~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Illuminated Sphere by J. Snuszka ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I=matrix(3,3,c*X^2+M,c*X*Y-(N*Z),c*X*Z+N*Y,c*X*Y+N*Z,c*Y^2+M,c*Y*Z-(N*X),c*X*Z-(N*Y),c*Y*Z+N*X,c*Z^2+M)

c=1-cos([2*pi*d]),X=cos([2*pi*g])*sin([2*pi*h]),Y=sin([2*pi*g])*sin([2*pi*h]),Z=cos([2*pi*h]),M=cos([2*pi*d]),N=sin([2*pi*d])

R=slider([0,0.1,100])

S_1=set(1/13),S_2=set(3/12,5/12,7/12,9/12,11/12,13/12),S_3=set(1/4),S_4=set(1/19)

S_5=set(2/6,3/6,4/6,5/6,6/6,7/6),S_6=set(1/7.8,1/2-1/7.8),S_7=set(1/44),S_8=set(1/19,1/2-1/19)

S_9=set(0,1/2),S_10=set(1/60),S_11=set(0),S_12=set(0)

vector(x,y,z)=I*vector(u*cos([2*pi*v])*sin([2*pi*b]),u*sin([2*pi*v])*sin([2*pi*b]),u*cos([2*pi*b])),in(b,S_1),in(g,S_2),in(h,S_3),in(d,S_3),'color'=n

vector(x,y,z)=I*vector(cos([2*pi*v])*sin([2*pi*u*b]),sin([2*pi*v])*sin([2*pi*u*b]),cos([2*pi*u*b])),in(b,S_1),in(g,S_2),in(h,S_3),in(d,S_3)

vector(x,y,z)=I*vector(u*cos([2*pi*v])*sin([2*pi*b]),u*sin([2*pi*v])*sin([2*pi*b]),u*cos([2*pi*b])),in(b,S_4),in(g,S_5),in(h,S_3),in(d,S_6),'color'=n

vector(x,y,z)=I*vector(cos([2*pi*v])*sin([2*pi*b*u]),sin([2*pi*v])*sin([2*pi*b*u]),cos([2*pi*b*u])),in(b,S_4),in(g,S_5),in(h,S_3),in(d,S_6)

vector(x,y,z)=I*vector(u*cos([2*pi*v])*sin([2*pi*b]),u*sin([2*pi*v])*sin([2*pi*b]),u*cos([2*pi*b])),in(b,S_7),in(g,S_2),in(h,S_3),in(d,S_8),'color'=n

vector(x,y,z)=I*vector(cos([2*pi*v])*sin([2*pi*u*b]),sin([2*pi*v])*sin([2*pi*u*b]),cos([2*pi*u*b])),in(b,S_7),in(g,S_2),in(h,S_3),in(d,S_8)

vector(x,y,z)=I*vector(u*cos([2*pi*v])*sin([2*pi*b]),u*sin([2*pi*v])*sin([2*pi*b]),u*cos([2*pi*b])),in(b,S_10),in(g,S_3),in(h,S_3),in(d,S_9),'color'=n

vector(x,y,z)=I*vector(cos([2*pi*v])*sin([2*pi*u*b]),sin([2*pi*v])*sin([2*pi*u*b]),cos([2*pi*u*b])),in(b,S_10),in(g,S_3),in(h,S_3),in(d,S_9)

Graph of the formula

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