Polynomial splines over hierarchical T-meshes

Graphical Models

Volumn 70, Issue 4, 2008, Pages 76-86

  Deng, Jiansong ^a   Chen, Falai ^a   Li, Xin ^a   Hu, Changqi ^a   Tong, Weihua ^a   Yang, Zhouwang ^a   Feng, Yuyu ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Local refinement; NURBS; Shape simplification; Surface fitting; T mesh; T splines

Indexed keywords

LINEAR EQUATIONS; LINEAR SYSTEMS; POLYNOMIAL APPROXIMATION; POLYNOMIALS;

ADAPTIVITY; B-SPLINES; CONSTRUCTION PROCESSES; CONTROL POINTS; FUNDAMENTAL OPERATIONS; GEOMETRIC OBJECTS; GEOMETRY PROCESSING; LOCAL REFINEMENT; LOCAL SUPPORTS; MESH MODELING; NON-NEGATIVITY; NURBS; NURBS SURFACES; PARTITION OF UNITY; POLYNOMIAL SPLINES; SHAPE SIMPLIFICATION; SPLINE BASIS FUNCTIONS; SURFACE FITTING; SURFACE MODELING; T-MESH; T-SPLINES;

SPLINES;

COMPUTER SIMULATION; GEOMETRY; NUMERICAL MODEL; SHAPE ANALYSIS;

EID: 52949151175     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.gmod.2008.03.001     Document Type: Article

References (25)

1. Chinvate P., and Jablokow A. Review of surface representation and fitting for reverse engineering. Computer Integrated Manufacturing Systems 8 3 (1995) 193-204
2. Deng J., Chen F., and Feng Y. Dimensions of spline spaces over T-meshes. Journal of Computational and Applied Mathematics 194 2 (2006) 267-283
3. Eck M., DeRose T., Duchamp T., Hoppe H., Lounsbery M., and Stuetzle W. Multiresolution analysis of arbitrary meshes. SIGGRAPH'95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques (1995), ACM Press, New York, NY, USA 173-182
4. Farin G. Curves and Surfaces for CAGD-A Practical Guide. 5th ed. (2002), Morgan Kaufmann Publishers
5. Floater M.S., and Hormann K. Parameterization of triangulations and unorganized points. In: Iske A., Quak E., and Floater M.S. (Eds). Tutorials on Multiresolution in Geometric Modelling (2002), Springer-Verlag 287-316
6. Floater M.S., and Hormann K. Surface parameterization: A tutorial and survey. In: Dodgson N.A., Floater M.S., and Sabin M.A. (Eds). Advances in Multiresolution for Geometric Modelling (2004), Springer-Verlag, Heidelberg 157-186
7. Forsey D.R., and Bartels R.H. Hierarchical B-spline refinement. Computer Graphics 22 4 (1988) 205-212
8. Forsey D.R., and Bartels R.H. Surface fitting with hierarchical splines. ACM Transactions on Graphics 14 2 (1995) 134-161
9. Franke R., and Nielson G.M. Scattered data interpolation and applications: a tutorial and survey. In: Hagen H., and Roller D. (Eds). Geometric Modeling (1991), Springer, Berlin 131-161
10. Gotsman C., Gu X., and Sheffer A. Fundamentals of spherical parameterization for 3D meshes. ACM Transactions on Graphics 22 3 (2003) 358-363
11. Grinspun E., Krysl P., and Schröder P. Charms: a simple framework for adaptive simulation. ACM Transactions on Graphics 21 3 (2002) 281-290
12. Gu X., Wang Y., Chan T.F., Thompson P.M., and Yau S.-T. Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Transaction on Medical Imaging 7 (2004) 949-958
13. Jüttler B. Least-squares fitting of algebraic spline curves via normal vector estimation. Proceedings of the 9th IMA Conference on the Mathematics of Surfaces (2000), Springer-Verlag 263-280
14. Jüttler B., and Felis A. Least-squares fitting of algebraic spline surfaces. Advances in Computational Mathematics 17 (2002) 135-152
15. Kraft R. Adaptive and linearly independent multilevel B-splines. In: Méhauté A.L., Rabut C., and Schumaker L.L. (Eds). Surface Fitting and Multiresolution Methods (1997), Vanderbilt University Press, Nashville 209-218
16. Lee S., Wolberg G., and Shin S.Y. Scattered data interpolation with multilevel B-splines. IEEE Transactions on Visualization and Computer Graphics 3 3 (1997) 228-244
17. Lee S.L., and Majid A.A. Closed smooth piecewise bicubic surfaces. ACM Transactions on Graphics 10 4 (1991) 342-365
18. Li C.J., Wang R.H., and Zhang F. Improvement on the dimension of spline on T-mesh. Journal of Information and Computational Science 3 2 (2006) 235-244
19. Praun E., and Hoppe H. Spherical parametrization and remeshing. ACM Transaction on Graphics 22 3 (2003) 340-349
20. Sederberg T.W., Cardon D.L., Finnigan G.T., North N.S., Zheng J., and Lyche T. T-spline simplification and local refinement. ACM Transactions on Graphics 23 3 (2004) 276-283
21. Sederberg T.W., Zheng J., Bakenov A., and Nasri A. T-splines and T-NURCCs. ACM Transactions on Graphics 22 3 (2003) 161-172
22. Weller F., and Hagen H. Tensor product spline spaces with knot segments. In: Daehlen M., Lyche T., and Schumaker L.L. (Eds). Mathematical Methods for Curves and Surfaces (1995), Vanderbilt University Press, Nashville 563-572
23. Yang Z., Deng J., and Chen F. Fitting point clouds with active implicit B-spline curves. The Visual Computer (Special Issue for Pacific Graphics 2005) 21 8-10 (2005) 831-839
24. Zheng J., Wang Y., and Seah H.S. Adaptive T-spline surface fitting to z-map models. GRAPHITE'05: Proceedings of the 3rd international conference on computer graphics and interactive techniques in Australasia and South East Asia (2005), ACM Press, New York, NY, USA 405-411
25. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method, Volume 1: The Basis. 5th ed. (2004), Elsevier (Singapore) Pte Ltd.