GraphingCalculator 4;
Window 65 46 720 1352;
PaneDivider 398;
DrawGraph 0;
FontSizes 16;
BackgroundType 0;
BackgroundColor 10 0 20;
StackPanes 1;
Slider 0 360;
SliderSteps 360;
SliderControlValue 117;
T 0 6.283185307179586;
U 0 6.283185307179586;
V 0 6.283185307179586;
4D.Show4DxyPlane 0;
4D.Show4Daxes 0;
4D.Depth 1.7330909743;
4D.View -0.01359715939864796 -0.4408116833802737 0.1402435248250403 0.8864716187195633 -0.9792943801179015 0.1371794980390333 0.145796435200169 0.03012809110602113 -0.03519719115913655 0.4987580993773496 -0.7824131032805782 0.3712563155873636 0.1988939216381872 0.7335579073404333 0.5889863233181428 0.2746436153719037;
Text "Clifford Torus and its Projection
by Guido 'wugi' Wuyts, 2016
http://home.scarlet.be/wugi/qbComplex.html ";
Color 4;
Expr h=n*(pi/180);
Text "The Clifford torus, rotating along x,v plane :";
Expr vector(x,y,u,v)=vector(cos(u)*cos([h])-(sin(v)*sin([h])),sin(u),cos(v),cos(u)*sin([h])+sin(v)*cos([h]));
Color 6;
Expr vector(x,y,u,v)=vector(cos(t)*cos([h])-(sin([a*(pi/9)])*sin([h])),sin(t),cos([a*(pi/9)]),cos(t)*sin([h])+sin([a*(pi/9)])*cos([h])),in(a,set(0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,8,17));
Color 5;
Expr vector(x,y,u,v)=vector(cos([a*(pi/9)])*cos([h])-(sin(t)*sin([h])),sin([a*(pi/9)]),cos(t),cos([a*(pi/9)])*sin([h])+sin(t)*cos([h])),in(a,set(0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,8,17));
Text "The 3D projection, from v axis unit toward x,y,u space, rotating along with its Cliffor torus :";
Color 3;
Expr d=2^0.5,p=19,q=20;
Color 7;
Expr vector(x,y,u,v)=vector(cos(u)*cos([h])-(sin(v)*sin([h])),sin(u),cos(v),0)*(d/(d-[cos(u)*sin([h])+sin(v)*cos([h])]));
Color 4;
Expr vector(x,y,u,v)=vector(cos(t)*cos([h])-(sin([a*(pi/9)])*sin([h])),sin(t),cos([a*(pi/9)]),0)*(d/(d-[cos(t)*sin([h])+sin([a*(pi/9)])*cos([h])])),in(a,set(0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,8,17));
Color 3;
Expr vector(x,y,u,v)=vector(cos([a*(pi/9)])*cos([h])-(sin(t)*sin([h])),sin([a*(pi/9)]),cos(t),0)*(d/(d-[cos([a*(pi/9)])*sin([h])+sin(t)*cos([h])])),in(a,set(0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,8,17));
Color 7;
Expr vector(0,0,0,0),vector(0,0,0,d);
Expr vector(1,0,0,0),vector(1,1,0,0),vector(0,1,0,0),vector(0,1,1,0),vector(0,0,1,0),vector(1,0,1,0),vector(1,0,0,0);
Expr vector(0,0,0,0),vector(1,0,0,0);
Expr vector(0,0,0,0),vector(0,1,0,0);
Expr vector(0,0,0,0),vector(0,0,1,0);