The reconstruction of a shape or surface from a finite set of points is a practically significant and theoretically challenging problem. This paper presents a unified view of algor...
The flow complex is a geometric structure, similar to the Delaunay tessellation, to organize a set of (weighted) points in Rk. Flow shapes are topological spaces corresponding to ...
Kevin Buchin, Tamal K. Dey, Joachim Giesen, Matthi...
—We study the problem of localizing a large sensor network having a complex shape, possibly with holes. A major challenge with respect to such networks is to figure out the corr...
We present a novel reconstruction algorithm that, given an input point set sampled from an object S, builds a one-parameter family of complexes that approximate S at different sca...
We give a provably correct algorithm to reconstruct a kdimensional manifold embedded in d-dimensional Euclidean space. Input to our algorithm is a point sample coming from an unkn...