A framework for quad/triangle subdivision surface fitting: Application to mechanical objects

Computer Graphics Forum

Volumn 26, Issue 1, 2007, Pages 1-14

  Lavoué, Guillaume ^a   Dupont, Florent ^a   Baskurt, Atilla ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

Approximation; CAD; Mesh; Subdivision curve; Subdivision surface

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER AIDED DESIGN; IMAGE COMPRESSION; ITERATIVE METHODS; OPTIMIZATION;

BOUNDARY CONTROL; SUBDIVISION CURVES; SURFACE APPROXIMATION;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 33947705320     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2007.00930.x     Document Type: Article

References (30)

1. ALLIEZ P., COHEN-STEINER D., DEVILLERS O., LEVY B., DESBRUN M.: Anisotropic polygonal remeshing. ACM Transactions on Graphics, 22(3): 485-493, 2003.
2. CATMULL E., CLARK J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design, 10(6): 350-355, 1978.
3. COHEN-STEINER D., MORVAN J.: Restricted Delaunay triangulations and normal cycle. In 19th Annual ACM Symposium of Computational Geometry, pp. 237-246, 2003.
4. CHENG K.-S.-D., WANG W., QIN H., WONG K.-Y.-K., YANG H.-R, LIU Y.: Fitting subdivision surfaces to unorganized point data using SDM. In IEEE Pacific graphics, pp. 16-24, 2004.
5. GARLAND M., HECKBERT P.: Surface simplification using quadric error metrics. ACM SIGGRAPH, pp. 209-216, 1997.
6. GUMHOLD S., STRASSER W.: Real time compression of triangle mesh connectivity. In ACM SIGGRAPH, pp. 133-140, 1998.
7. HOPPE H., DEROSE T., DUCHAMP T., HALSTEAD M., JIN H., MCDONALD J., SCHWEITZER J., STUETZLE W.: Piecewise smooth surface reconstruction. In ACM SIGGRAPH, vol. 28, pp. 295-302, 1994.
8. HERTEL S., MEHLHORN K.: Fast triangulation of simple polygons. Lecture Notes In Computer Science, Proceedings of the International FCT-Conference on Fundamentals of Computation Theory 158, 207-218, 1983.
9. HILDEBRANDT K., POLTHIER K., WARDETZKY M.: Smooth feature lines on surface meshes. In Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 85-90, 2005.
10. ISENBURG M., SNOEYINK J.: Face fixer: Compressing polygon meshes with properties. In ACM SIGGRAPH, pp. 263-270, 2001.
11. JEONG W., KIM C. H.: Direct reconstruction of displaced subdivision surface from unorganized points. Journal of Graphical Models, 64(2): 78-93, 2002.
12. KANAI T.: Meshtoss-converting subdivision surfaces from dense meshes. In 6th International Workshop on Vision, Modeling and Visualization, pp. 325-332, 2001.
13. KHODAKOVSKY A., SCHRODER P., SWELDENS W.: Progressive geometry compression. In ACM SIGGRAPH, pp. 271-278, 2000.
14. LAVOUÉ O., DUPONT F., BASKURT A.: A new CAD mesh segmentation method, based on curvature tensor analysis. Computer-Aided Design, 37(10): 975-987, 2005.
15. LAVOUÉ G., DUPONT F., BASKURT A.: A new sub-division based approach for piecewise smooth approximation of 3D polygonal curves. Pattern Recognition, 38(8): 1139-1151, 2005.
16. LITRE N., LEVIN A., SCHRODER P.: Fitting subdivision surfaces. In IEEE Visualization, pp. 319-324, 2001.
17. LEE A., MORETON H., HOPPE H.: Displaced subdivision surfaces. In ACM SIGGRAPH, pp. 85-94, 2000.
18. LOOP C.: Smooth Subdivision Surfaces Based on Triangles. Masterís thesis, Utah University, 1987.
19. MARINOV M., KOBBELT L.: Optimization methods for scattered data approximation with subdivision surfaces. Journal of Graphical Models 67(5): 452-473, 2005.
20. MA W., MA X., TSO S., PAN Z.: A direct approach for subdivision surface fitting from a dense triangle mesh. Computer Aided Design. 36(16): 525-536, 2004.
21. MPEG4: Iso-iec 14496-16, coding of audiovisual objects: Animation framework extension (afx).
22. MONGKOLNAM P., RAZDAN A., FARIN G.: Lossy 3D mesh compression using loop scheme. In International Conference on Computers, Graphics, and Imaging, pp. 103-110, 2003.
23. POTTMANN H., HOFER M.: Geometry of the squared distance function to curves and surfaces. Visualization and Mathematics III, 221-242, 2003.
24. POTTMANN H., LEOPOLDSEDER S.: A concept for parametric surface fitting which avoids the parametrization problem. Computer Aided Geometric Design, 20(6): 343-362, 2003.
25. STAM J., LOOP C.: Quad/triangle subdivision. Computer Graphics Forum, 22(1): 79-85, 2003.
26. SUSUKI H.: Subdivision surface fitting to a range of points. In IEEE Pacific graphics, pp. 158-167, 1999.
27. SCHAEFER S., WARREN J., ZORIN D.: Lofting curve networks using subdivision surfaces. In Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 105-116, 2004.
28. TOUMA C. A., GOTSMAN C.: Triangle mesh compression. In Graphic Interface Conference, pp. 26-34, 1998.
29. VALETTE S., PROST R.: A wavelet-based progressive compression scheme for triangle meshes: Wavemesh. In IEEE Visualization and Computer Graphics, 10(2): 123-129, 2004.
30. WU J., KOBBELT L.: Structure recovery via hybrid variational surface approximation. Computer Graphics Forum, 24(3): 277-284, 2005.