Sciweavers

TOG
2008

Green Coordinates

13 years 3 months ago
Green Coordinates
We introduce Green Coordinates for closed polyhedral cages. The coordinates are motivated by Green's third integral identity and respect both the vertices position and faces orientation of the cage. We show that Green Coordinates lead to space deformations with a shape-preserving property. In particular, in 2D they induce conformal mappings, and extend naturally to quasi-conformal mappings in 3D. In both cases we derive closed-form expressions for the coordinates, yielding a simple and fast algorithm for cage-based space deformation. We compare the performance of Green Coordinates with those of Mean Value Coordinates and Harmonic Coordinates and show that the advantage of the shape-preserving property is not achieved at the expense of speed or simplicity. We also show that the new coordinates extend the mapping in a natural analytic manner to the exterior of the cage, allowing the employment of partial cages.
Yaron Lipman, David Levin, Daniel Cohen-Or
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TOG
Authors Yaron Lipman, David Levin, Daniel Cohen-Or
Comments (0)