Isosurfaces on Optimal Regular Samples

Volumetric samples on Cartesian lattices are less efficient than samples on body-centred cubic (BCC) lattices. We show how to construct isosurfaces on BCC lattices using several different algorithms. Since the mesh that arises from BCC lattices involves a large number of cells, we show two alternate methods of reducing the number of cells by clumping tetrahedra into either octahedra or hexahedra. We also propose a theoretical model for estimating triangle counts for various algorithms, and present experimental results to show that isosurfaces generated using one of our algorithms can be competitive with isosurfaces generated using Marching Cubes on similar Cartesian grids.