Cubes.gcf

Six cubes, rotating around one central cube.

Nico Bakker
Hoorn, The Nederlands
ncm.bakker@quicknet.nl

Definition of the six planes of a cube.

a_1=vector(u,v,0),a_2=vector(u,v,1),a_3=vector(v,0,u),a_4=vector(v,1,u),a_5=vector(0,u,v),a_6=vector(1,u,v)

Definition of the rotation around the x-, y- and z-axes, as function of rotationangle h.

function(R_x,h)=matrix(3,3,1,0,0,0,-sin(2*pi*h),cos(2*pi*h),0,cos(2*pi*h),sin(2*pi*h)),function(R_y,h)=matrix(3,3,-sin(2*pi*h),0,cos(2*pi*h),0,1,0,cos(2*pi*h),0,sin(2*pi*h)),function(R_z,h)=matrix(3,3,-sin(2*pi*h),cos(2*pi*h),0,cos(2*pi*h),sin(2*pi*h),0,0,0,1)

m is the first or second half of the rotation.

Two yellow cubes.

vector(x,y,z)=function(R_x,n-(0.25*m)+0.25)*a_k+vector(0,m,0),k=set(1,2,3,4)

vector(x,y,z)=function(R_x,n-(0.25*m)+0.75)*a_k+vector(0,1-m,1),k=set(1,2,3,4)

Two blue cubes.

vector(x,y,z)=function(R_y,-n-(0.75*m)+0.75)*a_k+vector(0,0,m),k=set(1,2,5,6)

vector(x,y,z)=function(R_y,-n-(0.75*m)+0.25)*a_k+vector(1,0,1-m),k=set(1,2,5,6)

Two red cubes.

vector(x,y,z)=function(R_z,n-(0.25*m)+0.25)*a_k+vector(m,0,0),k=set(3,4,5,6)

vector(x,y,z)=function(R_z,n-(0.25*m)+0.75)*a_k+vector(1-m,1,0),k=set(3,4,5,6)

The central cube.

B=matrix(3,3,0.998,0,0,0,0.998,0,0,0,0.998)

vector(x,y,z)=B*a_k+vector(0.001,0.001,0.001),k=set(1,2,3,4,5,6)

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