Exact Geometrical Predicate: Point in circle

Abstract

This document describes the implementation in ITK of the “point in circle” geometrical predicate. Based on Jonathan Shewchuk’s work which implements an exact version of the predicate using standard floating point types and arithmetic, the implementation consist of an ITK wrapper around the public domain C routines made available by the author of the precedent paper. Wrapper using itk::PointSet, itk:CellInterface and itk:Mesh / itk:QuadEdgeMesh APIs are provided along with corresponding examples which should provide enough details for users to directly copy paste code in their application.The application in mind for us is an exact and robust implementation of a delaunay triangulation / voronoi tesselation in ITK, and will be presented in a separate paper.