An adaptive, error-free computation based on the 4×4 determinant method
- 30 Downloads
The 4×4 determinant method makes it possible to unify geometric processing by the computations of 4×4 determinants composed of homogeneous coordinants vectors of four points or coefficient vectors of four plane equations. Because the method needs not require a division operation, error-free geometric computation is not difficult to realize by means of integer arithemtic of appropriate data length. The present paper proposes an error-free, efficient computing method, which computes the 4×4 determinants by adaptively selecting integer arithmetic of variable data length. This technique is discussed theoretically and experimentally.
Key words4×4 determinant method Computational geometry Geometric modeling
Unable to display preview. Download preview PDF.
- 1.Mantyla M (1986) Boolean operations of 2-manifolds through vertex neighborhood classification. ACM Trans. Graph. 5(1) 1–29Google Scholar
- 2.Newman WM, Sproull RF (1979) Principles of interactive computer graphics (2nd edn.). McGraw-Hill, New YorkGoogle Scholar
- 3.Yamaguchi F (1985) A unified approach to interference problems using a triangle processor. Proc SIGGRAPH pp 141–149Google Scholar
- 4.Yamaguchi F (1985) Theoretical foundations for the 4×4 determinant approach in computer graphics and geometric modeling. The Visual Computer 3(2) 88–97Google Scholar
- 5.Yamaguchi F, Tatemichi T, Ebisawa R (1986) Applications of the triangle processor to various interference problems. Adv Comput Graph. Springer, New York Berlin HeidelbergGoogle Scholar
- 6.Yamaguchi F et al (1988) The polygon engine. The Visual Computer 4(4) 176–187Google Scholar