README
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Publication
A journal paper is being prepared based on this repository and that PR: https://github.com/deadsy/sdfx/pull/68
Its DOI will be available when ready.
Input & output
Input is triangle table. Output is tetrahedron table. The output is filled out manually by going over all the cases from 0 to 255.
Background
There is a source code that generates surface triangles. The isosurface is generated for the iso-value of 0. The source code uses a table for 2^8=256 possible inside/outside, i.e. negative/positive, combinations of 8 scalar values at 8 cube corners. The table returns an array. Every 3 consecutive array items would correspond to a triangle. The array items could be from 0 to 11, pointing to the 12 edges a cube has. Probably this table comes from a published paper in the field of mathematics or computer science:
https://github.com/deadsy/sdfx/blob/2d4e9502ec6fe898e8774020882cb8150f16a6a6/render/march3.go#L360
Objective
I'm trying to adapt the above marching cubes source code, and its tables, to generate tetrahedra throughout the volume of a 3D model. The code would extract tetrahedra elements with all the non-positive, i.e. <=0, values. Non-positive means the 3D space on and inside the isosurface of the 0 value.
Question
For some reason, I cannot find any publication for extracting a tetrahedral mesh on and inside the isosurface from a three-dimensional discrete scalar field. Maybe I'm not looking at the right places. Am I missing something? Or do I have to come up with the tables myself? It looks like a daunting task to me. Let's do it...
Reference
https://github.com/deadsy/sdfx/pull/68#issuecomment-1447714965
Node numbering
The node numbering follows the convention of CalculiX solver documentation. Like this:
Example
Case 0
Case 0 is trivial. No cube corner has zero/negative value. No tetrahedron is generated.
Case 1
Case 1 result is below. A cube corner has zero/negative value.
Directories