; a=rotz/57.29; %degrees to radians M5=sphere.vertices; M5=[cos(a)*M5(:,1)-sin(a)*M5(:,2), sin(a)*M5(:,1)+cos(a)*M5(:,2),M5(:,3)]; sphere.vertices=M5; a=roty/57.29; %degrees to radians M5=sphere.vertices; M5=[cos(a)*M5(:,1)+sin(a)*M5(:,3), M5(:,2), -sin(a)*M5(:,1)+cos(a)*M5(:,3)]; sphere.vertices=M5; a=rotx/57.29; %degrees to radians M5=sphere.vertices; M5=[M5(:,1), cos(a)*M5(:,2)-sin(a)*M5(:,3), sin(a)*M5(:,2)+cos(a)*M5(:,3)]; sphere.vertices=M5; M5=sphere.vertices; M5=[M5(:,1)+transx, M5(:,2)+transy, M5(:,3)+transz]; sphere.vertices=M5; part5=sphere; elseif (p5(2)==3) %part ID 3=UnitCube res=p5(3); %resolution scalex=p5(4); %length in x direction scaley=p5(5); %length in y direction scalez=p5(6); %length in z direction rotx=p5(7); %rotation about x axis roty=p5(8); %rotation about y axis rotz=p5(9); %rotation about z axis transx=p5(10); %translation in x direction transy=p5(11); %translation in y direction transz=p5(12); %translation in z direction F5=cube.vertices; F5=[F5(:,1)*scalex, F5(:,2)*scaley, F5(:,3)*scalez]; cube.vertices=F5; a=rotz/57.29; %degrees to radians F5=cube.vertices; F5=[cos(a)*F5(:,1)-sin(a)*F5(:,2), sin(a)*F5(:,1)+cos(a)*F5(:,2), F5(:,3)]; cube.vertices=F5; a=roty/57.29; %degrees to radians F5=cube.vertices; F5=[cos(a)*F5(:,1)+sin(a)*F5(:,3), F5(:,2), -sin(a)*F5(:,1)+cos(a)*F5(:,3)]; cube.vertices=F5; a=rotx/57.29; %degrees to radians F5=cube.vertices; F5=[F5(:,1), cos(a)*F5(:,2)-sin(a)*F5(:,3), sin(a)*F5(:,2)+cos(a)*F5(:,3)]; cube.vertices=F5; F5=cube.vertices; F5=[F5(:,1)+transx, F5(:,2)+transy, F5(:,3)+transz]; cube.vertices=F5; part5=cube; else p5(2)=0; end cube.vertices=[ 0 0 0; 1 0 0; 1 1 0; 0 1 0; 0 0 1; 1 0 1; 1 1 1; 0 1 1;] ; cube.faces=[ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8; ] ; cube.vertices = cube.vertices * 2 - 1; cylinder.vertices=[-1,0,-1;-1,0,0;-0.500000000000000,-0.856380903262898,-1;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,-1;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,-1;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,-1;-0.500000000000000,0.856380903262898,0;0,-1,-1;0,-1,0;0,1,-1;0,1,0;0.500000000000000,-0.856380903262898,-1;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,-1;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,-1;0.856380903262898,-0.500000000000000,0;1,0,-1;1,0,0;0.856380903262898,0.500000000000000,-1;0.856380903262898,0.500000000000000,0;-1,0,1;-0.500000000000000,-0.856380903262898,1;-0.856380903262898,-0.500000000000000,1;-0.856380903262898,0.500000000000000,1;-0.500000000000000,0.856380903262898,1;0,-1,1;0,1,1;0.5000000000000 