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.

@inproceedings{Lipman2007GPUassistedPositive, author = {Y. Lipman, J. Kopf, D. Cohen-Or, D. Levin}, booktitle = {Geometry Processing}, doi = {10.2312/SGP/SGP07/117-123}, editor = {Alexander Belyaev and Michael Garland}, isbn = {978-3-905673-46-3}, issn = {1727-8384}, publisher = {The Eurographics Association}, title = {GPU-assisted Positive Mean Value Coordinates for Mesh Deformations}, url = {http://www.math.tau.ac.il/%7Elipmanya/pmvc/pmvc.htm}, year = {2007} }