An exact general remeshing scheme applied to physically conservative voxelization

Understand

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes.

• In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation.
• We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems.
• We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh.