Spline approximations of real algebraic surfaces

Journal of Symbolic Computation

Volumn 23, Issue 2-3, 1997, Pages 315-333

  Bajaj, Chandrajit L ^a   Xu, Guoliang ^b  

^a Purdue University   (United States)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031071002     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1996.0091     Document Type: Article

References (27)

1. Allgower, E., Gnutzmann, S. (1987). An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces. SIAM J. Numer. Anal., 24:452-469.
2. Allgower, E., Gnutzmann, S. (1991). Simplicial pivoting for mesh generation of implicitly defined surfaces. Computer Aided Geometric Design, 8:305-325.
3. Bajaj, C. (1990). Geometric Computations with Algebraic Varieties of Bounded Degree. In Proc. of the Sixth ACM Symposium on Computational Geometry, pp. 148-156, Berkeley, CA.
4. Bajaj, C. (1993). The emergence of algebraic curves and surfaces in geometric design. In Martin, R., ed., Directions in Geometric Computing, pp. 1-29. Information Geometers Press.
5. Bajaj, C., Chen, J., Xu, G. (1995). Modeling with cubic A-patches. ACM Transactions on Graphics, 14, 2:103-133.
6. 1 smoothing of polyhedra with implicit algebraic splines. SIGGRAPH'92, Computer Graphics, 26(2):79-88.
7. Bajaj, C., Royappa, A. (1990). The GANITH Algebraic Geometry Toolkit. In Proc. of the First International Symposium on the Design and Implementation of Symbolic Computation Systems, pp. 268-269. LNCS 429, Springer-Verlag.
8. Bajaj, C., Xu, G. (1991). Piecewise rational approximation of real algebraic curves. J. Computational Mathematics, Vol. 15, No. 1, 1997, 55-71.
9. Bajaj, C., Xu, G. (1994a). Converting a rational curve to a standard rational Bézier representation. In Heckbert, P., ed., Graphics Gems IV, pp. 256-260. New York, Academic Press.
10. Bajaj, C., Xu, G. (1994b). NURBS approximation of surface-surface intersection curves. Advances in Computational Mathematics, 2:1-21.
11. Blinn, J.F. (1982). A generalization of algebraic surface drawing. ACM Transactions on Graphics, 11(3):235-256.
12. Bloomenthal, J. (1988). Polygonization of implicit surfaces. Computer Aided Geometric Design, 5(00):341-355.
13. Canny, J. (1988). The Complexity of Robot Motion Planning.
14. Hall, M., Warren, J. (1990). Adaptive polygonalization of implicitly defined surfaces. IEEE Computer Graphics and Applications, pp. 33-42.
15. Hanrahan, P. (1983). Ray tracing algebraic surfaces. Computer Graphics, 17(3):83-90.
16. 1 discrete triangular interpolation. SIAM J. Numer. Anal., 22(4):811-819.
17. Herron, G. (1985b). Smooth closed surfaces with discrete triangular interpolants. Computer Aided Geometric Design, 2(4):297-306.
18. Kalra, D., Barr, A. (1989). Guaranteed ray intersections with implicit surfaces. Proc. of the ACM Siggraph Computer Graphics, SIGGRAPH 89, 23(3):297-306.
19. Kolb, A., Pottmann, H., Seidel, H.-P. (1995). Surface reconstruction based upon minimum norm networks. In Daehlen, M., Schumaker, L.L., eds, Mathematical Methods in Curves and Surfaces, pp. 293-304. Nashville, Vanderbilt University Press.
20. Macaulay, F. (1916). The Algebraic Theory of Modular Systems.
21. Mann, S., Loop, C., Lounsberry, M., Meyers, D., Painter, J., DeRose, T., Sloan, K. (1992). A survey of parametric scattered data fitting using triangular interpolants. In Hagen, H., ed., Curve and Surface Design, pp. 145-172. Philadelphia, PA, SIAM.
22. Nasri, A. (1991). Surface interpolation on irregular networks with normal conditions. Computer Aided Geometric Design, 8:89-96.
23. 1 surface interpolation with linearly varying boundary normal. Computer Aided Geometric Design, 7:499-516.
24. Peterson, C.S. (1984). Adaptive contouring of three dimensional surfaces. Computer Aided Geometric Design, 1(00):61-74.
25. Pratt, V. (1987). Direct least squares fitting of algebraic surfaces. Computer Graphics, 21(3):145-152.
26. Sederberg, T., Zundel, A. (1989). Scan line display of algebraic surfaces. Computer Graphics, 23(3):147-156.
27. Wyvill, B., McPheeters, C., Wyvill, G. (1986). Animating soft objects. The Visual Computer, 2:235-242.