Speaker: Hamish Carr (University of British Columbia, Canada)
Geometric algorithms for analyzing and interpreting volumetric data draw from established methods in computational geometry. Geometrically, these algorithms often assume simple geometric primitives, such as tetrahedra. In practice, however, data commonly comes sampled on a cubic grid. Several responses to this are possible, such as modifying the experimental procedure, modifying the data, or modifying algorithm.
I shall discuss various approaches for dealing with this problem: where relevant, I shall use the problem of computing contour trees as a sample algorithm. These approaches include non-cubic sampling, correct analysis of the trilinear interpolant, working directly with marching cubes, and subdividing cubes into tetrahedra.
In particular, I will discuss the side-effects of simplicial subdivision on the final isosurfaces, and how to track the connectivity of the standard marching cubes cases.