00,-0.856380903262898,1;0.500000000000000,0.856380903262898,1;0.856380903262898,-0.500000000000000,1;1,0,1;0.856380903262898,0.500000000000000,1;]; cylinder.faces=[3,4,5;5,4,6;5,6,1;1,6,2;1,2,7;7,2,8;7,8,9;9,8,10;11,12,3;3,12,4;9,10,13;13,10,14;11,15,12;12,15,16;17,13,18;18,13,14;15,19,16;16,19,20;19,21,20;20,21,22;21,23,22;22,23,24;23,17,24;24,17,18;4,26,6;6,26,27;6,27,2;2,27,25;2,25,8;8,25,28;8,28,10;10,28,29;12,30,4;4,30,26;10,29,14;14,29,31;12,16,30;30,16,32;18,14,33;33,14,31;16,20,32;32,20,34;20,22,34;34,22,35;22,24,35;35,24,36;24,18,36;36,18,33;]; sphere.vertices=[0,0,-1;-0.500000000000000,-0.500000000000000,-0.686740068930804;-0.500000000000000,-0.686740068930804,-0.500000000000000;-0.686740068930804,-0.500000000000000,-0.500000000000000;-0.500000000000000,0,-0.856380903262898;-0.856380903262898,0,-0.500000000000000;-0.500000000000000,0.500000000000000,-0.686740068930804;-0.686740068930804,0.500000000000000,-0.500000000000000;-0.500000000000000,0.686740068930805,-0.500000000000000;0,-0.500000000000000,-0.856380903262898;0,-0.856380903262898,-0.500000000000000;0,0.500000000000000,-0.856380903262898;0,0.856380903262898,-0.500000000000000;0.500000000000000,-0.500000000000000,-0.686740068930804;0.500000000000000,-0.686740068930804,-0.500000000000000;0.500000000000000,0,-0.856380903262898;0.500000000000000,0.500000000000000,-0.686740068930804;0.500000000000000,0.686740068930805,-0.500000000000000;0.686740068930805,-0.500000000000000,- 0.500000000000000;0.856380903262898,0,-0.500000000000000;0.686740068930805,0.500000000000000,-0.500000000000000;-1,0,0;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,0;0,-1,0;0,1,0;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,0;1,0,0;0.856380903262898,0.500000000000000,0;-0.500000000000000,-0.686740068930804,0.500000000000000;-0.686740068930804,-0.500000000000000,0.500000000000000;-0.856380903262898,0,0.500000000000000;-0.686740068930804,0.500000000000000,0.500000000000000;-0.500000000000000,0.686740068930805,0.500000000000000;0,-0.856380903262898,0.500000000000000;0,0.856380903262898,0.500000000000000;0.500000000000000,-0.686740068930804,0.500000000000000;0.500000000000000,0.686740068930805,0.500000000000000;0.6 86740068930805,-0.500000000000000,0.500000000000000;0.856380903262898,0,0.500000000000000;0.686740068930805,0.500000000000000,0.500000000000000;-0.500000000000000,-0.500000000000000,0.686740068930805;-0.500000000000000,0,0.856380903262898;-0.500000000000000,0.500000000000000,0.686740068930805;0,-0.500000000000000,0.856380903262898;0,0,1;0,0.500000000000000,0.856380903262898;0.500000000000000,-0.500000000000000,0.686740068930805;0.500000000000000,0,0.856380903262898;0.500000000000000,0.500000000000000,0.686740068930805;]; sphere.faces=[2,3,4;2,4,5;5,4,6;5,6,7;7,6,8;7,8,9;2,10,3;3,10,11;1,10,2;1,2,5;1,5,7;1,7,12;7,9,12;12,9,13;10,14,11;11,14,15;10,1,16;10,16,14;16,1,12;16,12,17;12,13,17;17,13,18;14,19,15;14,16,19;19,16,20;16,17,20;20,17,21;17,18,21;3,23,4;4,23,24;4,24,6;6,24,22;6,22,8;8,22,25;8,25,9;9,25,26;11,27,3;3,27,23;13,9,28;28,9,26;15,29,11;11,29,27;18,13,30;30,13,28;15,19,29;29,19,31;19,20,31;31,20,32;20,21,32;32,21,33;21,18,33;33,18,30;23,34,24;24,34,35;24,35,22;22,35,36;25,22,36;25,36,37;25,37,26;26,37,38;23,27,39;23,39,34;26,38,28;28,38,40;27,29,41;27,41,39;30,28,42;42,28,40;29,31,41;41,31,43;31,32,43;43,32,44;32,33,45;32,45,44;33,30,45;45,30,42;34,46,35;35,46,36;36,46,47;36,47,37;37,47,48;37,48,38;39,49,34;34,49,46;46,49,47;47,49,50;47,50,48;48,50,51;40,38,51;51,38,48;41,52,39;39,52,49;49,52,50;50,52,53;53,54,50;50,54,51;42,40,54;54,40,51;41,43,52;43,44,52;52,44,53;44,45,53;53,45,54;45,42,54;]; if (p6(2)==1) %part ID 1=UnitCylinder res=p6(3); %resolution scalex=p6(4); %diameter of cylinder in x direction scaley=p6(5); %diameter of cylinder in y direction scalez=p6(6); %length of cylinder rotx=p6(7); %rotation about x axis roty=p6(8); %rotation about y axis rotz=p6(9); %rotation about z axis transx=p6(10); %translation in x direction transy=p6(11); %translation in y direction transz=p6(12); %translation in z direction V6=cylinder.vertices; V6=[V6(:,1)*scalex, V6(:,2)*scaley, V6(:,3)*scalez]; cylinder.vertices=V6; a=rotz/57.29; %degrees to radians V6=cylinder.vertices; V6=[cos(a)*V6(:,1)-sin(a)*V6(:,2), sin(a)*V6(:,1)+cos(a)*V6(:,2),V6(:,3)]; cylinder.vertices=V6; a=roty/57.29; %degrees to radians V6=cylinder.vertices; V6=[cos(a)*V6(:,1)+sin(a)*V6(:,3), V6(:,2), -sin(a)*V6(:,1)+cos(a)*V6(:,3)]; cylinder.vertices=V6; a=rotx/57.29; %degrees to radians V6=cylinder.vertices; V6=[V6(:,1), cos(a)*V6(:,2)-sin(a)*V6(:,3), sin(a)*V6(:,2)+cos(a)*V6(:,3)]; cylinder.vertices=V6; V6=cylinder.vertices; V6=[V6(:,1)+transx, V6(:,2)+transy, V6(:,3)+transz]; cylinder.vertices=V6; part6=cylinder; elseif (p6(2)==2) %part ID 2=UnitSphere res=p6(3); %resolution scalex=p6(4); %diameter of sphere in x direction scaley=p6(5); %diameter of sphere in y direction scalez=p6(6); %diameter of sphere in z direction rotx=p6(7); %rotation about x axis roty=p6(8); %rotation about y axis rotz=p6(9); %rotation about z axis transx=p6(10); %translation in x direction transy=p6(11); %translation in y direction transz=p6(12); %translation in z direction M6=sphere.vertices; M6=[M6(:,1)*scalex, M6(:,2)*scaley, M6(:,3)*scalez]; sphere.vertices=M6; a=rotz/57.29; %degrees to radians M6=sphere.vertices; M6=[cos(a)*M6(:,1)-sin(a)*M6(:,2), sin(a)*M6(:,1)+cos(a)*M6(:,2), M6(:,3)]; sphere.vertices=M6; a=roty/57.29; %degrees to radians M6=sphere.vertices; M6=[cos(a)*M6(:,1)+sin(a)*M6(:,3), M6(:,2), -sin(a)*M6(:,1)+cos(a)*M6(:,3)]; sphere.vertices=M6; a=rotx/57.29; %degrees to radians M6=sphere.vertices; M6=[M6(:,1), cos(a)*M6(:,2)-sin(a)*M6(:,3), sin(a)*M6(:,2)+cos(a)*M6(:,3)]; sphere.vertices=M6; M6=sphere.vertices; M6=[M6(:,1)+transx, M6(:,2)+transy, M6(:,3)+transz]; sphere.vertices=M6; part6=sphere; elseif (p6(2)==3) %part ID 3=UnitCube res=p6(3); %resolution scalex=p6(4); %length in x direction scaley=p6(5); %length in y direction scalez=p6(6); %length in z direction rotx=p6(7); %rotation about x axis roty=p6(8); %rotation about y axis rotz=p6(9); %rotation about z axis transx=p6(10); %translation in x direction transy=p6(11); %translation in y direction transz=p6(12); %translation