GPU-assisted Positive Mean Value Coordinates for Mesh Deformation

Yaron Lipman Johannes Kopf Daniel Cohen-Or David Levin

Symposium on Geometry Processing 2007

Abstract:

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.

Technical Report:

Acrobat, ~7 MB