Primitive-Based Morphing of Implicit Surfaces 
Primitive-Based Morphing of Implicit Surfaces
In order to make virtual human animation and tracking more realistic, the joints of the virtual human should not only be modelled in the most anatomically-correct way possible, but also apply joint limits derived from reality. In previous work [2], these joint limits have been represented as a closed volume in the form of an implicit surface. The data giving rise to this surface were recorded using optical motion capture and the resulting scattered data was approximated by a volume as per the method described in [1]. The result is shown in the Figure to the right below.
The captured motion corresponds to the range of motion of the shoulder, the entire shoulder compound being considered as one single 3-degree-of-freedom joint. However, the shoulder compound is comprised of three inter-dependent joints: the clavicle, scapula and shoulder joints. A given position of one joint determines the range of motion of the next joint, so for a given position of the clavicle, for example, we would have a determined range of motion for the scapula. This range of motion increases or decreases in a regular manner depending on the position of the preceding joint in the hierarchy. If we measure this range of motion at given positions, and then derived an implicit surface for each set of data, we could then perform implicit surface metamorphosis (or "morphing") in order to determine the range of motion at intermediate positions.
What's to be done :
What would be needed would therefore be a general implicit surface morphing tool, that would transform any source shape A into a target shape B. Article [3] describes a method for implementing such a tool.
In a nutshell, the trick is to raise the 3-dimensional problem to 4-D and to perform scattered data interpolation using "variational interpolation". This will give us an implicit function in 4-D, where each "slice" represents an intermediate shape of the morphing process.
It's not as complicated as it sounds!
Reading:
[1] Bittar E., Tsingos N., Gascuel M.P., "Implicit Surfaces for Semi-Automatic Medical Organ Reconstruction", Proceedings of Computer Graphics International, Leeds, UK, May 1995.
[2] Herda L., Urtasun R., Fua P., Hanson A., “Automatic Determination of Shoulder Joint Limits using Quaternion Field Boundaries”, 5th International Conference on Automatic Face and Gesture Recognition 2002.
[3] Turk G., O'Brien J.F., "Shape Transformation Using Variational Implicit Functions", Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 99), pages 335--342, August 1999.