Module splashsurf_lib::marching_cubes::marching_cubes_lut

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Classic marching cubes cases. There are 256 possible combinations of the above/below iso-surface states for the 8 vertices of a cube. The following lookup table maps each combination to the corresponding triangulation.

The index for a case is obtained with a bitfield of size 8, where a bit value of 1 indicates that the corresponding vertex of the cube is above the iso-surface threshold. Reversing the order of the bit pattern and interpreting it as an integer yields the case index.

For each case, the triangulation is represented by a 16 element array containing successive index triplets for each required triangle. The indices refer to the corresponding edges that are intersected by the triangle. Each case has at most three triangles and unused entries of the 16 element arrays are filled with -1 entries for padding.

Example:

  • Vertex 0 and 2 are above the iso-surface threshold.
  • The corresponding bit pattern is 10100000, the corresponding index is 5
  • The case with index 5 reads [ 0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]
  • The triangulation is given by the two triangles [0, 8, 3] and [1, 2, 10], with vertices on the edges identified by the given indices

Note that the raw table apparently uses a left-handed coordinate system and accordingly a clockwise winding order of the triangles. To avoid producing meshes with normals pointing into the reconstructed surface, the resulting triangles have to be flipped. This is already taken into account by the marching_cubes_triangulation_iter function.

Cube description:

        7 ________ 6           _____6__
        /|       /|         7/|       /|
      /  |     /  |        /  |     /5 |
  4 /_______ /    |      /__4____ /    10
   |     |  |5    |     |    11  |     |
   |    3|__|_____|2    |     |__|__2__|
   |    /   |    /      8   3/   9    /
   |  /     |  /        |  /     |  /1
   |/_______|/          |/___0___|/
  0          1
         Vertices              Edges

Functions