Optimization methods for scattered data approximation with subdivision surfaces

Graphical Models

Volumn 67, Issue 5, 2005, Pages 452-473

  Marinov, Martin ^a   Kobbelt, Leif ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Approximation; Fitting; Reverse engineering; Shape reconstruction; Subdivision surfaces

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DATA REDUCTION; REVERSE ENGINEERING; ROBUSTNESS (CONTROL SYSTEMS);

FITTING; SHAPE RECONSTRUCTION; SUBDIVISION SURFACES;

OPTIMIZATION;

GRAPHICAL METHOD;

EID: 24944470876     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.gmod.2005.01.003     Document Type: Conference Paper

References (33)

1. C. Loop, Smooth subdivision surfaces based on triangles. Master's thesis, Department of Mathematics, University of Utah, 1987.
2. E. Catmull, and J. Clark Recursively generated B-spline surfaces on arbitrary topological meshes Comput. Aided Geom. Des. 10 6 1978 350 355
3. J. Stam, Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values, in: SIGGRAPH'98, vol. 32, 1998. pp. 395-404.
4. J. Stam, Evaluation of Loop subdivision surfaces, in: SIGGRAPH'99 Course notes, 1999.
5. U. Dietz, Erzeugung glatter Flähen aus Messpunkten. Technikal Report 1717, Department of Mathematics, University of Darmstadt, Germany, 1995.
6. N.S. Sapidis Designing fair curves and surfaces: Shape quality in geometric modeling and computer-aided design 1994 Society for Industrial and Applied Mathematics Philadelphia, PA, USA
7. A. Cohen J. Merrien L.L. Schumaker Curve and surface fitting: Saint-Malo 2002 2003 Nashboro Press Brentwood, TN
8. M. Eck, H. Hoppe, Automatic reconstruction of B-spline surfaces of arbitrary topological type. Comput. Graph. 30 (Annual Conference Series), 1996, 325-334.
9. D. Zorin, P. Schröder, W. Sweldens, T. DeRose, L. Kobbelt, A. Levin, Subdivision for modeling and animation, in: SIGGRAPH'2000 Course notes, 2000.
10. M. Halstead, M. Kass, and T. DeRose Efficient, fair interpolation using Catmull-Clark surfaces Computer graphics 1993 ACM Press New York 35 44
11. H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, W. Stuetzle, Piecewise smooth surface reconstruction, in: SIGGRAPH'94, 1994, pp. 295-302.
12. H. Suzuki, and S. Takeuchi, T. Kanai, Subdivision surface fitting to a range of points, In: Pacific Graphics, 1999, pp. 158-167.
13. S. Takeuchi, H. Suzuki, F. Kimura, T. Kanai, K. Shimada, Subdivision surface fitting using QEM-based mesh simplification and reconstruction of approximated B-spline surfaces, in: Pacific Graphics, 2000.
14. W. Ma, N. Zhao, Catmull-Clark surface fitting for reverse engineering, in: Geometric Modeling and Processing, 2000, pp. 274-284.
15. N. Litke, A. Levin, P. Schröder, Fitting subdivision surfaces, in: IEEE Visualization 2001, pp. 319-324.
16. A. Lee, H. Moreton, and H. Hoppe Displaced subdivision surfaces K. Akeley SIGGRAPH'2000 2000 ACM Press/ACM SIGGRAPH/Addison Wesley/Longman 85 94
17. N. Litke, A. Levin, and P. Schröder Trimming for subdivision surfaces Comput. Aided Geom. Des. 18 5 2001 463 481
18. W.-K. Jeong, and C.-H. Kim Direct reconstruction of a displaced subdivision surface from unorganized points Graph. Models 64 2 2002 78 93
19. W. Ma, X. Ma, S.-K. Tso, Z. Pan, Subdivision surface fitting from a dense triangle mesh, in: Geometric Modeling and Processing, 2002, pp. 94-103.
20. H. Biermann, D. Kristjansson, D. Zorin. Approximate Boolean operations on free-form solids, in: SIGGRAPH'2001, 2001, pp. 185-194.
21. D. Zorin. Subdivision and Multiresolution Surface Representations. PhD thesis, Caltech, Pasadena, California, 1997.
22. D. Cheng, W. Wang, H. Qin, K.K. Wong, H. Yang, and Y. Liu. Fitting subdivision surfaces to unorganized point data using SDM, in: Proceedings of the 12th Pacific Conference on Computer Graphics and Applications, IEEE Computer Society, 2004, pp. 16-24.
23. H. Pottmann, and S. Leopoldseder A concept for parametric surface fitting which avoids the parametrization problem Comput. Aided Geom. Des. 20 2003 350 355
24. T. Elfving. On the Conjugate Gradient Method for Solving Linear Least Squares Problems. Tech. Report LiTH-MAT-R-78-3, Linköping University, Sweden, 1978.
25. J. Bolz, P. Schröder, Rapid evaluation of Catmull-Clark subdivision surfaces, in: Proceeding of the seventh international conference on 3D Web technology, ACM Press, 2002, pp. 11-17.
26. N. Aspert, D. Santa-Cruz, T. Ebrahimi, MESH: measuring errors between surfaces using the Hausdorff distance, in: Proceedings of the IEEE International Conference on Multimedia and Expo, Vol. I, pp. 705-708, 2002. Available from: < http://mesh.epfl.ch>.
27. R.P. Brent Algorithms for minimization without derivatives 1973 Prentice-Hall Englewood Cliffs, NJ
28. H. Pottmann, and M. Hofer Geometry of the squared distance function to curves and surfaces 2003 Springer Berlin
29. M. Meyer, M. Desbrun, P. Schröder, and A.H. Barr Discrete differential-geometry operators for triangulated 2-manifolds H. Hege K. Polthier Visualization and mathematics III 2003 Springer-Verlag Heidelberg 35 57
30. V. Surazhsky, C. Gotsman, Explicit surface remeshing, in: Proceedings of Eurographics Symposium on Geometry Processing, 2003, pp. 17-28.
31. M. Garland, P.S. Heckbert, Surface simplification using quadric error metrics, Comput. Graph. 31 (Annual Conference Series) (1997) 209-216.
32. D. Zorin, and D. Kristjansson Evaluation of piecewise smooth subdivision surfaces Visual Comput. 18 5-6 2002 299 315
33. I. Guskov, and Z. Wood, Topological noise removal, in: B. Watson, J.W. Buchanan, (Eds.), Proceedings of Graphics Interface, 2001, pp. 19-26.