Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length n + c n log n . We disprove a conjecture of Erd˝o...
We introduce an algorithm for reconstructing watertight surfaces from unoriented point sets. Using the Voronoi diagram of the input point set, we deduce a tensor field whose princ...
Pierre Alliez, David Cohen-Steiner, Yiying Tong, M...
The projection median of a finite set of points in R2 was introduced by Durocher and Kirkpatrick [5]. They proved the projection median in R2 provides a better approximation of th...
Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least-squares (MLS) fitting of algebraic spheres. In this paper we first revisi...
High-dimensional problems arising from robot motion planning, biology, data mining, and geographic information systems often require the computation of k nearest neighbor (knn) gr...