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Computer Graphics Forum
Volume 13, Issue 3 (1994)
pp. 55-64
Norimasa Yoshida, Masato Shiokawa, and Fujio Yamaguchi
Abstract:The technique of solid modeling is essential in CAD/CAM applications, and is currently well established. However, problems remain, such as the lack of uniformity in geometric computations and the lack of stability of Boolean operations of two solids. In this paper, we introduce a theoretical solid modeling system that operates on boundary representations of polyhedral objects and is based on a new paradigm. The characteristics of the system are the following: (I) in Boolean Operations and modeling transformations, all geometric computations are performed by the 4 x 4 determinant method or the 4 x 4 matrix method in homogeneous space, which allows the system to avoid division operations, (2) all geometric computations are performed by the exact integer arithmetic, which makes the geometric algorithms stable and simple, and (3) primitive solids are constructed consistently in the integer domain, and the consistency is assured throughout Boolean operations and transformations. Key Words: method, integer arithmetic solid modeling, Boolean operation, boundary representation, 4 x 4 determinant
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