We describe our experience with a new algorithm for the recon struction of surfaces from unorganized sample points in IR3. The algorithm is the first for this problem with provable guarantee s. Givenâ€¦ (More)

The power crust is a construction which takes a sample of points from the surface of a three-dimensional object and produces a surface mesh and an approximate medial axis. The approach is to firstâ€¦ (More)

The medial axis transform (or MAT) is a representation of an object as an in nite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a niteâ€¦ (More)

We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve,â€¦ (More)

We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve,â€¦ (More)

Randomized incremental constructions are widely used in computational geometry, but they perform very badly on large data because of their inherently random memory access patterns. We define a biasedâ€¦ (More)

The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicitâ€¦ (More)