“Physical Mesh Data Structures” by Akleman, Ke and Wu
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Entry Number: 09
Title:
- Physical Mesh Data Structures
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Abstract:
In this work, we demonstrate that existing mesh data structures in computer graphics can be used to categorize physical polygonal models. Based on this categorization, we develop a system to unfold any polygonal mesh based on widely used mesh-data structures. Using our system, any shape can be constructed by using laser-cut developable panels based on one of the existing mesh data structures. This categorization is also useful for the creation and classification of geometric toys. It is particularly useful to develop new construction methods for complicated sculptural and architectural shapes.
References:
Akleman, E., Chen, J., and Gross, J. L. 2010. Paper-strip sculptures. In Shape Modeling International Conference (SMI), 2010, IEEE, 236–240.
Akleman, E., Wu, Y., Ke, S., Borhani, A., Kalantar, N., and Chen, J. 2016. Construction with physical version of quad-edge data structures. Computers & Graphics (accepted).
Baumgart, B. G. 1972. Winged edge polyhedron representation. Tech. rep., Technical Report, Stanford University.
Gross, J. L., and Tucker, T. W. 2001. Topological graph theory. Courier Dover Publications.
Guibas, L., and Stolfi, J. 1985. Primitives for the manipulation of general subdivisions and the computation of voronoi. ACM Transactions on Graphics (TOG) 4, 2, 74–123.
Hart, G. 2004. slide-together: Geometric paper constructions. In Teachers’ workshop at Bridges Conference.
Hernandez, E. A. P., Hu, S., Kung, H. W., Hartl, D., and Akleman, E. 2013. Towards building smart self-folding structures. Computers & Graphics 37, 6, 730–742.
Mäntylä, M. 1988. An introduction to solid modeling. Computer Science Press.
Miller, J., and Akleman, E. 2008. Edge-based intersected polyhedral paper sculptures constructed by interlocking slitted planar pieces. In Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, Tarquin Publications, 259–264.
Reimann, D. A. 2015. Nonplanar expansions of polyhedral edges in platonic and archimedean solids. In Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture, Tessellations Publishing, Phoenix, Arizona, 143–150.
Xing, Q., Esquivel, G., Akleman, E., Chen, J., and Gross, J. 2011. Band decomposition of 2-manifold meshes for physical construction of large structures. In ACM SIGGRAPH 2011 Posters and Talks, ACM, 58.
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