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The Visual Computer

, Volume 9, Issue 4, pp 173–181 | Cite as

An adaptive, error-free computation based on the 4×4 determinant method

  • Fujio Yamaguchi
  • Kenji Toshimitsu
  • Hiroaki Sato
  • Junichi Nakagawa
Original Articles

Abstract

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 words

4×4 determinant method Computational geometry Geometric modeling 

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References

  1. 1.
    Mantyla M (1986) Boolean operations of 2-manifolds through vertex neighborhood classification. ACM Trans. Graph. 5(1) 1–29Google Scholar
  2. 2.
    Newman WM, Sproull RF (1979) Principles of interactive computer graphics (2nd edn.). McGraw-Hill, New YorkGoogle Scholar
  3. 3.
    Yamaguchi F (1985) A unified approach to interference problems using a triangle processor. Proc SIGGRAPH pp 141–149Google Scholar
  4. 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. 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. 6.
    Yamaguchi F et al (1988) The polygon engine. The Visual Computer 4(4) 176–187Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Fujio Yamaguchi
    • 1
  • Kenji Toshimitsu
    • 2
  • Hiroaki Sato
    • 3
  • Junichi Nakagawa
    • 4
  1. 1.Department of Mechanical EngineeringWaseda UniversityTokyoJapan
  2. 2.Toto CorporationJapan
  3. 3.Toshiba Electric Co.Japan
  4. 4.NTT CorporationJapan

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