Yaron Lipman, Johannes Kopf, Daniel Cohen-Or, and David Levin
In this paper we introduce positive mean value coordinates (PMVC) for mesh deformation. Following the observations
of DeRose and Meyer [DM07] 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
[DM07], 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.
In Symposium on Geometry Processing 2007 / ACM International Conference Proceeding Series, 257