WireWarping: A fast surface flattening approach with length-preserved feature curves

CAD Computer Aided Design

Volumn 40, Issue 3, 2008, Pages 381-395

  Wang, Charlie C L ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Feature curves; Freeform mesh surfaces; Length preserved; Sheet manufacturing industry; Surface flattening

Indexed keywords

OPTIMIZATION; SHEET METAL; THREE DIMENSIONAL; WIRE;

FEATURE CURVES; FREEFORM MESH SURFACES; SHEET MANUFACTURING INDUSTRY; SURFACE FLATTENING;

COMPUTER AIDED MANUFACTURING;

EID: 39949083957     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2007.11.011     Document Type: Article

References (45)

1. Azariadis P.N., and Aspragathos N.A. Design of plane development of doubly curved surface. Computer-Aided Design 29 (1997) 675-685
2. Azariadis P.N., and Aspragathos N.A. Geodesic curvature preservation in surface flattening through constrained global optimization. Computer-Aided Design 33 8 (2001) 581-591
3. Aono M., Breen D.E., and Wozny M.J. Modeling methods for the design of 3D broadcloth composite parts. Computer-Aided Design 33 (2001) 989-1007
4. Aono M., Breen D.E., and Wozny M.J. Fitting a woven-cloth model to a curved surface: Mapping algorithms. Computer-Aided Design 26 (1994) 278-292
5. Azariadis P.N., and Sapidis N.S. Planar development of free-form surfaces: quality evaluation and visual inspection. Computing 72 1-2 (2004) 13-27
6. Belkin M., and Niyogi P. Laplacian Eigenmaps for dimensionality reduction and data representation. Neural Computation 15 (2003) 1373-1396
7. Chapra S.C., and Canale R.P. Numerical methods for engineers: With software and programming applications. 4th ed. (2003) p. 289-95
8. Bennis C., Vezjen J.-M., and Iglesias G. Piecewise surface flattening for non-distorted texture mapping. Computer Graphics 24 4 (1991) 237-246
9. Chen H.-Y., Lee I.-K., Leopoldseder S., Pottmann H., Randrup T., and Wallner J. On surface approximation using developable surfaces. Graphical Models and Image Processing 61 (1999) 110-124
10. Chu C.H., and Séquin C.H. Developable Bézier patches: Properties and design. Computer-Aided Design 34 7 (2002) 511-527
11. Duff I.S., Erisman A.M., and Reid J.K. Direct methods for sparse matrices (1989), Clarendon Press, Oxford
12. Decaudin P., Julius D., Wither J., Boissieux L., Sheffer A., and Cani M.-P. Virtual garments: A fully geometric approach for clothing design. Computer Graphics Forum 25 3 (2006) 625-634
13. Desbrun M., Meyer M., and Alliez P. Intrinsic parameterizations of surface meshes. Computer Graphics Forum 21 3 (2002) 209-218
14. do Carmo MP. Differential geometry of curves and surfaces. Englewood Cliffs (NJ): Prentice-Hall
15. 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 (2005), Springer-Verlag, Heidelberg 157-186
16. Karni Z, Gotsman C, Gortler SJ. Free-boundary linear parameterization of 3D meshes in the presence of constraints. In: Proceedings of shape modeling international. 2005. p. 266-75
17. Li S, Demmel J, Gilbert J. SuperLU, http://crd.lbl.gov/xiaoye/SuperLU/, February 2006
18. Lee Y., Kim H.-S., and Lee S. Mesh parameterization with a virtual boundary. Computers & Graphics 26 (2002) 677-686
19. Leopoldseder S., and Pottmann H. Approximation of developable surfaces with cone spline surfaces. Computer-Aided Design 30 (1998) 571-582
20. Lévy B., Petitjean S., Ray N., and Maillot J. Least squares conformal maps for automatic texture atlas generation. ACM Transactions on Graphics 21 (2002) 362-371
