INTERVAL METHODS FOR B-REP MODEL VERIFICATION AND RECTIFICATION

Proceedings of the ASME Design Engineering Technical Conference

Volumn 2, Issue , 2000, Pages 523-533

  Shen, Guoling ^a   Sakkalis, Takis ^a   Patrikalakis, Nicholas M ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY REPRESENTATION MODELS; BREP MODELS; INTERVAL ARITHMETIC; INTERVAL METHODS; MODEL CONVERSION; MODEL VERIFICATION; NUMERICAL ERRORS; SOLID MODELLING; TOPOLOGICAL STRUCTURE;

EID: 0003086981     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2000/DAC-14277     Document Type: Conference Paper

References (22)

1. S. L. Abrams, W. Cho, C.-Y. Hu, T. Maekawa, N. M. Patrikalakis, E. C. Sherbrooke, and X. Ye. Efficient and reliable methods for rounded interval arithmetic. Computer Aided Design, 30(8):657-665,1998.
2. G. Alefeld and J. Herzberger. Introduction to Interval Computations. Academic Press, New York, 1983.
3. I. C. Braid, R. C. Hillyard, and I. A. Stroud. Stepwise construction of polyhedra in geometric modeling. In K. W. Brodlie, editor, Mathematical Methods in Computer Graphics and Design, pages 123-141, Academic Press, London, 1980.
4. C. M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc., San Mateo, California, 1989.
5. C. M. Hoffmann. The problems of accuracy and robustness in geometric computation. Computer, 22(3):31-41, March 1989.
6. C. Y. Hu, T. Maekawa, N. M. Patrikalakis, and X. Ye. Robust interval algorithm for surface intersections. Computer Aided Design, 29(9):617-627, September 1997.
7. C. Y. Hu, T. Maekawa, E. C. Sherbrooke, and N. M. Patrikalakis. Robust interval algorithm for curve intersections. Computer Aided Design, 28(6/7):495-506, June/July 1996.
8. Y. Hu and T. Sun. Moving a B-spline surface to a curve - a trimmed surface matching algorithm. Computer Aided Design, 29(6):449-455,1997.
9. International Techne Group Inc. Case studies and articles. < http://www.cadfix.com/>.
10. D. E. LaCourse. Handbook of Solid Modeling. McGraw-Hill Inc., New York, 1995.
11. M. Mantyla. A note on the modeling space of Euler operators. Computer Vision, Graphics and Image Processing, 26 (1): 45-60, 1984.
12. M. Mantyla. An Introduction to Solid Modeling. Computer Science Press, Rockville, Maryland, 1988.
13. R. E. Moore. Interval Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1966.
14. N. M. Patrikalakis, T. Sakkalis, and G. Shen. Boundary representation models: Validity and rectification. Proceedings of the 9th IMA Conference on the Mathematics of Surfaces. University of Cambridge, UK., 2000. In press.
15. T. J. Peters, N. F. Stewart, D. R. Ferguson, and P. S. Fussell. Algorithmic tolerances and semantics in data exchange. In Computational Geometry '97, Nice, France, 1997.
16. A. A. G. Requicha. Representations of solid objects - theory, methods and systems. ACM Computing Surveys, 12(4):437-464, December 1980.
17. T. Sakkalis, G. Shen, and N. M. Patrikalakis. Representational Validity of Boundary Representation Models. Computer Aided Design, 2000. In press.
18. T. W. Sederberg and R. T. Farouki. Approximation by interval Bezier curves. IEEE Computer Graphics and Applications, 12(5):87-95, September 1992.
19. G. Shen. Analysis of Boundary Representation Model Rectification. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, February 2000.
20. G. Shen and N. M. Patrikalakis. Numerical and geometric properties of interval B-splines. International Journal of Shape Modeling, 4(1 and 2):35-62, March and June 1998.
21. E. C. Sherbrooke and N. M. Patrikalakis. Computation of the solutions of nonlinear polynomial systems. Computer Aided Geometric Design, 10(5):379-405, October 1993.
22. S. T. Tuohy, T. Maekawa, G. Shen, and N. M. Patrikalakis. Approximation of measured data with interval B-splines. Computer Aided Design, 29(11):791-799, November 1997.