Surface visualization and compression with signed-distance functions

This dissertation presents a surface compression method that stores surfaces as wavelet-compressed signed-distance volumes. This approach enables the representation of surfaces with complex topology and arbitrary numbers of components within a single multiresolution data structure. This data structure elegantly handles topological modification at high compression rates. The method does not require the costly base mesh construction step required by subdivision surface approaches. Several improvements over previous attempts at compressing signed-distance functions are presented, including an O(n) distance transform, a zero set initialization method for triangle meshes, and a specialized thresholding algorithm. The potential of sampled distance volumes for surface compression and progressive reconstruction is demonstrated for complex high genus surfaces.; An adaptive signed distance transform algorithm for curves in the plane is also presented. This algorithm demonstrates potential research directions towards the goal of eliminating redundant computations in both the distance and wavelet transforms. The algorithm is demonstrated on the isocontours of a turbulence simulation. The algorithm provides guaranteed error bounds with a selective refinement approach. The domain over which the signed distance function is desired is adaptively triangulated and piece-wise discontinuous linear approximations are constructed within each triangle. The resulting transform performs work only where requested and does not rely on a predefined sampling rate.