Abstract
This paper presents an iterative method to remesh an arbitrary surface into a mesh with all edge lengths within an interval. The process starts with a triangular 2-manifold mesh. It uses stellar operations to achieve the necessary amount of vertices and triangles. Subsequently, it applies a constrained version of the Laplacian filter in order achieve a more uniform distribution of the vertices over the surface. In order to prevent the natural shrink caused by the Laplacian filter, we perform a projection over the original surface. We also apply a post processing step to correct the lengths of troubling edges. Our method results in a regular mesh, with vertices uniformly distributed. The dual mesh obtained can be useful for several applications. The main contribution of this work is a new approach for edge length equalization, with explicit constraints definition, lower global geometry losses and lower memory cost if compared to previous works.
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References
Rocchini, C., Cignoni, P., Montani, C., Pingi, P., Scopigno, R.: A low cost 3d scanner based on structured light. Computer Graphics Forum 20(3), 299–308 (2001)
Vieira, M.B., Velho, L., Sa, A., Carvalho, P.C.: A camera-projector system for real-time 3d video. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition-Workshops, CVPR Workshops, pp. 96–96. IEEE (2005)
Dembogurski, R., Dembogurski, B., de Souza da Silva, R.L., Vieira, M.B.: Interactive mesh generation with local deformations in multiresolution. In: Murgante, B., Misra, S., Carlini, M., Torre, C.M., Nguyen, H.-Q., Taniar, D., Apduhan, B.O., Gervasi, O. (eds.) ICCSA 2013, Part I. LNCS, vol. 7971, pp. 646–661. Springer, Heidelberg (2013)
Schöberl, J.: Netgen an advancing front 2d/3d-mesh generator based on abstract rules. Computing and Visualization in Science 1(1), 41–52 (1997)
Iijima, S., et al.: Helical microtubules of graphitic carbon. Nature 354(6348), 56–58 (1991)
Rapaport, D.C.: The Art of Molecular Dynamics Simulation. Cambridge University Press, New York (1996)
Bommes, D., Zimmer, H., Kobbelt, L.: Mixed-integer quadrangulation. ACM Trans. Graph. 77, 1–77 (2009)
Ray, N., Vallet, B., Li, W.C., Lévy, B.: N-symmetry direction field design. ACM Transactions on Graphics (2008); Presented at SIGGRAPH
Huang, J., Zhang, M., Pei, W., Hua, W., Bao, H.: Controllable highly regular triangulation. Science China Information Sciences 54(6), 1172–1183 (2011)
Pampanelli, P.C.P.: Mesh generation through the mapping of triangular models into rhomboid space. M.sc. dissertation, Universidade Federal de Juiz de Fora, Advisor: Marcelo Bernardes Vieira, Co-advisors: Marcelo Lobosco and Sócrates de Oliveira Dantas (2011)
Pampanelli, P.P., Peanha, J., Campos, A.M., Vieira, M.B., Lobosco, M., de Oliveira Dantas, S.: Rectangular hexagonal mesh generation for parametric modeling. In: 2009 XXII Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI), pp. 120–125. IEEE (2009)
Pietroni, N., Tarini, M., Cignoni, P.: Almost isometric mesh parameterization through abstract domains. IEEE Transactions on Visualization and Computer Graphics 16(4), 621–635 (2010)
Liu, Y., Pan, H., Snyder, J., Wang, W., Guo, B.: Computing self-supporting surfaces by regular triangulation. ACM Trans. Graph. 32(4), 92:1–92:10 (2013)
Aurenhammer, F.: Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16(1), 78–96 (1987)
Botsch, M., Kobbelt, L.: A remeshing approach to multiresolution modeling. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 185–192. ACM (2004)
Surazhsky, V., Gotsman, C.: High quality compatible triangulations. Engineering with Computers 20(2), 147–156 (2004)
de Oliveira, J.P.P.N.: Iterative method for edge length equalization. In: International Conference on Computational Science, Barcelona, Spain, pp. 481–490 (2013)
Taubin, G.: A signal processing approach to fair surface design. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1995, pp. 351–358. ACM, New York (1995)
Alliez, P., Meyer, M., Desbrun, M.: Interactive geometry remeshing. ACM Trans. Graph. 21(3), 347–354 (2002)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge University Press, New York (1992)
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de Sá Hauck, J.V., da Silva, R.N., Vieira, M.B., da Silva, R.L.d.S. (2014). Iterative Remeshing for Edge Length Interval Constraining. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8584. Springer, Cham. https://doi.org/10.1007/978-3-319-09153-2_23
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DOI: https://doi.org/10.1007/978-3-319-09153-2_23
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