The Folding
of a Cube Net
How to animate the folding of geometric objects.

How to fold of a cube?
A cube consists of 6 squares folded against its neighbor square by 90°.
So we start by declaring a 'Square' object.
(First declare the according textures as you like it!)

// -------------------- dimensions #declare D = 0.00001; #declare S = 1; #declare Rl = 0.02;// "edge" radius #declare Rp = 0.04;//"point" radius // ------------------------- square // Quadrat, quadrato, carré #declare Square = union{ // the corners union{ sphere{ <0,0,0>, Rp } sphere{ <S,0,0>, Rp } sphere{ <S,0,S>, Rp } sphere{ <0,0,S>, Rp } texture{ Corner_Texture } } // the edges union{ cylinder{ <0,0,0>,<S,0,0>, Rl } cylinder{ <S,0,0>,<S,0,S>, Rl } cylinder{ <0,0,S>,<S,0,S>, Rl } cylinder{ <0,0,0>,<0,0,S>, Rl } texture{ Edge_Texture } } // the face box{ <0,-D,0>,<1,D,1> texture{ Face_Texture }} } // end of union ------------------

A square for folding of a Cube

A net of a cube

Building a chain of squares:
For folding a cube net (like here above right)
we have to make a chain of the squares A,B,C and D by nested unions.
We need to remember that rotation by 'rotate' always turns around the axes!
So we first have to apply the rotation and then the translation as shown in the image here right with the first two squares A and B.
Note: 'rotation around an axis' and 'translation' commonly are not commutative or not interchangeable, that means: We cannot change the sequence arbitrary!



Here how to animate the folding:
To achieve a smooth starting and ending movement we use the following macro:

#macro Cos_010( X ) //----- (0.5-0.5*cos(2*pi*X)) #end //-------------------- #declare Fold_Angle = -90*Cos_010(clock); //---------------------------------

The assembling of the cube components:

union{ // A + B + C object{ Square } // C ------ union{ // A + B object{ Square } // B ------ object{ Square // A ------ rotate<Fold_Angle,0,0> translate<0,0,S> } //-------------- rotate<Fold_Angle,0,0> translate<0,0,S> } // end A + B rotate<Fold_Angle,0,0> translate<0,0,S> } // end A + B + C object{ Square } // D ------ object{ Square // E ------ translate<-S,0,0> rotate<0,0,Fold_Angle> } //------------------ object{ Square // F ------ rotate<0,0,-Fold_Angle> translate<S,0,0> } //------------------

Folding a cube: rotate, move, add next!

The macro 'Cos_010(...)'

Folding a cube
Scene descriptions for POV-Ray:
"Folding_a_Cube_2.ini" and
"Folding_a_Cube_2.pov"