We examine the problem of computing exactly the Voronoi diagram (via the dual Delaunay graph) of a set of, possibly intersecting, smooth convex pseudocircles in the Euclidean plane, given in parametric form. Pseudo-circles are (convex) sites, every pair of which has at most two intersecting points. The Voronoi diagram is constructed incrementally. Our first contribution is to propose robust and...

This paper proposes a function approximation scheme based on Voronoi diagram, a technique of computational geometry, toward optimization cost saving in real engineering applications. The scheme consists of a blending function of local information over spatial structure among sample points that is topologically represented with Voronoi diagram, an estimation method of function gradients through ...

This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvature-adapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d or larger). In this high dimensional space, the mesh is optimized by computing a Centroidal Voron...

We describe a new algorithm for computing the Voronoi diagram of a set of n points in constant-dimensional Euclidean space. The running time of our algorithm is O(f log n log ∆) where f is the output complexity of the Voronoi diagram and ∆ is the spread of the input, the ratio of largest to smallest pairwise distances. Despite the simplicity of the algorithm and its analysis, it improves on the...

We present the first time-optimal algorithm for computing the Voronoi Diagram under the metric induced by a transportation network with discrete entry and exit points. For input with n sites, k stations, and e transportation lines, the algorithm computes the Voronoi Diagram in O ( (n+ k) log(n+ k) + e ) time.

We describe the structure of the Voronoi diagram of lines for a set of points in the plane, thereby making use of an extra dimension. In contrast to previous results in this respect, which were based on the dual representation of the Voronoi diagram under consideration, our approach applies to the primal plane. We also generalize it to higher-dimensional hyperplane spaces.

Voronoi diagrams are powerful for understanding spatial properties. However, few reports have been made moving generators despite their important applications. We present a topology-oriented event-increment (TOI-E) algorithm constructing diagram of circular disks in the plane over time horizon $[0, t^{\infty })$ . The propos...