Pushkar Joshi, Mark Meyer, Tony DeRose, Brian Green, Tom Sanocki
In this paper we consider the problem of creating and controlling
volume deformations used to articulate characters for use
in high-end applications such as computer generated feature films.
We introduce a method we call harmonic coordinates
that significantly improves upon existing volume deformation
techniques. Our deformations are controlled using a topologically flexible
structure, called a cage, that consists of a closed three dimensional mesh.
The cage can optionally be augmented with additional interior vertices,
edges, and faces to more precisely control the interior behavior of
the deformation. We show that harmonic coordinates are generalized barycentric
coordinates that can be extended to any dimension. Moreover, they
are the first system of generalized barycentric coordinates that are
non-negative even in strongly concave situations, and their magnitude
falls off with distance as measured within the cage.
Additional materials: [SiggraphSlides.pdf], [HarmonicCoordinates.divx]
Available in the proceedings of Siggraph 2007.
Available as Pixar Technical Memo #06-02b