We present a new continuation method for computing implicitly defined manifolds. The
manifold is represented as a set of overlap** neighborhoods, and extended by an added …

This well-accepted introduction to computational geometry is a textbook for high-level
undergraduate and low-level graduate courses. The focus is on algorithms and hence the …

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric
domain such that the generating points of the tessellations are also the centroids (mass …

The straight skeleton of a polygon is a variant of the medial axis, introduced by Aichholzer et
al., defined by a shrinking process in which each edge of the polygon moves inward at a …

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the
generating points of the tessellations are also the centroids of the corresponding Voronoi …

In this second part of a series of surveys on the geometry of finite dimensional Banach
spaces (Minkowski spaces) we discuss results that refer to the following three topics: bodies …

We give a linear-time algorithm for computing the medial axis of a simple polygon P. This
answers a long-standing open question—previously, the best deterministic algorithm ran in …

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that
subdivides the embedding space into regions, each region consisting of the points that are …

Voronoi diagrams of curved objects can show certa” n phenomena that are often considered
artifacts: The Voronoi diagram is not connected; there are pairs of objects whose bisector is …

Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can
be computed by computing two planar Voronoi diagrams of suitably transformed sites in the …