Discrete fairing and variational subdivision for freeform surface design

Visual Computer

Volumn 16, Issue 3, 2000, Pages 142-158

  Kobbelt, Leif P ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; COMPUTER AIDED DESIGN; COMPUTER SIMULATION; CONSTRAINT THEORY; INTEGRAL EQUATIONS; INTERPOLATION; MATRIX ALGEBRA; OPTIMIZATION;

FREEFORM SURFACE DESIGN; GEOMETRIC MODELING; VARIATIONAL SUBDIVISION;

COMPUTER GRAPHICS;

EID: 0033704837     PISSN: 01782789     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003710050204     Document Type: Article

References (42)

1. Carmo M do (1976) Differential geometry of curves and surfaces. Prentice Hall, Englewood Cliffs, New Jersey
2. Catmull E, Clark J (1978) Recursively generated B-spline surfaces on arbitrary topological meshes. CAD 10:350-355
3. Celniker G, Gossard D (1991) Deformable curve and surface finite elements for free-form shape design. Proceedings of SIGGRAPH '91, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 257-265
4. Ciampalini A, Cignoni P, Montani C, Scopigno R (1997) Multiresolution decimation based on global error. Visual Comput 13:228-246
5. Doo D, Sabin M (1978) Behaviour of recursive division surfaces near extraordinary points. CAD 10:356-360
6. Dyn N, Gregory J, Levin D (1990) A butterfly subdivision scheme for surface interpolation with tension controll. ACM Trans Graph 9:160-169
7. Dyn N (1991) Subdivision schemes in computer aided geometric design. In: Light WA (ed) Advances in numerical analysis II. Oxford University Press, Oxford, UK, pp 36-104
8. Farin G (1996) Curves and surfaces for CAGD. 4th edn. Academic Press, San Diego, CA
9. Forsey D, Bartels R (1998) Hierarchical B-spline refinement. Proceedings of SIGGRAPH '88, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 205-212
10. Forsey D, Bartels R (1995) Surface fitting with hierarchical splines. ACM Trans Graph 14:134-161
11. Garland M, Heckbert P (1997) Surface simplification using quadric error metrics. Proceedings of SIGGRAPH '97, Annual Conference Series on Computer Graphics, ACM SIGGRAPH. Addison Wesley, pp 209-218
12. Greiner G (1994) Variational design and fairing of spline surfaces. Comput Graph Forum 13:143-154
13. Guskov I, Sweldens W, Schröder P, (1999) Multiresolution Signal Processing for Meshes. Proceedings of SIGGRAPH '99, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 325-334
14. Hackbusch W (1985) Multi-grid methods and applications. Springer, Berlin
15. Hagen H, Schulze G (1987) Automatic smoothing with geometric surface patches. CAGD 4:231-235
16. Halstead M, Kass M, DeRose T (1993) Efficient fair interpolation using catmull-clark surfaces. Proceedings of SIGGRAPH '93, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 35-44
17. Hoppe H (1996) Progressive meshes. Proceedings of SIGGRAPH '96, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 99-108
18. Hoschek J, Lasser D (1993) Fundamentals of computer-aided geometric design. A.K. Peters, Natick, MA
19. Klein R (1995) Netzgenerierung impliziter und parametrisierter Kurven und Flächen in einem objektorientierten System Ph Thesis, Computer Science Department, University of Tübingen, Tübingen
20. Kobbelt L (1996) A variational approach to subdivision. CAGD 13:743-761
21. Kobbelt L (1996) Interpolatory subdivision on open quadrilateral nets with arbitrary topology. Comput Graph Forum 15:409-420
22. Kobbelt L (1997) Discrete fairing. Proceedings of the 7th IMA Conference on the Mathematics of Surfaces, Dundee, UK, Information Geometers, Winchester, UK, pp 101-131
23. Kobbelt L, Campagna S, Seidel H-P (1998) A general framework for mesh decimation. Proceedings of the Graphics Interface conference '98, Vancouver, CAN, Morgan Kaufmann Publishers, pp 43-50
24. Kobbelt L, Campagna S, Vorsatz J, Seidel H-P (1998) Interactive multi-resolution modeling on arbitrary meshes. Proceedings of SIGGRAPH '98, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 105-114
25. Lane J, Riesenfeld R (1980) A theoretical development for the computer generation and display of piecewise polynomial surfaces. IEEE Trans Patt Anal Machine Intell 2:35-46
26. Loop C (1987) Smooth subdivision surfaces based on triangles. Master's Thesis, Utah University, Salt Lake City, Utah
27. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. Proceedings of SIGGRAPH '87 Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 163-169
28. Levy B, Mallet J (1998) Non-distorted texture mapping for sheared triangulated meshes. Proceedings of SIGGRAPH '98, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 343-352
29. Mandal C, Qin H, Vemuri B (1997) Dynamic smooth subdivision surfaces for data visualization. IEEE Vis'97 proceedings, Phoenix, AZ, pp 371-377
30. Moreton H, Séquin C (1992) Functional optimization for fair surface design. Proceedings of SIGGRAPH '92, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 167-176
31. Prautzsch H, Kobbelt L (1994) Convergence of subdivision and degree elevation. Adv Comput Math 2:143-154
32. Reif U (1995) A unified approach to subdivision algorithms near extraordinary vertices. CAGD 12:153-174
33. Ronfard R, Rossignac J (1996) Full-Range Approximation of Triangulated Polyhedra. Comput Graph Forum 15:C67-C76
34. Sapidis N (ed) (1994) Designing fair curves and surfaces. SIAM, Philadelphia
35. Schroeder W, Zarge J, Lorensen W (1992) Decimation of triangle meshes. Proceedings of SIGGRAPH '92, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 65-70
36. Taubin G (1995) A signal processing approach to fair surface design. Proceedings of SIGGRAPH '95, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 351-358
37. Warren J (1998) Subdivision schemes for variational splines. CAGD (to appear)
38. Weimer H, Warren J (1998) Subdivision schemes for thin plate splines. Comput Graph Forum 17:C303-C313
39. Welch W, Witkin A (1992) Variational surface modeling. Proceedings of SIGGRAPH '92, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 157-166
40. Welch W, Witkin A (1994) Free-form shape design using triangulated surfaces. Proceedings of SIGGRAPH '94, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 247-256
41. k Continuity of subdivision surfaces. Ph Thesis, Computer Science Department, California Institute of Technology, Pasadena, CA
42. Zorin D, Schröder P, Sweldens W (1996) Interpolating subdivision for meshes with arbitrary topology. Proceedings of SIGGRAPH '96, Annual Conference Series on Computer Graphics, ACM SIGGRAPH, Addison Wesley, pp 189-192