// cube_transforms.inc

// View transform generators for cube-based symmetries.
// The cube is of side two centered at the origin.
// Meant to be #include'd in the top of TPMS datafiles.
// See cube_views.cmd for commands using these.

// For labelling types of edges.
define edge attribute edgetype integer
parameter gridedge    = 0  // general edge, usually not shown in images
parameter c2edge      = 1  // C2 axis
parameter cubefaceedge  = 2  // on outer surface of cube
parameter diagfaceedge = 3   // on x=y face of tetrahedron
parameter slantfaceedge = 4  // on slanted, lower face of tetrahedron
parameter vertfaceedge = 5  // on x=0 (or y=0) face of tetrahedron
parameter cubeedge    = 6  // outline edge for cube
parameter cubeletedge = 7  // outline edge for cubelet, but not cubeedge
parameter tetraedge   = 8  // other tetrahedron outline
parameter outlineedge = 9  // other outline edge
parameter mirroredge  = 10  // valence 1 on mirror plane

// Types of fundamental regions, one to be assigned to cube_symmetry_type:

parameter quadri_full            = 1001
parameter quadri_up_half         = 1002
parameter quadri_down_half       = 1003

parameter trirect_full           = 1004

parameter disphenoid_full        = 1005
parameter disphenoid_short       = 1006  // with short C2 axis
parameter disphenoid_long        = 1007  // with C2 from (1/2,-1/2,1/2) to (1/2,1/2,3/2)
parameter disphenoid_short_long  = 1008  // as in dcell.fe
parameter disphenoid_two_long    = 1009
parameter disphenoid_three       = 1010

parameter equilateral_prism      = 1011
parameter rectangular_parallelpiped = 1012
parameter isoscoles_prism        = 1013
parameter prism_30_60_90         = 1014

parameter cubelet_sym            = 1015
parameter cube_sym               = 1016

view_transform_generators 22
0,1,0,0  // a: x = y mirror
1,0,0,0  
0,0,1,0  
0,0,0,1  

swap_colors
-1,0,0,1  // b: C2 axis of first orthant top front 
0,0,-1,1  // quadrirectangular tetrahedron, (1/2,0,1) to (1/2,1/2,1/2)
0,-1,0,1  
0,0,0,1  

-1 0 0 0   // c: x = 0 mirror
0 1 0 0 
0 0 1 0 
0 0  0 1

1 0 0 0   // d: y = 0 mirror
0 -1 0 0 
0 0 1 0
0 0 0 1

1 0 0 0  // e: z = 0 mirror
0 1 0 0
0 0 -1 0
0 0 0 1

-1 0 0 2 // f:  x = 1 mirror
 0 1 0 0
 0 0 1 0
 0 0 0 1

-1 0 0 -2 // g: x = -1 mirror
 0 1 0 0
 0 0 1 0
 0 0 0 1

 1 0 0 0 // h: y = 1 mirror
 0 -1 0 2 
 0 0 1 0
 0 0 0 1

 1 0 0 0 // i: y = -1 mirror
 0 -1 0 -2 
 0 0 1 0
 0 0 0 1

 1,0,0,0  // j: z = 1 mirror
 0,1,0,0  
 0,0,-1,2  
 0,0,0,1  

 1,0,0,0  // k: z = -1 mirror
 0,1,0,0  
 0,0,-1,-2  
 0,0,0,1  

0,0,1,0  // l: x = z mirror
0,1,0,0  
1,0,0,0  
0,0,0,1  

swap_colors
1 0 0 0   // m: short C2 axis for tetragonal disphenoid
0 -1 0 0
0 0 -1 2
0 0 0 1

1 0 0 0   // n: X axis as C2 axis
0 -1 0 0
0  0 -1 0
0  0  0 1

-1 0 0 0   // o: Y axis as C2 axis
0  1 0 0
0  0 -1 0
0  0  0 1

-1 0 0 0   // p: Z axis as C2 axis
0 -1 0 0
0  0 1 0
0  0  0 1

swap_colors
-1 0 0 0   // q: vertical edge on +y face of cube as C2 axis
 0 -1 0 2
 0 0 1 0
 0 0 0 1

swap_colors // r: horizontal edge on +z face of cube as C2 axis
-1 0 0 0
 0 1 0 0
 0 0 -1 2
 0 0 0 1

// s: horizontal top front edge of cube as C2 axis
-1 0 0 2
 0 1 0 2
 0 0 -1 0
 0 0 0 1

// t: translation by 2 in x
swap_colors
1 0 0 2
0 1 0 0
0 0 1 0
0 0 0 1

// u: translation by 2 in y
swap_colors
1 0 0 0
0 1 0 2
0 0 1 0
0 0 0 1

// v: translation by 2 in z
swap_colors
1 0 0 0 
0 1 0 0
0 0 1 2
0 0 0 1