in z direction F6=cube.vertices; F6=[F6(:,1)*scalex, F6(:,2)*scaley, F6(:,3)*scalez]; cube.vertices=F6; a=rotz/57.29; %degrees to radians F6=cube.vertices; F6=[cos(a)*F6(:,1)-sin(a)*F6(:,2), sin(a)*F6(:,1)+cos(a)*F6(:,2), F6(:,3)]; cube.vertices=F6; a=roty/57.29; %degrees to radians F6=cube.vertices; F6=[cos(a)*F6(:,1)+sin(a)*F6(:,3), F6(:,2), -sin(a)*F6(:,1)+cos(a)*F6(:,3)]; cube.vertices=F6; a=rotx/57.29; %degrees to radians F6=cube.vertices; F6=[F6(:,1), cos(a)*F6(:,2)-sin(a)*F6(:,3), sin(a)*F6(:,2)+cos(a)*F6(:,3)]; cube.vertices=F6; F6=cube.vertices; F6=[F6(:,1)+transx, F6(:,2)+transy, F6(:,3)+transz]; cube.vertices=F6; part6=cube; else p6(2)=0; end cube.vertices=[ 0 0 0; 1 0 0; 1 1 0; 0 1 0;0 0 1; 1 0 1; 1 1 1; 0 1 1;] ; cube.faces=[ 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8; 1 2 3 4; 5 6 7 8; ] ; cube.vertices = cube.vertices * 2 - 1; cylinder.vertices=[-1,0,-1;-1,0,0;-0.500000000000000,-0.856380903262898,-1;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,-1;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,-1;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,-1;-0.500000000000000,0.856380903262898,0;0,-1,-1;0,-1,0;0,1,-1;0,1,0;0.500000000000000,-0.856380903262898,-1;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,-1;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,-1;0.856380903262898,-0.500000000000000,0;1,0,-1;1,0,0;0.856380903262898,0.500000000000000,-1;0.856380903262898,0.500000000000000,0;-1,0,1;-0.500000000000000,-0.856380903262898,1;-0.856380903262898,-0.500000000000000,1;-0.856380903262898,0.500000000000000,1;-0.500000000000000,0.856380903262898,1;0,-1,1;0,1,1;0.5000000000000 00,-0.856380903262898,1;0.500000000000000,0.856380903262898,1;0.856380903262898,-0.500000000000000,1;1,0,1;0.856380903262898,0.500000000000000,1;]; cylinder.faces=[3,4,5;5,4,6;5,6,1;1,6,2;1,2,7;7,2,8;7,8,9;9,8,10;11,12,3;3,12,4;9,10,13;13,10,14;11,15,12;12,15,16;17,13,18;18,13,14;15,19,16;16,19,20;19,21,20;20,21,22;21,23,22;22,23,24;23,17,24;24,17,18;4,26,6;6,26,27;6,27,2;2,27,25;2,25,8;8,25,28;8,28,10;10,28,29;12,30,4;4,30,26;10,29,14;14,29,31;12,16,30;30,16,32;18,14,33;33,14,31;16,20,32;32,20,34;20,22,34;34,22,35;22,24,35;35,24,36;24,18,36;36,18,33;]; sphere.vertices=[0,0,-1;-0.500000000000000,-0.500000000000000,-0.686740068930804;-0.500000000000000,-0.686740068930804,-0.500000000000000;-0.686740068930804,-0.500000000000000,-0.500000000000000;-0.500000000000000,0,-0.856380903262898;-0.856380903262898,0,-0.500000000000000;-0.500000000000000,0.500000000000000,-0.686740068930804;-0.686740068930804,0.500000000000000,-0.500000000000000;-0.500000000000000,0.686740068930805,-0.500000000000000;0,-0.500000000000000,-0.856380903262898;0,-0.856380903262898,-0.500000000000000;0,0.500000000000000,-0.856380903262898;0,0.856380903262898,-0.500000000000000;0.500000000000000,-0.500000000000000,-0.686740068930804;0.500000000000000,-0.686740068930804,-0.500000000000000;0.500000000000000,0,-0.856380903262898;0.500000000000000,0.500000000000000,-0.686740068930804;0.500000000000000,0.686740068930805,-0.500000000000000;0.686740068930805,-0.500000000000000,- 