The Problems of Accuracy and Robustness in Geometric Computation

Computer

Volumn 22, Issue 3, 1989, Pages 31-39

  Hoffmann, Christoph M ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING--ALGORITHMS;

ACCURACY; COMPUTATIONAL GEOMETRY; ROBUSTNESS;

MATHEMATICAL TECHNIQUES;

EID: 0024627489     PISSN: 00189162     EISSN: None     Source Type: Trade Journal    
DOI: 10.1109/2.16223     Document Type: Article

References (12)

1. D. Dobkin and D. Silver, “Recipes for Geometry and Numerical Analysis, Part I: An Empirical Study,” Proc. Fourth ACM Symp. on Computer Geometry, June 1988, pp. 93–105.
2. C. Hoffmann, Geometric and Solid Modeling, Morgan Kaufman, San Francisco, to be published in 1989, chapter 4.
3. G. Golub and C. van Loan, Matrix Computations, Johns Hopkins Press, Baltimore, chapter 2.
4. K. Sugihara, “An Approach to Error-Free Solid Modeling,” IMA Summer Program on Robotics, Inst. Math, and Applications, Univ. of Minnesota, Minneapolis, Minn., 1987.
5. B. Buchberger, G. Collins, and B. Kutzler, “Algebraic Methods for Geometric-Reasoning,” Ann. Reviews in Computer Science, Ann. Reviews, Inc., Palo Alto, Calif., Vol. 3, 1988, pp. 85–119.
6. J. Hong, “Proving by Example and Gap Theorems,” Proc. 27th Symp. Foundations of Computer Science, November 1986, pp. 107–116.
7. C. Hoffmann, J. Hopcroft, and M. Karasick, “Towards Implementing Robust Geometric Computations,” Proc. Fourth ACM Symp. on Computer Geometry, June 1988, pp. 106–117.
8. V. Milenkovic, “Verifiable Implementations of Geometric Algorithms Using Finite Precision Arithmetic,” Tech. Report CS-88–168, Carnegie Mellon Univ., Pittsburgh, 1988.
9. D. Greene and F. Yao, “Finite Resolution Computational Geometry,” Proc. 27th IEEE Symp. Foundations of Computer Science, November 1986, pp. 143–152.
10. M. Segal and C. Sequin, “Consistent Calculations for Solids Modeling,” Artificial Intelligence, D. Kapur and J. Mundy, eds., special issue on geometric reasoning, Elsevier, North-Holland, Vol. 37, 1988. H.H. Edelsbrunner and E. Mücke, “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms,” Proc. Fourth ACM Symp. on Computer Geometry, June 1988, pp. 118–133.
11. C. Yap, “A Geometric Consistency Theorem for a Symbolic Perturbation Theorem,” Proc. Fourth ACM Symp. on Computer Geometry, June 1988, pp. 134–142.
12. C. Hoffmann, J. Hopcroft, and M. Karasick, “Robust Set Operations on Polyhedral Solids,” Tech. Report 723, Computer Science Dept., Purdue University, W. Lafayette, Ind., 1988.