Achieving developability of a polygonal surface by minimum deformation: A study of global and local optimization approaches

Visual Computer

Volumn 20, Issue 8-9, 2004, Pages 521-539

  Wang, Charlie C L ^a   Tang, Kai ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Assembled patches; Deformation; Developable surface; Optimization; Polygonal mesh

Indexed keywords

ALGORITHMS; COMPUTER GRAPHICS; COMPUTER SCIENCE; CONFORMAL MAPPING; DEFORMATION; ITERATIVE METHODS; MATHEMATICAL MODELS; OPTIMIZATION; POLYNOMIALS; PRODUCT DESIGN; REAL TIME SYSTEMS; SHEET METAL; SURFACES; TOPOLOGY;

ASSEMBLED PATCHES; DEVELOPABLE SURFACES; ELASTIC ENERGY; POLYGONAL MESHES;

COMPUTATIONAL GEOMETRY;

EID: 10044269983     PISSN: 01782789     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00371-004-0256-0     Document Type: Article

References (46)

1. do Carmo MP (1976) Differential geometry of curves and surfaces. Prentice-Hall, Englewood Cliffs, NJ
2. Singh K, Fiume E (1998) Wires: a geometric deformation technique. SIGGRAPH 1998 Conference Proceedings, ACM, pp 405-414
3. Schroeder WJ, Zarge JA, Lorensen WE (1992) Decimation of triangle meshes. Comput Graph 26(2):65-70
4. Garland M, Heckbert PS (1997) Surface simplification using quadric error metrics. SIGGRAPH 97 Conference Proceedings, pp 209-16
5. Wu J-H, Hu S-M, Tai C-L, Sun J-G (2001) An effective feature-preserving mesh simplification scheme based on face constriction. Proceedings of the Ninth Pacific Conference on Computer Graphics and Applications, Tokyo, 16-18 October 2001, pp 12-21
6. Taubin G (1995) A signal processing approach to fairing surface design. SIGGRAPH 95 Conference Proceedings, ACM, pp 351-58
7. Kobbelt L, Campagna S, Vorsatz J, Seidel HP (1998) Interactive multi-resolution modeling on arbitrary meshes. SIGGRAPH 98 Conference Proceedings, ACM, pp 105-114
8. Desbrun M, Meyer M, Schroder P, Barr AH (1999) Implicit fairing of irregular meshes using diffusion and curvature flow. SIGGRAPH 99 Proceedings, ACM, pp 409-416
9. 1 boundary conditions. Proceedings Geometric Modeling and Processing 2000 Theory and Applications. IEEE Comput Soc 2000, pp 251-261, Los Alamitos, CA
10. Schneider R, Kobbelt L (2001) Geometric fairing of irregular meshes for free-form surface design. Comput Aided Geom Des 18(4):359-379
11. Zeleznik RC, Herndon KP, Hughes JF (1996) SKETCH: an interface for sketching 3D scenes. SIGGRAPH 96 Proceedings, ACM, pp 163-170
12. Igarashi T, Matsuoka S, Tanaka H (1999) Teddy: a sketching interface for 3D freeform design. SIGGRAPH 99 Proceedings, ACM, pp 409-416
13. Bloomenthal J, Wyvill B (1990) Interactive techniques for implicit modeling. 1990 Symposium on Interactive 3D Graphics, pp 109-116
14. Markosian L, Cohen J M, Crulli T, Hughes J (1999) Skin: a constructive approach to modeling free-form shapes. SIGGRAPH 99 Conference Proceedings, ACM, pp 393-400
15. Suzuki H, Sakurai Y, Kanai T, Kimura F (2000) Interactive mesh dragging with an adaptive remeshing technique. Vis Comput 16(3-4):159-76
16. Zorin D, Schroder P, Sweldens W (1997), Interactive multiresolution mesh editing. SIGGRAPH 97 Proceedings, ACM, pp 259-268
17. Khodakovsky A, Schroder P (1999) Fine level feature editing for subdivision surfaces. Proceedings Fifth Symposium on Solid Modeling and Applications. ACM Press, New York, pp 203-211
18. Aumann G (1991) Interpolation with developable Bézier patches. Comput Aided Geom Des 8:409-420
19. Maekawa T, Chalfant J (1998) Design and tessellation of B-spline developable surfaces. ASME Trans J Mech Des 120:453-461
20. Frey WH, Bindschadler D (1993) Computer aided design of a class of developable Bézier surfaces. GM Research Publication, GMR-8057
