Dynamic catmull-clark subdivision surfaces

IEEE Transactions on Visualization and Computer Graphics

Volumn 4, Issue 3, 1998, Pages 215-229

  Qin, Hong ^a   Mandai, Chhandomay ^a   Vemuri, Baba C ^a  

^a Stony Brook University   (United States)

Author keywords

CAGD; Computer graphics; Deformable models; Dynamics; Finite elements; Interactive techniques; Subdivision surfaces; Visualization

Indexed keywords

COMPUTER AIDED DESIGN; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATHEMATICAL MODELS; RECURSIVE FUNCTIONS; SURFACES; VISUALIZATION;

DYNAMIC SUBDIVISION;

COMPUTER GRAPHICS;

EID: 0032119549     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/2945.722296     Document Type: Article

References (50)

1. G.M. Chaikin, "An Algorithm for High Speed Curve Generation," Computer Vision, Graphics, and Image Processing, vol. 3, no. 4, pp. 346-349,1974.
2. D. Doo, "A Subdivision Algorithm for Smoothing Down Irregularly Shaped Polyhedrons," Proc. Interactive Techniques in Computer Aided Design, pp. 157-165,1978.
3. M. Sabin, "The Use of Piecewise Forms for the Numerical Representation of Shape," PhD thesis, Hungarian Academy of Sciences, Budapest, 1976.
4. E. Catmull and J. Clark, "Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes," Computer Aided Design, vol. 10, no. 6, pp. 350-355,1978.
5. C. Loop, "Smooth Subdivision Surfaces Based on Triangles," M.S. thesis, Univ. of Utah, Dept. of Math., 1987.
6. H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, and W. Stuetzle, "Piecewise Smooth Surface Reconstruction," Computer Graphics Proc., ACM SIGGRAPH, pp. 295302, July 1994.
7. M. Halstead, M. Kass and T. DeRose, "Efficient, Fair Interpolation Using Catmull-Clark Surfaces," Computer Graphics Proc., ACM SIGGRAPH, pp. 35-44, Aug. 1993.
8. J. Peters and U. Reif, "The Simplest Subdivision Scheme for Smoothing Polyhedra," ACM Trans. Graphics, vol. 16, no. 4, pp. 420431, Oct. 1997.
9. N. Dyn, D. Levin, and J.A. Gregory, "A Butterfly Subdivision Scheme for Surface Interpolation With Tension Control," ACM Trans. Graphics, vol. 9, no. 2, pp. 160-169, Apr. 1990.
10. N. Dyn, S. Hed, and D. Levin, "Subdivision Schemes for Surface Interpolation," Proc. Workshop Computational Geometry, A.Conte et al., eds., pp. 97-118. World Scientific, 1993.
11. D. Zorin, P. Schröder, and W. Sweldens, "Interpolating Subdivision for Meshes with Arbitrary Topology," Computer Graphics Proc., ACM SIGGRAPH, pp. 189-192, Aug. 1996.
12. L. Kobbelt, "Interpolatory Refinement by Variational Methods," Approximation Theory Vlll, C. Chui and L. Schumaker, eds., vol. 2 of Wavelets and Multilevel Approximation, pp. 217-224. World Scientific Publishing, 1995.
13. L. Kobbelt, "A Variational Approach to Subdivision," Computer-Aided Geometric Design, vol. 13, pp. 743-761,1996.
14. L. Kobbelt and P. Schröder, "Constructing Variationally Optimal Curves Through Subdivision," Technical Report CS-TR-97-05, California Inst. of Technology, Computer Science Dept, 1997.
15. D. Doo and M. Sabin, "Analysis of the Behavior of Recursive Division Surfaces Near Extraordinary Points," Computer Aided Design, vol. 10, no. 6, pp. 356-360,1978.
16. A.A. Ball and D.J.T. Storry, "Conditions for Tangent Plane Continuity Over Recursively Generated B-Spline Surfaces," ACM Trans. Graphics, vol. 7, no. 2, pp. 83-102,1988.
17. A.A. Ball and D.J.T. Storry, "An Investigation of Curvature Variations Over Recursively Generated B-Spline Surfaces," ACM Trans. Graphics, vol. 9, no. 4, pp. 424- 437,1990.
18. U. Reif, "A Unified Approach to Subdivision Algorithms Near Extraordinary Points," Computer Aided Geometric Design, vol. 12, no. 2, pp. 153-174,1995.
19. J.E. Schweitzer, "Analysis and Application of Subdivision Surfaces," PhD thesis, Univ. of Washington, Seattle, 1996.
20. A. Habib and J. Warren, "Edge and Vertex Insertion for a Class of C Subdivision Surfaces," Computer Aided Geometric Design, to appear.
21. J. Peters and U. Reif, "Analysis of Generalized B-Spline Subdivision Algorithms," SIAM }. Numerical Analysis, to appear, available at ftp://ftp.cs.purdue.edU/pub/jorg/9697agb.ps.Z.
22. D. Zorin, "Smoothness of Stationary Subdivision on Irregular Meshes," Constructive Approximation, submitted, available as Stanford Computer Science Lab Technical Report CSL-TR-98-752, Stanford Univ., Stanford, Calif.
23. D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, "Elastically Deformable Models," Computer Graphics Proc., ACM SIGGRAPH, pp. 205-214,1987.
