Euclidean voronoi diagram for circles in a circle

Euclidean Voronoi Diagrams for Circles in a Circle

A sweepline algorithm for Euclidean Voronoi diagram of circles

Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others. The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bot...

Voronoi Diagram in the Laguerre Geometry and its Applications

We extend the concept of Voronoi diagram in the ordinary Euclidean geometry for n points to the one in the Laguerre geometry for n circles in the plane, where the distance between a circle and a point is defined by the length of the tangent line, and show that there is an O(n log n) algorithm for this extended case. The Voronoi diagram in the Laguerre geometry may be applied to solving effectiv...

Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set on a plane, where the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work in conjunction with the first paper of the series dealing with the construction of the correct top...

Predicates for the Exact Voronoi Diagram of Ellipses under the Euclidean Metric

This article examines the computation of the Voronoi diagram of a set of ellipses in the Euclidean plane. We propose the first complete methods, under the exact computation paradigm, for the predicates of an incremental algorithm: κ1 decides which one of two given ellipses is closest to a given exterior point; κ2 decides the position of a query ellipse relative to an external bitangent line of ...