Constructing developable surfaces by wrapping cones and cylinders

CAD Computer Aided Design

Volumn 58, Issue , 2015, Pages 230-235

  Hwang, Hae Do ^a   Yoon, Seung Hyun ^a  

^a Dongguk University   (South Korea)

Author keywords

Cone; Cylinder; Developable surface; Direct manipulation; Paper bending

Indexed keywords

CONES; MAPPING;

ARBITRARY POINTS; DEVELOPABLE SURFACES; DIFFERENT SIZES; DIRECT MANIPULATION; INTUITIVE CONTROLS; NEW POSITION; NUMERICAL TECHNIQUES;

CYLINDERS (SHAPES);

EID: 84920720744     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2014.08.025     Document Type: Article

References (20)

1. Do Carmo M. Differential geometry for curves and surfaces. Prentice-Hall; 1976.
2. Pottmann H, Wallner J. Computational geometry for line geometry. Springer; 2001.
3. Tachi T. Origamizing polyhedral surfaces. IEEE Trans Vis Comput Graphics 2010;16(2):298-311.
4. Liu Y, Pottmann H, Wallner J, Yang Y-L, Wang W. Geometric modeling with conical meshes and developable surfaces. ACM Trans Graph 2006;25(3):681-9.
5. Kilian M, Flöry S, Chen Z, Mitra NJ, Sheffer A, Pottmann H. Curved folding. ACM Trans Graph 2008;27(3): 75:1-75:9.
6. Pottmann H, Farin G. Developable rational Bézier and B-spline surfaces. Comput Aided Geom Design 1995;12(5):513-31.
7. Pottmann H, Wallner J. Approximation algorithms for developable surfaces. Comput Aided Geom Design 1999;16(6):539-56.
8. Chu C-H, Séquin CH. Developable Bézier patches: properties and design. Comput-Aided Des 2002;34(7):511-27.
9. Aumann G. Degree elevation and developable Bézier surfaces. Comput Aided Geom Design 2004;21(7):661-70.
10. Chen H-Y, Lee I-K, Leopoldseder S, Pottmann H, Randrup T, Wallner J. On surface approximation using developable developable surfaces. Graph Models Image Process 1999;61:110-24.
11. Peternell M. Developable surface fitting to point clouds. Comput Aided Geom Design 2004;21(8):785-803.
12. Sun M, Fiume E. A technique for constructing developable surfaces. In: Proceedings of graphics interface. 1996. p. 176-85.
13. Rose K, Sheffer A, Wither J, Cani M-P, Thibert B. Developable surfaces from arbitrary sketched boundaries. In: Proceedings of the fifth eurographics symposium on geometry processing. 2007. p. 163-72.
14. Mitani J, Suzuki H. Making papercraft toys from meshes using strip-based approximate unfolding. ACM Trans Graph 2004;23(3):259-63.
15. Wang CCL, Tang K. Achieving developability of a polygonal surface by minimum deformation: a study of global and local optimization approaches. Vis Comput 2004;20(8-9):521-39.
16. Kergosien YL, Gotoda H, Kunii TL. Bending and creasing virtual paper. IEEE Comput Graph Appl 1994;14(1):40-8.
17. Hong L, Card SK, Chen JJ. Turning pages of 3D electronic books. In: Proceedings of the 3D user interfaces conference. 2006. p. 159-65.
18. Bo P, Wang W. Geodesic-controlled developable surfaces for modeling paper bending. Comput Graph Forum 2007;26(3):365-74.
19. Solomon J, Vouga E, Wardetzky M, Grinspun E. Flexible developable surfaces. Comput Graph Forum 2012;31(5):1567-76.
20. Press W-H, Teukolsky S-A, Vetterling W-T, Flannery B-P. Numerical recipes in C. Cambridge University Press; 1992.