In this book, the author develops a generative theory of shape with two properties fundamental to intelligence: maximization of transfer and maximization of recoverability. The advantages of applying this new theory to computational disciplines such as CAD, visual perception, and robotics are shown. A significant aspect of this book is the development of an object-oriented theory of geometry including an algebraic theory of object-oriented inheritance based on group theory. It is shown that any complex object can be derived from a root object -its structural core is referred to as an 'alignment kernel'. This principle is applied to robot manipulators, surface primitives, and mechancical and architectural CAD. The book is completed by a comparison of this new theory with Felix Klein's Erlanger program, showing why the new theory is appropriate for computer vision and CAD whereas Klein's Erlanger program is not.
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