“Fabrication of freeform objects by principal strips” by Takezawa, Imai, Shida and Maekawa
Conference:
Type(s):
Title:
- Fabrication of freeform objects by principal strips
Session/Category Title: Fabrication
Presenter(s)/Author(s):
Abstract:
Current CAD modeling techniques enable the design of objects with aesthetically pleasing smooth freeform surfaces. However, the fabrication of these freeform shapes remains challenging. Our novel method uses orthogonal principal strips to fabricate objects whose boundary consists of freeform surfaces. This approach not only lends an artistic touch to the appearance of objects, but also provides directions for reinforcement, as the surface is mostly bent along the lines of curvature. Moreover, it is unnecessary to adjust the bending of these orthogonal strips during the construction process, which automatically reforms the design shape as if it is memorized, provided the strips possess bending rigidity. Our method relies on semi-isometric mapping, which preserves the length of boundary curves, and approximates angles between boundary curves under local minimization. Applications include the fabrication of paper and sheet metal craft, and architectural models using plastic plates. We applied our technique to several freeform objects to demonstrate the effectiveness of our algorithms.
References:
1. Akleman, E., Chen, J., Xing, Q., and Gross, J. L. 2009. Cyclic plain-weaving on polygonal mesh surfaces with graph rotation systems. ACM Transactions on Graphics 28, 3, 78.
2. Alliez, P., Cohen-Steiner, D., Devillers, O., Lévy, B., and Desbrun, M. 2003. Anisotropic polygonal remeshing. ACM Transactions on Graphics 22, 3, 485–493.
3. Dietz, U. 1998. Fair surface reconstruction from point clouds. In Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997, Vanderbilt University, 79–86.
4. Elber, G. 1995. Model fabrication using surface layout projection. Computer-Aided Design 27, 4, 283–291. Cross Ref
5. Fischer-Cripps, A. C. 2007. Introduction to contact mechanics. Springer.
6. Garg, A., Sageman-Furnas, A. O., Deng, B., Yue, Y., Grinspun, E., Pauly, M., and Wardetzky, M. 2014. Wire mesh design. ACM Transactions on Graphics 33, 4, 66.
7. Hirano, D., Funayama, Y., and Maekawa, T. 2009. 3D shape reconstruction from 2D images. Computer-Aided Design and Applications 6, 5, 701–710. Cross Ref
8. Joo, H. K., Yazaki, T., Takezawa, M., and Maekawa, T. 2014. Differential geometry properties of lines of curvature of parametric surfaces and their visualization. Graphical Models 76, 4, 224–238.
9. Kilian, M., Flöry, S., Mitra, N. J., and Pottmann, H. 2008. Curved folding. ACM Transactions on Graphics 27, 3, 75.
10. Kreyszig, E. 1968. Differential Geometry. Dover Publications, Inc., NY.
11. Liu, Y., Pottmann, H., Wallner, J., Yang, Y. L., and Wang, W. 2006. Geometric modeling with conical meshes and developable surfaces. ACM Transactions on Graphics 25, 3, 681–689.
12. Maekawa, T., Wolter, F. E., and Patrikalakis, N. M. 1996. Umbilics and lines of curvature for shape interrogation. Computer Aided Geometric Design 13, 2, 133–161.
13. Marinov, M., and Kobbelt, L. 2004. Direct anisotropic quad-dominant remeshing. In Proceeding of the Computer Graphics and Applications, 12th Pacific Conference, IEEE Computer Society, 207–216.
14. Martin, R. R. 1983. Principal patches – a new class of surface patch based on differential geometry. In Eurographics ’83, P. J. W. T. Hagen, Ed., 47–55.
15. Massarwi, F., Gotsman, C., and Elber, G. 2008. Paper-craft from 3D polygonal models using generalized cylinders. Computer Aided Geometric Design 25, 8, 576–591.
16. Matsuo, K., and Matsuoka, K. 2010. Development of new system for developing curved shell plates of ships. Transactions of the Japan Society of Mechanical Engineers. C 76, 771, 2797–2802. In Japanese. Cross Ref
17. Mitani, J., and Suzuki, H. 2004. Making papercraft toys from meshes using strip-based approximate unfolding. ACM Transactions on Graphics 23, 3, 259–263.
18. Patrikalakis, N. M., and Maekawa, T. 2002. Shape Interrogation for Computer Aided Design and Manufacturing. Springer-Verlag, Heidelberg.
19. Pottmann, H., Schiftner, A., Wien, P. B. T., Schmied-hofer, H., Wang, W., Baldassini, N., and Wallner, J. 2008. Freeform surfaces from single curved panels. ACM Transactions on Graphics 27, 3, 76.
20. Pratt, M. 1990. Cyclides in computer aided geometric design. Computer Aided Geometric Design 7, 221–242.
21. Shatz, I., Tal, A., and Leifman, G. 2006. Paper craft models from meshes. The Visual Computer 22, 9, 825–834.
22. Tang, C., Sun, X., Gomes, A., Wallne, J., and Pottmann, H. 2014. Form-finding with polyhedral meshes made simple. ACM Transactions on Graphics 33, 4, 70.
23. Tang, C., Bo, P., Wallner, J., and Pottmann, H. 2016. Interactive design of developable surfaces. ACM Transactions on Graphics 35, 2, 12.
24. Willmore, T. J. 1959. An Introduction to Differential geometry. Clarendon Press, Oxford.
25. Zhang, E., Hays, J., and Turk, G. 2007. Interactive tensor field design and visualization on surfaces. IEEE Transactions on Visualization and Computer Graphics 13, 1, 94–107.


