Abstract
In this paper we describe a new mesh parametrization method which combines the mean value coordinates and the Locally Linear Embedding (LLE) method. The mean value method is extended to compute the linearly reconstructing weights of both the interior and the boundary vertices of a 3D triangular mesh, and the weights are further used in the LLE algorithm to compute the vertex coordinates of a 2D planar triangular mesh parametrization. Examples are provided to show the effectiveness of this parametrization method.
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References
Floater, M.S.: Parametrization and smooth approximation of surface triangulations. Comp. Aided. Geom. Design. 14, 231–250 (1997)
Floater, M.S.: Mean value coordinates. Comp. Aided. Geom. Design. 20, 19–27 (2003)
Floater, M.S., Hormann, K.: Surface Parameterization: a Tutorial and Survey. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds.) Advances in Multiresolution for Geometric Modelling, pp. 157–186. Springer, Heidelberg (2004)
Praun, E., Hoppe, H.: Spherical parametrization and remeshing. ACM Trans. Graphics 22, 340–349 (2003)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)
Saul, L.K., Roweis, S.T.: An introduction to locally linear embedding. Report at AT & T Labs-Research (2000)
Surazhsky, V., Gotsman, C.: Intrinsic morphing of compatible triangulations. Int. J. Shape Modelling 9, 191–201 (2003)
Tutte, W.T.: How to draw a graph. Proc. London Math. Soc. 13, 743–768 (1963)
Zigelman, G., Kimmel, R., Kiryati, N.: Texture mapping using surface flattening via multi-dimensional scaling. IEEE Trans. Visualization Comp. Graphics 8, 198–207 (2002)
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Sun, X., Hancock, E.R. (2005). 3D Triangular Mesh Parametrization Using Locally Linear Embedding. In: Gagalowicz, A., Philips, W. (eds) Computer Analysis of Images and Patterns. CAIP 2005. Lecture Notes in Computer Science, vol 3691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556121_13
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DOI: https://doi.org/10.1007/11556121_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28969-2
Online ISBN: 978-3-540-32011-1
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