Energy Minimizers for Curvature-Based Surface Functionals

Computer-Aided Design and Applications

Volumn 4, Issue 5, 2007, Pages 607-617

  Joshi, Pushkar ^a   Séquin, Carlo ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Aesthetic design; Bending energy; Curvature variation; Surface optimization

Indexed keywords

AESTHETIC DESIGN; BENDING ENERGY; CURVATURE VARIATION; SURFACE OPTIMIZATION;

COMPUTER AIDED DESIGN; FUNCTION EVALUATION; VARIATIONAL TECHNIQUES;

CURVE FITTING;

EID: 34250744622     PISSN: 16864360     EISSN: None     Source Type: Journal    
DOI: 10.1080/16864360.2007.10738495     Document Type: Article

References (26)

1. Benson, S.,; Curfman, L.,; More, J.,; Sarich, J., :TAO user manual (revision 1.8). Technical Report ANL/MCS-TM-242, Mathematics and Computer Science Division, Argonne National Laboratory (2005) http://www.mcs.anl.gov/tao
2. Biermann, H.,; Levin, A.,; Zorin, D., :Piecewise smooth subdivision surfaces with normal control, ACM SIGGRAPH (2000).
3. Birkhoff, G. D., :Aesthetic Measure. Harvard University Press, Cambridge, Mass. (1933).
4. Brakke, K., :The Surface Evolver. Experimental Mathematics, 1(2), 1992, 141–165.
5. Bobenko, A.,; Schroeder, P., :Discrete Willmore flow, Eurographics Symposium on Geometry Processing, 2005.
6. Catmull, E.,; Clark, J., :Recursively generated B-spline surfaces on arbitrary topological surfaces, Computer-Aided Design, 10(6), 1978, 350–355.
7. DeRose, T.,; Kass, M.,; Truong, T., :Subdivision Surfaces in Character Animation, ACM SIGGRAPH, 1998, 85–94.
8. Gravesen, J.,; Ungstrup, M., :Constructing Invariant Fairness Measures for Surfaces, Advances in Computational Mathematics, 17, 2002, 67–88.
9. Grimm, C.,; Hughes, J., :Modeling surfaces of arbitrary topology using manifolds, ACM SIGGRAPH, 1995.
10. Grinspun, E.,; Gingold, Y.,; Reisman, J.,; Zorin, D., :Computing discrete shape operators on general meshes, Eurographics, 2006
11. Hari, L.,; Rivoli, D.,; Rubinstein, J., :Computation of open Willmore-type surfaces, Appl. Numeri. Math., 37(1–2) 2001
12. Hsu, L.,; Kusner, R.,; Sullivan, J., :Minimizing the squared mean curvature integral for surfaces in space forms, Experimental Math 1, 3, 1992, 191–207
13. Lawson, H., Jr.: Complete minimal surfaces in S3. Ann. Of Math., 92(2), 1970
14. Levin, A., :Modified subdivision surfaces with continuous curvature, ACM SIGGRAPH, 2006
15. Kusner, R., :Conformal geometry and complete minimal surfaces, Bulletin of American Math Society, 17, 1987
16. Mehlum, E.,; Tarrou, C., :Invariant fairness measures for surfaces, Adv. in Comp. Math., 8(1), 1998, 49–63
17. Moreton, H.,; Séquin, C. H., :Functional optimization for fair surface design, ACM SIGGRAPH, 1992, 167–176
18. Reif, U.,; Schroeder, P., :Curvature integrability of subdivision surfaces, Adv. in Comp. Math., 14, 2001
19. Sabin, M.,; Dodgson, N.,; Hassan, M.,; Ivrissimtzis, I., :Curvature behaviours at extraordinary points of subdivision surfaces, Computer-Aided Design, 35, 2003, 1047–1051, 2003
20. Scherk, H. F., :Bemerkungen über die kleinste Flache innerhalb gegebener Grenzen, J. Reine Angew. Math. (Crelle’s Journal) 13, 1835, 185–208
21. Séquin, C. H., :CAD Tools for Aesthetic Engineering, Computer-Aided Design & Applications, 1(1-4),2004, 301–309
22. Séquin, C.,; Chang, P.,; Moreton, H., :Scale-invariant functionals for smooth curves and surfaces, Dagstuhl Seminar on Geometric Modelling, 1993
23. Stam, J., :Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values, ACM SIGGRAPH, 1998, 395–404
24. Willmore, T., :Note on embedded surfaces, Anal. Stunt. Ale Univ. Sect. I. a Math., 11, 1965
25. Xu, G.,; Pan, Q.,; Bajaj, C., :Discrete surface modelling using partial differential equations, Computer Aided Geometric Design, 23, 2006, 125–145
26. Ying, L.,; Zorin, D., :A simple manifold-based construction of surfaces of arbitrary smoothness, ACM SIGGRAPH, 2004