Green coordinates

Yaron Lipman*, David Levin, Daniel Cohen-Or

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


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.

Original languageEnglish
StatePublished - 2008
EventACM SIGGRAPH 2008 Papers 2008, SIGGRAPH'08 - Los Angeles, CA, United States
Duration: 11 Aug 200815 Aug 2008


ConferenceACM SIGGRAPH 2008 Papers 2008, SIGGRAPH'08
Country/TerritoryUnited States
CityLos Angeles, CA


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