Generalized Barycentric Coordinates on Irregular Polygons

Abstract

In this paper we present an easy computation of a generalized form of barycentric coordinates for irregular, convex n-sided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to ray-tracing. Our new equations preserve many of the familiar properties of the triangular barycentric coordinates with an equally simple calculation, contrary to previous formulations. We illustrate the properties and behavior of these new generalized barycentric coordinates through several example applications.