The `thermodynamics´ of shape

Shape modeling is still in its infancy. Fifty years of research has produced only a few isolated techniques that describe a tiny subset of shapes usefully. We need to find some more general principles that coordinate shape description just as scientific laws coordinate a description of nature. Underlying the laws of science are even more general principles of thermodynamics. Although we are not yet ready to describe the `laws of shape´, we can begin to establish some underlying principles that these laws must follow. In trying to do this we have uncovered some interesting inconsistencies in existing practice