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.