In this paper, we present a Voronoi based algorithm for closed curve reconstruction and medial axis approximation from planar points. In principle, the algorithm estimates one of the poles (farthest Voronoi vertices of a Voronoi cell) and hence the normals at each sample point by drawing an analogy between a residential water distribution system and Voronoi diagram of input samples. The algorit...

We show that the complexity of the farthest-site Voronoi diagram of n segments (or lines) in R is Θ(n) in the worst case, and it can be computed in O(n log n) time, using O(n) space. In R, the complexity of the diagram is Θ(nd−1) in the worst case.

We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram VD(S) (and several variants thereof) of a set S of n sites in the plane as sites are added to the set. To that effect, we define a general update operation for planar graphs that can be used to model the incremental construction of several variants of...

In this paper, the computation of positiveα-hull for a set of planar closedC-continuous curves has been addressed without sampling the curves into point-sets or polylines. Positive α-hull, so far, has been computed only for a set of points, using the farthest Delaunay triangulation, a dual of farthest Voronoi diagram. However, Delaunay triangulation does not exist for a set of curved boundaries...

We show that the number of 3-dimensional cells in the farthest-site Voronoi diagram of n segments (or lines) in R is Θ(n) in the worst case, and that the diagram can be computed in O(k log n) time, where k is the complexity of the diagram, using O(k) space. In R, the number of d-dimensional cells in the diagram is Θ(nd−1) in the worst case.

Let P be a planar n-point set in general position. For k ∈ {1, . . . , n − 1}, the Voronoi diagram of order k is obtained by subdividing the plane into regions such that points in the same cell have the same set of nearest k neighbors in P . The (nearest point) Voronoi diagram (NVD) and the farthest point Voronoi diagram (FVD) are the particular cases of k = 1 and k = n − 1, respectively. It is...

The construction of a minimum-width annulus of a set of objects in the plane has useful applications in diverse fields, such as tolerancing metrology and facility location. We present a novel implementation of an algorithm for obtaining a minimum-width annulus containing a given set of disks in the plane, in case one exists. The algorithm extends previously known methods for constructing minimu...