Computer graphics, computer-aided design, and computer-aided manufacturing are tools that have become indispensable to a wide array of activities in contemporary society. Euclidean processing provides the basis for these computer-aided design systems although it contains elements that inevitably lead to an inaccurate, non-robust, and complex system. The primary cause of the deficiencies of Euclidean processing is the division operation, which becomes necessary if an n-space problem is to be processed in n-space. 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 four-dimensional 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.A new form of data structure called the quarter-edge data structure which is suited to dual processing is employed to ... 3. Transformations are performed by the homogeneous matrix method *), while interference tests are performed by the anbsp;...
|Title||:||Computer-Aided Geometric Design|
|Publisher||:||Springer Science & Business Media - 2011-06-28|