A watertight mesh is one which does not have holes, and for which each face has a designated inside and outside. Such a mesh can be "tetrahedralized", has a defined volume, and can be an operand in a polyhedral boolean operation.

I'm looking for a method to represent such watertight meshes that reduces the amount of invalid states or singularities. As an example of what I mean, consider a simple mesh of vertex positions and triplets of indices that represent triangles. This is a poor way to represent a watertight mesh because the set of representable meshes largely does not intersect the set of watertight meshes. As a somewhat opposite example, consider a convex hull described by a set of points. This representation has the opposite problem: while every representable mesh is watertight (for now overlooking singularities like a hull defined exclusively by points lying within the same plane), watertight meshes with concavity are not representable.

One possible solution would be to store a set of points, then a set of indices into these points that describe a convex hull that completely encloses the watertight mesh. In addition to these, store zero or more sets of indices that describe convex hulls to be subtracted from the first convex hull to add concavity. This would, with a few singularities, restrict representable meshes to the set of watertight meshes. Requiring each set of indices to contain at least 4 vertices would further reduce the number of singularities in this system.

Are there other ways to represent watertight meshes and operate on them? Possibly a more commonly used, better-researched, or more intuitive way? Common useful operations would include boolean operations or tetrahedralization/triangulation of the resulting mesh.

posted over 2 years ago

CC BY-SA 4.0

2y ago

Josh Hyatt‭

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