A sweepline algorithm for Euclidean Voronoi diagram of circles

Euclidean voronoi diagram for circles in a circle

Presented in this paper is an algorithm to compute a Euclidean Voronoi diagram for circles contained in a large circle. The radii of circles are not necessarily equal and no circle inside the large circle wholly contains another circle. The proposed algorithm uses the ordinary point Voronoi diagram for the centers of inner circles as a seed. Then, we apply a series of edge-flip operations to th...

Parallel computing 2D Voronoi diagrams using untransformed sweepcircles

Voronoi diagrams are among the most important data structures in geometric modeling. Among many efficient algorithms for computing 2D Voronoi diagrams, Fortune’s sweepline algorithm (Fortune, 1986 [5]) is popular due to its elegance and simplicity. Dehne and Klein (1987) [8] extended sweepline to sweepcircle and suggested computing a type of transformed Voronoi diagram, which is parallel in nat...

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...

Euclidean Voronoi Diagrams for Circles in a Circle

The Voronoi Diagram of Convex Objects in the Plane

This paper presents a dynamic algorithm for the construction of the Euclidean Voronoi diagram of a set of convex objects in the plane. We consider first the Voronoi diagram of smooth convex objects forming pseudo-circles set. A pseudo-circles set is a set of bounded objects such that the boundaries of any two objects intersect at most twice. Our algorithm is a randomized dynamic algorithm. It d...