24. D. Terzopoulos and K. Fleischer, "Deformable Models," The Visual Computer, vol. 4, no. 6, pp. 306-331,1988.
25. A. Pentland and J. Williams, "Good Vibrations: Modal Dynamics for Graphics and Animation," Computer Graphics Proc., ACM SIGGRAPH, pp. 215-222,1989.
26. D. Metaxas and D. Terzopoulos, "Dynamic Deformation of Solid Primitives with Constraints," Computer Graphics Proc., ACM SIGGRAPH, pp. 309-312, July 1992.
27. B.C. Vemuri and A. Radisavljevic, "Multiresolution Stochastic Hybrid Shape Models With Fractal Priors," ACM Trans. Graphics, vol. 13, no. 2, pp. 177-207, Apr. 1994.
28. G. Celniker and D. Gossard, "Deformable Curve and Surface Finite Elements for Free-Form Shape Design," Computer Graphics Proc., ACM SIGGRAPH, pp. 257-266, July 1991.
29. M.I.J. Bloor and M.J. Wilson, "Representing PDE Surfaces in Terms of B-Splines," Computer Aided Design, vol. 22, no. 6, pp. 324331,1990.
30. M.I.J. Bloor and M.J. Wilson, "Using Partial Differential Equations to Generate Free-Form Surfaces," Computer Aided Design, vol. 22, no. 4, pp. 202-212,1990.
31. G. Celniker and W. Welch, "Linear Constraints for Deformable BSpline Surfaces," Proc. Symp. Interactive 3D Graphics, pp. 165-170, New York, 1992.
32. W. Welch and A. Witkin, "Variational Surface Modeling," Computer Graphics Proc., ACM SIGGRAPH, pp. 157-166, July 1992.
33. H. Qin and D. Terzopoulos, "Dynamic NURBS Swung Surfaces for Physics-Based Shape Design," Computer-Aided Design, vol. 27, no. 2, pp. 111-127,1995.
34. H. Qin and D. Terzopoulos, "D-NURBS: A Physics-Based Framework for Geometric Design," IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 1, pp. 85-96, Mar. 1996.
35. D. Terzopoulos and H. Qin, "Dynamic NURBS with Geometric Constraints for Interactive Sculpting," ACM Trans. Graphics, vol. 13, no. 2, pp. 103-136, Apr. 1994.
36. L.D. Cohen and I. Cohen, "Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 11, pp. 1,131-1,147, Nov. 1993.
37. D. Terzopoulos and D. Metaxas, "Dynamic 3D models With Local and Global Deformations: Deformable superquadrics," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 703-714, July 1991.
38. D. Metaxas and D. Terzopoulos, "Shape and Nonrigid Motion Estimation Through Physics-Based Synthesis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 6, pp. 580-591, June 1993.
39. A. Pentland and B. Horowitz, "Recovery of Nonrigid Motion and Structure," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 730-742, July 1991.
40. Y. Chen and G. Medioni, "Surface Description of Complex Objects from Multiple Range Images," Proc. Conf. Computer Vision and Pattern Recognition, pp. 153-158, Seattle, Wash., June 1994.
41. W.C. Huang and D. Goldgof, "Adaptive-Size Physically-Based Models for Nonrigid Motion Analysis," Proc. Conf. Computer Vision and Pattern Recognition, pp. 833-835, Urbana-Champaign, 111., June 1992.
42. E. Koh, D. Metaxas, and N. Badler, "Hierarchical Shape Representation Using Locally Adaptive Finite Elements," Lecture Notes in Computer Science, Computer Vision-ECCV 1994, J.O. Eklundh, ed., vol. 800, pp. 441-446. Berlin: Springer-Verlag, 1994.
43. T. Mclnerney and D. Terzopoulos, "A Finite Element Model for 3D Shape Reconstruction and Nonrigid Motion Tracking," Proc. Int'l Conf. Computer Vision, pp. 518-523, Berlin, May 1993.
44. H. Tanaka and F. Kishino, "Adaptive Mesh Generation for Surface Reconstruction: Parallel Hierarchical Triangulation Without Discontinuities," Proc. Conf. Computer Vision and Pattern Recognition, pp. 88-94, New York, June 1993.
45. M. Vasilescu and D. Terzopoulos, "Adaptive Meshes and Shells: Irregular Triangulation, Discontinuities and Hierarchical Subdivision," Proc. Conf. Computer Vision and Pattern Recognition, pp. 829832, Urbana-Champaign, 111., June 1992.
46. B.R. Gossick, Hamilton's Principle and Physical Systems. New York: Academic Press, 1967.
47. D. Terzopoulos, "Regularization of Inverse Visual Problems Involving Discontinuities," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 4, pp. 413-424, July 1986.
48. H. Kardestuncer, The Finite Element Handbook. New York: McGrawHill, 1987.
49. O. Monga and R. Deriche, "3D Edge Detection Using Recursive Filtering," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 28-35, June 1989.
50. G.H. Golub and V.H. Van Loan, Matrix Computation. The Johns Hopkins Univ. Press, 1989.