A variational approach to spline curves on surfaces

Computer Aided Geometric Design

Volumn 22, Issue 7 SPEC. ISS., 2005, Pages 693-709

  Pottmann, Helmut ^a   Hofer, Michael ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Curves in manifolds; Shape optimization; Spline approximation; Spline interpolation; Variational curve design

Indexed keywords

APPROXIMATION THEORY; IMAGE PROCESSING; INTERPOLATION; MATHEMATICAL MODELS; MOTION PLANNING; NUMERICAL ANALYSIS; OPTIMIZATION;

CURVES IN MANIFOLDS; SHAPE OPTIMIZATION; SPLINE APPROXIMATION; SPLINE INTERPOLATION; VARIATIONAL CURVE DESIGN;

COMPUTER AIDED DESIGN;

EID: 24644482697     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2005.06.006     Document Type: Conference Paper

References (41)

1. A. Blake, and M. Isard Active Contours 1998 Springer Berlin
2. Bohl, H., 1999. Kurven minimaler Energie auf getrimmten Flächen. PhD thesis, Univ. Stuttgart, Germany
3. G. Brunnett, and P.E. Crouch Elastic curves on the sphere Adv. Comp. Math. 2 1994 23 40
4. G. Brunnett, P.E. Crouch, and F. Silva Leite Spline elements on spheres M. Daehlen T. Lyche L. Schumaker Mathematical Methods for Curves and Surfaces 1995 Vanderbilt Univ. Press 49 54
5. G. Brunnett, H. Hagen, and P. Santarelli Variational design of curves and surfaces Surv. Math. Ind. 3 1993 1 27
6. M. Camarinha, F. Silva Leite, and P.S. Crouch On the geometry of Riemannian cubic polynomials Differential Geom. Appl. 15 2001 107 135
7. B.-T. Cheng, P. Burchard, B. Merriman, and S. Osher Motion of curves constrained on surfaces using a level set approach J. Comput. Phys. 175 2 2002 604 644
8. R. Dietz, J. Hoschek, and B. Jüttler An algebraic approach to curves and surfaces on the sphere and on other quadrics Computer Aided Geometric Design 10 1993 211 229
9. C. Geiger, and C. Kanzow Theorie und Numerik restringierter Optimierungsaufgaben 2002 Springer Heidelberg
10. I.M. Gelfand, and S.V. Fomin Calculus of Variations 1963 Prentice-Hall Englewood Cliffs, NJ
11. M. Hofer, H. Pottmann, and B. Ravani Geometric design of motions constrained by a contacting surface pair Computer Aided Geometric Design 20 2003 523 547
12. M. Hofer, and H. Pottmann Energy-minimizing splines in manifolds Proceedings of ACM SIGGRAPH 2004 Trans. Graph. 23 3 2004 284 293
13. J. Hoschek, and D. Lasser Fundamentals of Computer Aided Geometric Design 1993 A.K. Peters Wellesley, MA
14. B. Jüttler, and M. Wagner Kinematics and animation G. Farin M.-S. Kim J. Hoschek Handbook of Computer Aided Geometric Design 2002 North Holland Amsterdam 723 748
15. C.T. Kelley Iterative Methods for Optimization 1999 SIAM Philadelphia
16. M.-J. Kim, M.-S. Kim, and S. Shin A general construction scheme for unit quaternion curves with simple high order derivatives SIGGRAPH '95 Comput. Graph. 29 1995 369 376
17. R. Kimmel, R. Malladi, and N. Sochen Images as embedded maps and minimal surfaces: movies, color, texture and volumetric medical images Internat. J. Computer Vision 39 2000 111 129
18. F. Memoli, and G. Sapiro Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces J. Comp. Phys. 173 2001 730 764
19. H. Moreton, and C. Sequin Scale-invariant minimum-cost curves: fair and robust design implements Comput. Graph. Forum 12 1993 473 484
20. J.W. Neuberber Sobolev Gradients and Differential Equations 1997 Springer Heidelberg
21. L. Noakes, G. Heinzinger, and B. Paden Cubic splines on curved spaces IMA J. Math. Control Inform. 6 1989 465 473
22. L. Noakes Non-linear corner cutting Adv. Comp. Math. 8 1998 165 177
23. L. Noakes Accelerations of Riemannian quadratics Proc. Amer. Math. Soc. 127 1999 1827 1836
24. L. Noakes Null cubics and Lie quadratics J. Math. Phys. 44 3 2003 1436 1448
25. S. Osher N. Paragios Geometric Level Set Methods 2003 Springer New York
26. F.C. Park, and B. Ravani Bézier curves on Riemannian manifolds and Lie groups with kinematic applications ASME J. Mech. Design 115 1995 36 40
27. F.C. Park, and B. Ravani Smooth invariant interpolation of rotations ACM Trans. Graph. 16 1997 277 295
28. H. Pottmann, and J. Wallner Computational Line Geometry 2001 Springer Heidelberg
29. R. Ramamoorthi, and A. Barr Fast construction of accurate quaternion splines SIGGRAPH '97 Comput. Graph. 31 1997 287 292
30. C.H. Reinsch Smoothing by spline functions Numer. Math. 10 1967 177 183
31. G. Renner, and V. Weiss Exact and approximate computation of B-spline curves on surfaces Computer-Aided Design 36 2004 351 362
32. O. Röschel Rational motion design - a survey Computer-Aided Design 30 1998 169 178
33. G. Sapiro Geometric Partial Differential Equations and Image Analysis 2001 Cambridge Univ. Press Cambridge
34. D. Schweikert An interpolation curve using a spline in tension J. Math. Phys. 45 1966 312 317
35. K. Shoemake Animating rotations with quaternion curves SIGGRAPH '85 Comput. Graph. 19 1985 245 254
36. Sprott, K., Ravani, B., 1997. Ruled surfaces, Lie groups and mesh generation. In: Proc. ASME Design Eng. Techn. Conf. No DETC97/DAC-3966
37. K. Strubecker Differentialgeometrie II: Theorie der Flächenmetrik 1969 Walter de Gruyter Berlin
38. T. Várady, and R. Martin Reverse Engineering G. Farin J. Hoschek M.-S. Kim Handbook of Computer Aided Geometric Design 2002 Elsevier Amsterdam 651 681
39. G. Wahba Spline Models for Observational Data 1990 SIAM Philadelphia
40. J. Wallner Existence of set-interpolating and energy-minimizing curves Computer Aided Geometric Design 21 9 2004 837 857
41. 1 analysis of subdivision schemes on manifolds by proximity. Computer Aided Geometric Design 22. In press