Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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PAPER TEMPLATES FOR TRIANGULATED SURFACES

  • Received : 2011.09.26
  • Accepted : 2011.12.06
  • Published : 2011.12.25
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Abstract

We introduce an algorithm that automatically generates paper templates of a triangulated surface. The surface can be built by cutting, folding, and pasting the paper templates. The algorithm is branched to two strategies : one is to select the longest neghboring edge among many choices, and the other is to select the largest neighboring triangle. Three surfaces, whose triangulation sizes widely range, are successfully built by the algorithm. The two strategies are empirically evaluated in building the surfaces with respect to paper consumption, a measure of cost efficiency, and boundary length, a measure of speed efficiency. Strategy 1 performs in most cases better than the other one with respect to boundary length, but sometimes wins and sometimes loese with respect to paper consumption.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. N. Amcnta, M. Bcrn, and M. Kamvysselis. A new voronoi-based surface reconstruction algorithm. proc. SIGGRAPH 98, pages 425-421, 1998.
  2. B.P. Carnerio, C. Silva, and A.E. Kaufman. Tetra-cubes: An algorithm to generate 3d isosurfaces bases upon tetrahedra. Anais do IX SIBGRAPI, pages 205-210, 1996.
  3. J. C. Carr, R. K. Beatson, J. B. Cherric, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans. reconstruction and representation of 3d objects with radial basis functions. Computt. Grapg. (SIGGRAPH Proc.), pages 67-76, 2001.
  4. J. C. Carr, R. K. Beatson, B. C. McCallum, W. R. Fright, T. J. McLennan, and T. J. Mitchell. Smooth surface reconstruction from noisy range data. In Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia, GRAPHITE'03, pages 119-ff, New York, NY, USA, 2003. ACM.
  5. A. Drozdek. Data structures and algorithms in c++. Course Technology, 2004.
  6. H. Edelsbrunner Shape reconstruction with delaunay complex. 1380:119-132, 1998. 10.1007/BFb0054315.
  7. W. Lorensen and H. Cline. Marching cubcs: A high-resolution 3d surface construction algorithm. Comput. Graph. (SIGGRAPH Proc.), 21:168-169, 1987.
  8. C. Min. Simplicial isosurfacing in arbitrary dimension and codimension. J. Comput. Phys., 190:295-310, 2003. https://doi.org/10.1016/S0021-9991(03)00275-4
  9. C, Montani, R. Scateni, and R. Scopigno. A modified look-up table for implicit disambiguation of marching cubes. The Visual Computer, 10:353-355, 1994. 10.1007/BF01900830.
  10. G. Turk and M. Levoy. Zippered polygon meshes from range images. Computer Graphics, SIGGRAPH, pages 311-318, 1994.
  11. H. K. Zhao, S. Osher, B. Merriman, and M. Kang. Implicit and non-parametric Shape reconstruction from unorganized points using variational level set method. Comput. Vis. lmage Unders., 80:295-319, 2000. https://doi.org/10.1006/cviu.2000.0875
  12. H.-K. Zhao, Stanley Osher, and Ronald Fedkiw. Fast surface reconstructionction using the level set method. In 1st lEEE Wrkshp. on Variational and Level Set Meth., 8th lnt. Conf. on Comput. vis., pages 194-202, 2001.
  13. G. M. Ziegler. Lectures on polytopes. Graduate texts in Math. Springer-Verlag, 1995.