21. Chu CH, Séquin CH (2002) Developable Bézier patches: properties and design. Comput-Aided Des 34(7):511-527
22. Hoschek J, Pottmann H (1995) Interpolation and approximation with developable B-spline surfaces, In: Daehlen M, Lyche T, Schumaker LL (eds) Mathematical methods for curves and surfaces. Vanderbilt University Press, Nashville, TN, pp 255-264
23. Chen HY, Lee IK, Leopoldseder S, Pottmann H, Randrup T, Wallner J (1999) On surface approximation using developable surfaces. Graph Models Image Process 61(2):110-124
24. Pottmann H, Wallner J (1999) Approximation algorithms for developable surfaces. Comput Aided Geom Des 16(6):539-556
25. Redont P (1989) Representation and deformation of developable surfaces. Comput Aided Des 21(1):13-20
26. Randrup T (1998) Approximation of surfaces by cylinders. Comput Aided Des 30(7):807-812
27. Park FC, Yu J, Chun C (2002) Design of developable surfaces using optimal control. ASME Trans J Mech Des 124:602-608
28. Shimada T, Tada Y (1991) Approximate transformation of an arbitrary curved surface into a plane using dynamic programming. Comput Aided Des 23(2):155-159
29. Panda L, Mudur SP (1993) Constraint-satisfying planar development of complex surfaces. Comput Aided Des 25(3):225-232
30. McCartney J, Hinds BK, Seow BL (1999) The flattening of triangulated surfaces incorporating darts and gussets. Comput Aided Des 31(3):249-260
31. Wang CCL, Smith SSF, Yuen MMF (2002) Surface flattening based on energy model. Comput Aided Des 34(8):823-833
32. Yu G, Patrikalakis NM, Maekawa T (2000) Optimal development of doubly curved surfaces. Comput Aided Geom Des 17:545-577
33. Sheffer A, de Sturler E (2000) Parameterization of faceted surfaces for meshing using angle based flattening. Eng Comput 17(3):326-337
34. Sheffer A, de Sturler E (2002) Smoothing an overlay grid to minimize linear distortion in texture mapping. ACM Trans Graph 21(3):874-890
35. Azariadis PN, Aspragathos NA (2000) On using planar developments to perform texture mapping on arbitrarily curved surfaces. Comput Graph 24(4):539-554
36. Azariadis PN, Aspragathos NA (2001) Geodesic curvature preservation in surface flattening through constrained global optimization. Compu Aided Des 33(8):581-591
37. Azariadis PN, Nearchou A, Aspragathos NA (2002) An evolutionary algorithm for generating planar developments of arbitrarily curved surfaces. Comput Ind 47(3):357-368
38. Aono M, Denti P, Breen DE, Wozny MJ (1996) Fitting a woven cloth model to a curved surface: dart insertion. IEEE Comput Graph Appl 16(4):60-70
39. Aona M, Breen DE, Wozny MJ (2001) Modeling methods for the design of 3D broadcloth composite parts. Comput Aided Des 33(10):989-1007
40. Calladine CR (1986) Gaussian curvature and shell structures. In: Proceedings of Mathematics of Surfaces, pp 179-196, Oxford, UK, Conference Information: Manchester, UK, 17-19 Sept. 1984
41. Kobbelt LP, Bischoff S, Botsch M, Kähler K, Rössl C, Schneider R, Vorsatz J (2000) Geometric modeling based on polygonal meshes. EUROGRAPHICS 2000 Tutorial
42. Sheffer A (2002) Spanning tree seams for reducing parameterization distortion of triangulated surface. SMI 2002: International Conference on Shape Modelling and Applications, pp 261-272
43. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1993) Mesh optimization, SIGGRAPH 93 Proceedings, ACM, pp 19-26
44. Ganapathy S, Dennehy TG (1982) A new general triangulation method for planar contours. Comput Graph 16(3):69-75
45. Belegundu AD, Chandrupatla TR (1999) Optimization concepts and applications in engineering. Prentice-Hall, Upper Saddle River, NJ
46. Moreton HP, Sequin CH (1992) Functional optimization for fair surface design. ACM Comput Graph 26(2):167-176