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Solid Modeling Based on a New Paradigm
Author(s) -
Yoshida Norimasa,
Shiokawa Masato,
Yamaguchi Fujio
Publication year - 1994
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.1330055
Subject(s) - computation , geometric design , geometric modeling , computer science , integer (computer science) , boundary representation , domain (mathematical analysis) , theoretical computer science , consistency (knowledge bases) , algorithm , simple (philosophy) , division (mathematics) , boolean data type , matrix (chemical analysis) , boolean algebra , boundary (topology) , mathematics , arithmetic , geometry , artificial intelligence , mathematical analysis , philosophy , epistemology , composite material , programming language , materials science
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 × 4 determinant method or the 4 × 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.