Edge Flows: Stratified Morse Theory for Simple, Correct Isosurface Extraction
نویسندگان
چکیده
We present a method to characterize the topology of the level sets of trilinearly interpolated scalar fields. Our characterization is based on Morse theory, and in particular a variant called Stratified Morse theory capable of treating the piecewise-smooth aspect of trilinear interpolation. Algorithms such as Marching Cubes generate approximations to these level sets to a varying degree of fidelity. It is now folklore that the standard Marching Cubes algorithm has inconsistencies, and while corrected versions are well-established, it is still the case that versions which strive for homeomorphism have complicated case tables. Our characterization explains exactly what is the source of topological problems in Marching Cubes, suggests simpler algorithms that generate isosurfaces homeomorphic to the level sets, and allows short, complete proofs of correctness that can also be used to prove homeomorphism for a subset of the outputs of Marching Cubes itself. We provide an open-source implementation of this algorithm and report on the results of its verification. Edge Flows: Stratified Morse Theory for Simple, Correct Isosurface
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