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ComputerAided Geometric Design: A Totally FourDimensional Approach,New
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Computer graphics, computeraided design, and computeraided manufacturing are tools that have become indispensable to a wide array of activities in contemporary society. Euclidean processing provides the basis for these computeraided design systems although it contains elements that inevitably lead to an inaccurate, nonrobust, and complex system. The primary cause of the deficiencies of Euclidean processing is the division operation, which becomes necessary if an nspace problem is to be processed in nspace. The difficulties that accompany the division operation may be avoided if processing is conducted entirely in (n+1)space. The paradigm attained through the logical extension of this approach, totally fourdimensional processing, is the subject of this book. This book offers a new system of geometric processing techniques that attain accurate, robust, and compact computations, and allow the construction of a systematically structured CAD system.
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