A shift of playground for geometric processing from euclidean to homogeneous
A shift of playground for geometric processing from euclidean to homogeneous
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几何处理的游乐场从欧几里德到齐次的转变
DOI：
10.1007/s003710050143
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
F. Yamaguchi
中科院分区：
文献类型：
--
作者：
F. Yamaguchi
作者认为，只要欧几里德处理为CAD提供了基础，系统中可实现的可靠性水平总是有限制的。换句话说，CAD系统中包含的元素不可避免地导致系统的不准确性、不稳定性和复杂性，因为除法运算是所有邪恶的根源。作者提出了一种不需要进行除法运算的几何处理场，即全四维齐次处理场。从几何处理的理论背景、几何定义、几何计算、拓扑定义、拓扑运算等方面对几何处理进行了论述。
The author argues that as long as euclidean processing provides the basis for CAD, there will always be a limit to the level of reliability achievable in a system. In other words, a CAD system contains within it elements that inevitably lead to the system's inaccuracy, instability, and complexity because ªa division operation is the root cause of all evilº. The author proposes a geometric processing playground in which there is no need of performing a division operation; that is, ªtotally four-dimensional homogeneous processingº. He discusses the geometric processing from the points of its theoretical backgrounds, geometric definitions, geometric computations, topological definitions, and topological operations.