The following is part of the source code of marching_tetrahedra.jl in the Meshing.jl module.
The tetEdgeCrnrs and tetTri fields of the VoxelIndices immutable don’t really make sense to me, so I would appreciate the help. Thank you.
"""
Voxel corner and edge indexing conventions
Z
|
5------5------6 Extra edges not drawn
/| /| -----------
8 | 6 | - face diagonals
/ 9 / 10 - 13: 1 to 3
8------7------7 | - 14: 1 to 8
| | | | - 15: 1 to 6
| 1------1--|---2 -- Y - 16: 5 to 7
12 / 11 / - 17: 2 to 7
| 4 | 2 - 18: 4 to 7
|/ |/ - body diagonal
4------3------3 - 19: 1 to 7
/
X
"""
immutable VoxelIndices{T <: Integer}
voxCrnrPos::NTuple{8,NTuple{3,T}}
voxEdgeCrnrs::NTuple{19, NTuple{2,T}}
voxEdgeDir::NTuple{19,T}
voxEdgeIx::NTuple{8,NTuple{8,T}}
subTets::NTuple{6,NTuple{4,T}}
tetEdgeCrnrs::NTuple{6,NTuple{2,T}}
tetTri::NTuple{16,NTuple{6,T}}
function VoxelIndices()
voxCrnrPos = ((0, 0, 0),
(0, 1, 0),
(1, 1, 0),
(1, 0, 0),
(0, 0, 1),
(0, 1, 1),
(1, 1, 1),
(1, 0, 1))
# the voxel IDs at either end of the tetrahedra edges, by edge ID
voxEdgeCrnrs = ((1, 2),
(2, 3),
(4, 3),
(1, 4),
(5, 6),
(6, 7),
(8, 7),
(5, 8),
(1, 5),
(2, 6),
(3, 7),
(4, 8),
(1, 3),
(1, 8),
(1, 6),
(5, 7),
(2, 7),
(4, 7),
(1, 7))
# direction codes:
# 0 => +x, 1 => +y, 2 => +z,
# 3 => +xy, 4 => +xz, 5 => +yz, 6 => +xyz
voxEdgeDir = (1,0,1,0,1,0,1,0,2,2,2,2,3,4,5,3,4,5,6)
# For a pair of corner IDs, the edge ID joining them
# 0 denotes a pair with no edge
voxEdgeIx = ((0,1,13,4,9,15,19,14),
(1,0,2,0,0,10,17,0),
(13,2,0,3,0,0,11,0),
(4,0,3,0,0,0,18,12),
(9,0,0,0,0,5,16,8),
(15,10,0,0,5,0,6,0),
(19,17,11,18,16,6,0,7),
(14,0,0,12,8,0,7,0))
# voxel corners that comprise each of the six tetrahedra
subTets = ((1,3,2,7),
(1,8,4,7),
(1,4,3,7),
(1,2,6,7),
(1,5,8,7),
(1,6,5,7))
# tetrahedron corners for each edge (indices 1-4)
tetEdgeCrnrs = ((1,2),
(2,3),
(1,3),
(1,4),
(2,4),
(3,4))
# triangle cases for a given tetrahedron edge code
tetTri = ((0,0,0,0,0,0),
(1,3,4,0,0,0),
(1,5,2,0,0,0),
(3,5,2,3,4,5),
(2,6,3,0,0,0),
(1,6,4,1,2,6),
(1,5,6,1,6,3),
(4,5,6,0,0,0),
(4,6,5,0,0,0),
(1,6,5,1,3,6),
(1,4,6,1,6,2),
(2,3,6,0,0,0),
(3,2,5,3,5,4),
(1,2,5,0,0,0),
(1,4,3,0,0,0),
(0,0,0,0,0,0))
new(voxCrnrPos,
voxEdgeCrnrs,
voxEdgeDir,
voxEdgeIx,
subTets,
tetEdgeCrnrs,
tetTri)
end
end