0.500000000000000;0.856380903262898,0,-0.500000000000000;0.686740068930805,0.500000000000000,-0.500000000000000;-1,0,0;-0.500000000000000,-0.856380903262898,0;-0.856380903262898,-0.500000000000000,0;-0.856380903262898,0.500000000000000,0;-0.500000000000000,0.856380903262898,0;0,-1,0;0,1,0;0.500000000000000,-0.856380903262898,0;0.500000000000000,0.856380903262898,0;0.856380903262898,-0.500000000000000,0;1,0,0;0.856380903262898,0.500000000000000,0;-0.500000000000000,-0.686740068930804,0.500000000000000;-0.686740068930804,-0.500000000000000,0.500000000000000;-0.856380903262898,0,0.500000000000000;-0.686740068930804,0.500000000000000,0.500000000000000;-0.500000000000000,0.686740068930805,0.500000000000000;0,-0.856380903262898,0.500000000000000;0,0.856380903262898,0.500000000000000;0.500000000000000,-0.686740068930804,0.500000000000000;0.500000000000000,0.686740068930805,0.500000000000000;0.6 86740068930805,-0.500000000000000,0.500000000000000;0.856380903262898,0,0.500000000000000;0.686740068930805,0.500000000000000,0.500000000000000;-0.500000000000000,-0.500000000000000,0.686740068930805;-0.500000000000000,0,0.856380903262898;-0.500000000000000,0.500000000000000,0.686740068930805;0,-0.500000000000000,0.856380903262898;0,0,1;0,0.500000000000000,0.856380903262898;0.500000000000000,-0.500000000000000,0.686740068930805;0.500000000000000,0,0.856380903262898;0.500000000000000,0.500000000000000,0.686740068930805;]; sphere.faces=[2,3,4;2,4,5;5,4,6;5,6,7;7,6,8;7,8,9;2,10,3;3,10,11;1,10,2;1,2,5;1,5,7;1,7,12;7,9,12;12,9,13;10,14,11;11,14,15;10,1,16;10,16,14;16,1,12;16,12,17;12,13,17;17,13,18;14,19,15;14,16,19;19,16,20;16,17,20;20,17,21;17,18,21;3,23,4;4,23,24;4,24,6;6,24,22;6,22,8;8,22,25;8,25,9;9,25,26;11,27,3;3,27,23;13,9,28;28,9,26;15,29,11;11,29,27;18,13,30;30,13,28;15,19,29;29,19,31;19,20,31;31,20,32;20,21,32;32,21,33;21,18,33;33,18,30;23,34,24;24,34,35;24,35,22;22,35,36;25,22,36;25,36,37;25,37,26;26,37,38;23,27,39;23,39,34;26,38,28;28,38,40;27,29,41;27,41,39;30,28,42;42,28,40;29,31,41;41,31,43;31,32,43;43,32,44;32,33,45;32,45,44;33,30,45;45,30,42;34,46,35;35,46,36;36,46,47;36,47,37;37,47,48;37,48,38;39,49,34;34,49,46;46,49,47;47,49,50;47,50,48;48,50,51;40,38,51;51,38,48;41,52,39;39,52,49;49,52,50;50,52,53;53,54,50;50,54,51;42,40,54;54,40,51;41,43,52;43,44,52;52,44,53;44,45,53;53,45,54;45,42,54;]; if (p7(2)==1) %part ID 1=UnitCylinder res=p7(3); %resolution scalex=p7(4); %diameter of cylinder in x direction scaley=p7(5); %diameter of cylinder in y direction scalez=p7(6); %length of cylinder rotx=p7(7); %rotation about x axis roty=p7(8); %rotation about y axis rotz=p7(9); %rotation about z axis transx=p7(10); %translation in x direction transy=p7(11); %translation in y direction transz=p7(12); %translation