Abstract
Theories of the 4×4 determinant method to resolve interference problems are described, in detail, in succession to the former paper [1]. First, various cases of the 4×4 determinant are discussed including the geometric implications by deriving a few fundamental relations. Secondly, normalization of the determinant is proposed. Thirdly, an intersection formula in homogeneous coordinates is verified which makes it possible to do consistent homogenous coordinate processing from the very beginning of geometric modelling to the very last of the objects displayed. Lastly an outline of how the 4×4 determinant method is applied to basic geometric problems is described.
This article will provide, theoretical foundations for the 4×4 determinant method in computer graphics and geometric modelling.
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References
Yamaguchi F (1985), A unified approach to interference problems using a triangle processor. Siggraph '85 Conf Proc, vol 19, no 3 (July 1985)
Yamaguchi F, Takaomi T, Ryoji E (1986) Applications of the 4×4 determinant method and the TRIANGLE PROCESSOR to various interference problems. Computer Graphics Tokyo '86
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Roberts LG (1965), Homogeneous matrix representation and manipulation ofN-dimensional constructs. MIT Lincoln Lab, MS 1405 (May 1965)
Newman WM, Sproull RF (1979) Principles of interactive computer graphics, 2nd ed. McGraw-Hill
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Yamaguchi, F. Theoretical foundations for the 4×4 determinant method in computer graphics and geometric modelling. The Visual Computer 3, 88–97 (1987). https://doi.org/10.1007/BF02153665
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DOI: https://doi.org/10.1007/BF02153665