Recent methods for surface shape optimization

Computer Aided Geometric Design

Volumn 15, Issue 5, 1998, Pages 417-436

  Sarraga, Ramon F ^a  

^a GENERAL MOTORS CORPORATION   (United States)

Author keywords

CAGD; C 1 surfaces; Invariant functionals; Optimization; Smoothing; Triangular B zier patches

Indexed keywords

COMPUTER AIDED DESIGN; COMPUTER SIMULATION; FUNCTIONS; MATHEMATICAL OPERATORS; OPTIMIZATION; TENSORS;

GAUSSIAN CURVATURE; INVARIANT FUNCTIONALS; LAPLACE-BELTRAMI OPERATOR; TRIANGULAR BEZIER PATCHES;

COMPUTATIONAL GEOMETRY;

EID: 0032073331     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(97)00030-7     Document Type: Article

References (34)

1. Bloor, M.I.G. and Wilson, M.J. (1990a), Using partial differential equations to generate free-form surfaces, Computer-Aided Design 22, 202-212.
2. Bloor, M.I.G. and Wilson, M.J. (1990b), Representing PDE surfaces in terms of B-splines, Computer-Aided Design 22, 324-331.
3. Bloor, M.I.G., Wilson, M.J. and Hagen, H. (1995), The smoothing properties of variational schemes for surface design, Computer Aided Geometric Design 12, 381-394.
4. Boehm, W., Farin, G. and Kahmann, J. (1984), A survey of curve and surface methods in CAGD, Computer Aided Geometric Design 1, 1-60.
5. Brunnett, G., Hagen, H. and Santarelli, P. (1993), Variational design of curves and surfaces, Surv. Math. Ind. 3, 1-27.
6. Cavendish, J.C. and Marin, S.P. (1992), Feature-based surface design and machining, IEEE Computer Graphics and Applications 12, 61-68.
7. Celniker, G. (1990). ShapeWright: Finite element based free-form shape design. Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology.
8. Celniker, G. and Gossard, D. (1991), Deformable curve and surface finite-element for free-form shape design, ACM Computer Graphics 25, 257-266.
9. Farin, G. (1993), Curves and Surfaces for Computer Aided Design, A Practical Guide, 2nd ed., Academic Press, Cambridge, MA.
10. Fasshauer, G.E. and Schumaker, L.L. (1996), Multi patch parametric surfaces with minimal energy, Computer Aided Geometric Design 13, 45-79.
11. Gregory, J.A. (1974), Smooth Interpolation without Twist Constraints, in: Barnhill, R.E. and Riesenfeld, R.F., eds., Computer Aided Geometric Design, Academic Press, New York, 71-87.
12. Greiner, G. (1992), Blending techniques based on variational principles, Curves and Surfaces in Computer Vision and Graphics III, SPIE 1830, 174-183.
13. Greiner, G. (1994a), Surface construction based on variational principles, in: Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., Wavelets, Images, and Surface Fitting, A K Peters, Wellesley, MA, 277-286.
14. Greiner, G. (1994b), Variational design and fairing of spline surfaces, Computer Graphics Forum 13, 143-154.
15. Greiner, G. (1995), Data dependent fairness functionals, Computer Aided Geometric Design, submitted for publication.
16. Hagen, H. and Bonneau, G.P. (1993), Variational design of smooth rational Bezier-surfaces, Computing Suppl. 8, 133-138.
17. Hoschek, J. and Lasser, D. (1993), Fundamentals of Computer Aided Geometric Design, A K Peters, Wellesley, MA.
18. Kallay, M. (1993), Constrained optimization in surface design, in: Falcidieno, B. and Kunii, T.L., eds., Modeling in Computer Graphics, Springer, Berlin, 85-93.
19. Klingenberg, W. (1978), A Course in Differential Geometry, Springer, Berlin.
20. 2 surfaces, Computer-Aided Design 27, 277-282.
21. Lovelock, D. and Rund, H. (1989), Tensors, Differential Forms, and Variational Principles, Dover Publications, New York.
22. McConnell, A.J. (1957), Applications of Tensor Analysis, Dover Publications, New York.
23. Moreton, H.P. (1993), Minimum curvature variation curves, networks, and surfaces for fair free-form shape design, Ph.D. thesis, Computer Science Division, University of California, Berkeley.
24. Moreton, H.P. and Séquin, C. (1992), Functional optimization for fair surface design, ACM Computer Graphics 26, 167-176.
25. Moreton, H.P. and Séquin, C. (1993), Scale-invariant minimum-cost curves: Fair and robust design implements, Computer Graphics Forum 12, 473-484.
26. Nielson, G.M. (1983), A method for interpolating scattered data based upon a minimum norm network, Mathematics of Computation 40, 253-271.
27. 2 surface interpolation, Mathematical Modelling and Numerical Analysis 26, 1113-1135.
28. Peters, J. (1991), Smooth interpolation of a mesh of curves, Constructive Approximation 7, 221-246.
29. Piegl, L. and Tiller, W. (1995), The NURBS Book, Springer, Berlin.
30. Pottmann, H. (1991), Scattered data interpolation based upon generalized minimum norm networks, Constructive Approximation 7, 247-256.
31. Sapidis, N.S., ed. (1994), Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design, SIAM, Philadelphia.
32. Schumaker, L.L. (1987), Triangulation methods, in: Chui, C.K., Schumaker, L.L. and Utreras, F., eds., Topics in Multivariate Approximation, Academic Press, Boston, 219-232.
33. Terzopoulos, D. and Qin, H. (1994), Dynamic NURBS with geometric constraints for interactive sculpting, ACM Transactions on Graphics 13, 103-136.
34. Welch, W. and Witkin, A. (1992), Variational surface modeling, ACM Computer Graphics 26, 157-166.