21. Liu Y., Pottmann H., Wallner J., Yang Y.-L., and Wang W. Geometric modeling with conical meshes and developable surfaces. ACM Transactions on Graphics 25 3 (2006) 681-689
22. Liu YS, Yu PQ, Du MC, Yong JH, Zhang H, Paul JC. Mesh parameterization for an open connected surface without partition. In: Proceedings of the ninth international conference on computer aided design and computer graphics. 2005. p. 306-10
23. Manning J.R. Computerized pattern cutting: Methods based on an isometric tree. Computer-Aided Design 12 1 (1980) 43-47
24. Autodesk Maya, http://www.autodesk.com/maya
25. McCartney J., Hinds B.K., and Seow B.L. The flattening of triangulated surfaces incorporating darts and gussets. Computer-Aided Design 31 (1999) 249-260
26. Mortenson M.E. Geometric modeling. 2nd ed. (1997), Wiley, New York
27. Meyer M., Desbrun M., Schröder P., and Barr A.H. Discrete differential-geometry operators for triangulated 2-manifolds. Visualization and mathematics III (2003), Springer 35-58
28. Nutbourne A.W., McLellan P.M., and Kensit R.M.L. Curvature profiles for plane curves. Computer-Aided Design 4 4 (1972) 176-184
29. Nocedal J., and Wright S.J. Numerical optimization (1999), Springer-Verlag
30. Peternell M. Recognition and reconstruction of developable surfaces from point clouds. In: Proceedings of geometric modeling and processing. 2004. p. 301-10
31. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical recipes in C: The art of scientific computing. 2nd ed. (1995), Cambridge University Press, Cambridge
32. Peternell M., and Steiner T. Reconstruction of piecewise planar objects from point clouds. Computer-Aided Design 36 (2004) 333-342
33. Pottmann H., and Wallner J. Approximation algorithms for developable surfaces. Computer Aided Geometric Design 16 (1999) 539-556
34. Sun X, Hancock ER. Fast isometric parametrization of 3D triangular mesh. In: Proceedings of british machine vision conference. 2005
35. Sheffer A., Lévy B., Mogilnitsky M., and Bogomjakov A. ABF++: fast and robust angle based flattening. ACM Transactions on Graphics 24 2 (2005) 311-330
36. Sheffer A., and de Sturler E. Parameterization of faceted surfaces for meshing using angle based flattening. Engineering with Computers 17 3 (2001) 326-337
37. Wang C.C.L. Towards flattenable mesh surfaces. Computer-Aided Design (2007) 10.1016/j.cad.2007.06.001
38. Wang C.C.L. Computing length-preserved free boundary for quasi-developable mesh segmentation. IEEE Transactions on Visualization and Computer Graphics 14 1 (2008) 25-36
39. Wang C.C.L., Smith S.S.F., and Yuen M.M.F. Surface flattening based on energy model. Computer-Aided Design 34 11 (2002) 823-833
40. Wang C.C.L., and Tang K. Achieving developability of a polygonal surface by minimum deformation: A study of global and local optimization approaches. The Visual Computer 20 8-9 (2004) 521-539
41. Wang C.C.L., Tang K., and Yeung B.M.L. Freeform surface flattening by fitting a woven mesh model. Computer-Aided Design 37 (2005) 799-814
42. Wang C.C.L., Wang Y., and Yuen M.M.F. On increasing the developability of a trimmed NURBS surface. Engineering with Computers 20 1 (2004) 54-64
43. McCartney J., Hinds B.K., and Chong K.W. Pattern flattening for orthotropic materials. Computer-Aided Design 37 (2005) 631-644
44. Zigelman G., Kimmel R., and Kiryati N. Texture mapping using surface flattening via multi-dimensional scaling. IEEE Transactions on Visualization and Computer Graphics 8 (2002) 198-207
45. Zhong Y., and Xu B. A physically based method for triangulated surface flattening. Computer-Aided Design 38 (2006) 1062-1073