Voronoi diagram and medial axis algorithm for planar domains with curved boundaries — II: Detailed algorithm description

Voronoi diagram and medial axis algorithm for planar domains with curved boundaries — II: Detailed algorithm description

Details of algorithms to construct the Voronoi diagrams and medial axes of planars domain bounded by free-form (polynomial or rational) curve segments are presented, based on theoretical foundations given in the rst installment Ramamurthy and Farouki, J. Comput. Appl. Math. (1999) 102 119–141 of this two-part paper. In particular, we focus on key topological and computational issues that arise ...

Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations

In this rst installment of a two-part paper, the underlying theory for an algorithm that computes the Voronoi diagram and medial axis of a planar domain bounded by free-form (polynomial or rational) curve segments is presented. An incremental approach to computing the Voronoi diagram is used, wherein a single boundary segment is added to an existing boundary-segment set at each step. The introd...

Constructing medial axis transform of planar domains with curved boundaries

The paper describes an algorithm for generating an approximation of the medial axis transform (MAT) for planar objects with free form boundaries. The algorithm generates the MAT by a tracing technique that marches along the object boundary rather than the bisectors of the boundary entities. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteri...

Hierarchical planar voronoi diagram approximations

Anomaly Detection with the Voronoi Diagram Evolutionary Algorithm

This paper presents the Voronoi diagram-based evolutionary algorithm (VorEAl). VorEAl partitions input space in abnormal/normal subsets using Voronoi diagrams. Diagrams are evolved using a multiobjective bio-inspired approach in order to conjointly optimize classification metrics while also being able to represent areas of the data space that are not present in the training dataset. As part of ...