in z direction V7=cylinder.vertices; V7=[V7(:,1)*scalex, V7(:,2)*scaley, V7(:,3)*scalez]; cylinder.vertices=V7; a=rotz/57.29; %degrees to radians V7=cylinder.vertices; V7=[cos(a)*V7(:,1)-sin(a)*V7(:,2), sin(a)*V7(:,1)+cos(a)*V7(:,2), V7(:,3)]; cylinder.vertices=V7; a=roty/57.29; %degrees to radians V7=cylinder.vertices; V7=[cos(a)*V7(:,1)+sin(a)*V7(:,3), V7(:,2), -sin(a)*V7(:,1)+cos(a)*V7(:,3)]; cylinder.vertices=V7; a=rotx/57.29; %degrees to radians V7=cylinder.vertices; V7=[V7(:,1),cos(a)*V7(:,2)-sin(a)*V7(:,3),sin(a)*V7(:,2)+cos(a)*V7(:,3)]; cylinder.vertices=V7; V7=cylinder.vertices; V7=[V7(:,1)+transx, V7(:,2)+transy, V7(:,3)+transz]; cylinder.vertices=V7; part7=cylinder; elseif (p7(2)==2) %part ID 2=UnitSphere res=p7(3); %resolution scalex=p7(4); %diameter of sphere in x direction scaley=p7(5); %diameter of sphere in y direction scalez=p7(6); %diameter of sphere in z direction rotx=p7(7); %rotation about x axis roty=p7(8); %rotation about y axis rotz=p7(9); %rotation about z axis transx=p7(10); %translation in x direction transy=p7(11); %translation in y direction transz=p7(12); %translation in z direction M7=sphere.vertices; M7=[M7(:,1)*scalex, M7(:,2)*scaley, M7(:,3)*scalez]; sphere.vertices=M7; a=rotz/57.29; %degrees to radians M7=sphere.vertices; M7=[cos(a)*M7(:,1)-sin(a)*M7(:,2),sin(a)*M7(:,1)+cos(a)*M7(:,2), M7(:,3)]; sphere.vertices=M7; a=roty/57.29; %degrees to radians M7=sphere.vertices; M7=[cos(a)*M7(:,1)+sin(a)*M7(:,3), M7(:,2), -sin(a)*M7(:,1)+cos(a)*M7(:,3)]; sphere.vertices=M7; a=rotx/57.29; %degrees to radians M7=sphere.vertices; M7=[M7(:,1), cos(a)*M7(:,2)-sin(a)*M7(:,3), sin(a)*M7(:,2)+cos(a)*M7(:,3)]; sphere.vertices=M7; M7=sphere.vertices; M7=[M7(:,1)+transx, M7(:,2)+transy, M7(:,3)+transz]; sphere.vertices=M7; part7=sphere; elseif (p7(2)==3) %part ID 3=UnitCube res=p7(3); %resolution scalex=p7(4); %length in x direction scaley=p7(5); %length in y direction scalez=p7(6); %length in z direction rotx=p7(7); %rotation about x axis roty=p7(8); %rotation about y axis rotz=p7(9); %rotation about z axis transx=p7(10); %translation in x direction transy=p7(11); %translation in y direction transz=p7(12); %translation in z direction F7=cube.vertices; F7=[F7(:,1)*scalex, F7(:,2)*scaley, F7(:,3)*scalez]; cube.vertices=F7; a=rotz/57.29; %degrees to radians F7=cube.vertices; F7=[cos(a)*F7(:,1)-sin(a)*F7(:,2), sin(a)*F7(:,1)+cos(a)*F7(:,2),F7(:,3)]; cube.vertices=F7; a=roty/57.29; %degrees to radians F7=cube.vertices; F7=[cos(a)*F7(:,1)+sin(a)*F7(:,3),F7(:,2), -sin(a)*F7(:,1)+cos(a)*F7(:,3)]; cube.vertices=F7; a=rotx/57.29; %degrees to radians F7=cube.vertices; F7=[F7(:,1), cos(a)*F7(:,2)-sin(a)*F7(:,3),sin(a)*F7(:,2)+cos(a)*F7(:,3)]; cube.vertices=F7; F7=cube.vertices; F7=[F7(:,1)+transx, F7(:,2)+transy, F7(:,3)+transz]; cube.vertices=F7; part7=cube; else p7(2)=0; end if (p7(2)>0) Out=[part1,part2,part3,part4,part5,part6,part7]; count=renderpatch(part1)+renderpatch(part2)+renderpatch(part3)+renderpatch(part4)+renderpatch(part5)+renderpatch(part6)+renderpatch(part7); elseif (p6(2)>0) Out=[part1,part2,part3,part4,part5,part6]; count=renderpatch(part1)+renderpatch(part2)+renderpatch(part3)+renderpatch(part4)+renderpatch(part5)+renderpatch(part6); elseif (p5(2)>0) Out=[part1,part2,part3,part4,part5]; count=renderpatch(part1)+renderpatch(part2)+renderpatch(part3)+renderpatch(part4)+renderpatch(part5); elseif (p4(2)>0) Out=[part1,part2,part3,part4]; count=renderpatch(part1)+renderpatch(part2)+renderpatch(part3)+renderpatch(part4); elseif (p3(2)>0) Out=[part1,part2,part3]; count=renderpatch(part1)+renderpatch(part2)+renderpatch(part3); elseif (p2(2)>0) Out=[part1,part2]; count=renderpatch(part1)+renderpatch(part2); else Out=part1; count=renderpatch(part1); end axis off; grid on daspect([1 1 1]) light('position',[10,-10,10]) rotate3d on
From: Walter Roberson on 18 May 2010 10:29 Meagan wrote: > other problem is that when the airplane is made, most of the shapes > intersect so a lot of the vertices for a particular component are not > necessarily on the outside of the plane. Ick. Finding the "outside" of complicated figures is a pain. An airplane is NOT a convex shape! For convex figures, every line that goes directly between any two points on the figure must be contained entirely within the figure: that is not the case on an airplane, where a line between the tips of the wings and the nose would go through space rather than within the figure. Algorithms for finding the shortest path on a convex shape are not the same as finding the shortest path on a concave shape.
From: Meagan on 18 May 2010 10:43 Walter Roberson <roberson(a)hushmail.com> wrote in message <ovxIn.11220$wV.3023(a)newsfe11.iad>... > Meagan wrote: > > > other problem is that when the airplane is made, most of the shapes > > intersect so a lot of the vertices for a particular component are not > > necessarily on the outside of the plane. > > Ick. Finding the "outside" of complicated figures is a pain. > > An airplane is NOT a convex shape! For convex figures, every line that > goes directly between any two points on the figure must be contained > entirely within the figure: that is not the case on an airplane, where a > line between the tips of the wings and the nose would go through space > rather than within the figure. Algorithms for finding the shortest path > on a convex shape are not the same as finding the shortest path on a > concave shape. Sorry I guess I was confused as to what you meant by convex and concave.
From: Bruno Luong on 18 May 2010 10:57
Walter Roberson <roberson(a)hushmail.com> wrote in message <ovxIn.11220$wV.3023(a)newsfe11.iad>... > > Algorithms for finding the shortest path > on a convex shape are not the same as finding the shortest path on a > concave shape. What is a concave shape? Is it a complement of a convex shape? Or do you mean a non-convex shape? Bruno |