Tetrahedra based adaptive polygonization of implicit surface patches

Computer Graphics Forum

Volumn 18, Issue 1, 1999, Pages 57-68

  Hui, K C ^a   Jiang, Z H ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; NUMERICAL ANALYSIS; VISUALIZATION;

IMPLICIT SURFACE PATCHES; TETRAHEDRA BASED ADAPTIVE POLYGONIZATION;

COMPUTER GRAPHICS;

EID: 0032674379     PISSN: 01677055     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-8659.00302     Document Type: Article

References (25)

1. C. Hoffmann, Geometric and solid modeling: An Introduction. Morgan Kaufmann Publishers, (1989).
2. C. Bajaj and M. Kim, "Compliant motion planning with geometric models", in Proc. of the 9th ACM Symposium on Computational Geometry, pp. 171-180, (1987).
3. T. W. Sederberg, "Piecewise algebraic surface patches", Computer Aided Geometric Design, 2, pp. 53-59 (1985).
4. B. Guo, Modeling arbitrary smooth objects with algebraic surfaces. Doctoral dissertation, Dept. Computer Science, Cornell Univ., Ithaca, N.Y., (June 1991).
5. J. P. Menon, "Constructive shell representations for freeform surfaces and solids", IEEE Computer Graphics and Applications, 14, pp. 24-36 (1994).
6. S. Mann, C. Loop, and M. Lounsbery, "A survey of parametric scattered data fitting using triangular interpolants", in Curve and Surface Design, pp. 145-172, Philadelphia: H. Hagen, SIAM, (1992).
7. W. Boehm, G. Farin, and J. Kahmann, "A survey of curve and surface methods in CAGD", Computer Aided Geometric Design, 1, pp. 1-60 (1984).
8. T. W. Sederberg, "Scan line display of algebraic surfaces", Computer Graphics, 23, pp. 147-155 (1989).
9. M. Schmidt, "Cutting cubes - visualizing implicit surfaces by adaptive polygonization", Visual Computer, 10, pp. 101-105 (1993).
10. J. Bloomenthal, "Polygonization of implicit surfaces", Computer Aided Geometric Design, 5, pp. 341-355 (1988).
11. L. Velho, "Adaptive polygonization of implicit surfaces using simplicial decomposition and boundary constraints", in Proc. of EUROGRAPHICS'90, pp. 125-36, (1990).
12. C. Petersen, B. Piper, and A. Worsey, "Adaptive contouring of a trivariate interpolant", in Geometric Modeling: Algorithms and New Trends, pp. 385-395, Philadelphia: G. Farin, SIAM, (1987).
13. L. H. Figueiredo and J. M. Gomes, "Physically-based methods for polygonization of implicit surfaces", in Proc. of Graphics Interface'92, pp. 250-57, (1992).
14. A. Gueziec, "Exploiting triangulated surface extraction using tetrahedral decomposition", IEEE Trans. on Visualization and Computer Graphics, 1, pp. 328-42 (1995).
15. D. Kenwright, "Interactive time-dependent particle tracing using tetrahedral decomposition", IEEE Trans. on Visualization and Computer Graphics, 2, pp. 120-29 (1996).
16. E. Allgower and S. Gnutzmann, "An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces", SIAM Journal of Numerical Analysis, 24, pp. 452-469 (1987).
17. M. Hall and J. Warren, "Adaptive Polygonalization of Implicitly Defined Surfaces", IEEE Computer Graphics and Applications, 10(6), pp. 33-42 (1990).
18. D. W. Moore, Simplicial Mesh Generation with Applications. Doctoral dissertation, Dept. Computer Science, Cornell Univ., Ithaca, N.Y., (August 1992).
19. B. V. Herzen, "Accurate Triangulations of Deformed, Intersecting Surfaces", Computer Graphics (SIGGRAPH '87 Proceedings), 21(4), pp. 103-110 (1987).
20. C. Bajaj, C. Hoffmann, J. Hopcroft, and R. Lynch, "Tracing surface intersections", Computer Aided Geometric Design, 5, pp. 285-307 (1988).
21. T. Stoyanov, "Marching along surface/surface intersection curves with an adaptive step length", Computer Aided Geometric Design, 9, pp. 485-489 (1992).
22. M. Hohmeyer, "A surface intersection algorithm based on loop detection", in Proc. of the Symposium on Solid Modeling Foundations and CAD/CAM Applications, pp. 197-207, (1991).
23. L. Chang, W. Bein, and E. Angel, "Surface intersections using parallel subdivision", Supercomputer, 7, pp. 62-70 (1990).
24. E. Houghton, R. Emnett, J. Factor, and C. Sabharwal, "Implementation of a divide-and-conquer method for intersection of parametric surfaces", Computer Aided Geometric Design, 2, pp. 173-183 (1985).
25. J. P. Thiron and A. Gourdon, "The 3D Marching Lines Algorithm", Graphical Model and Image Processing, 58(6), pp. 503-509 (1996).