Michael Leyton, Rutgers University
A Generative Theory of Shape
This talk summarizes my recent book A Generative Theory of Shape (Springer-Verlag, 550 pages). The theory is based on two properties fundamental to intelligent design: maximizing transfer of structure, and maximizing recoverability of generative operations. It is applied in considerable detail to CAD, perception, and robotics. A significant aspect is the development of an object-oriented theory of geometry. This includes a group-theoretic formulation of object-oriented inheritance. In particular, a class of groups is developed called "unfolding groups", which define any complex shape as unfolded from a maximally collapsed version of itself called an "alignment kernel". The advantages of the theory are demonstrated with lengthy studies of robot manipulators, perceptual organization, constructive solid geometry, assembly planning, architectural CAD, and mechanical CAD/CAM.