GPU-assisted Positive Mean Value Coordinates for Mesh Deformations

Abstract

In this paper we introduce positive mean value coordinates (PMVC) for mesh deformation. Following the observations of Joshi et al. [JMD*07] we show the advantage of having positive coordinates. The control points of the deformation are the vertices of a "cage" enclosing the deformed mesh. To define positive mean value coordinates for a given vertex, the visible portion of the cage is integrated over a sphere. Unlike MVC [JSW05], PMVC are computed numerically. We show how the PMVC integral can be efficiently computed with graphics hardware. While the properties of PMVC are similar to those of Harmonic coordinates [JMD*07], the setup time of the PMVC is only of a few seconds for typical meshes with 30K vertices. This speed-up renders the new coordinates practical and easy to use.