Abstract
We present a new object-based algorithm for morphing between two shapes with an arbitrary number of polygons and arbitrarily different topology. Many solutions have been proposed for morphing between two polygons. However, there has been little attention to morphing between different numbers of polygons, across a change in topology. A modified conforming Delaunay triangulation is used to build the vertex correspondence. Polygon evolution is used to smooth the morph. The morph requires no user interaction, avoids self-intersection, uses dynamic vertex correspondence, and follows nonlinear vertex paths.
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References
Alexa, M., Cohen-Or, D., Koltun, V. (2001) Object-space morphing. Tutorial notes, Shape Modeling International (2001)
Bruckstein, A., Sapiro, G., Shaked, D.: Evolutions of planar polygons. International Journal of Pattern Recognition and Artificial Intelligence 9(6), 991–1014 (1995)
Chew, L.P.: Constrained Delaunay triangulations. In: Proceedings of the third annual symposium on Computational geometry, June 08-10, pp. 215–222 (1987)
Cohen-Or, D., Levin, D., Solomovici, A.: Three-dimensional distance field metamorphosis. ACM Transactions on Graphics 17(2), 116–141 (1998)
DeCarlo, D., Gallier, J.: Topological Evolution of Surfaces. Graphics Interface 1996, 194–203 (1996)
Gage, M., Hamilton, R.: The heat equation shrinking convex plane curves. J. Differential Geometry 23, 69–96 (1986)
Gomes, J., Darsa, L., Costa, B., Velho, L.: Warping and morphing of graphical objects. Morgan Kaufmann Publishers, Inc., San Francisco (1998)
Goldstein, E., Gotsman, C.: Polygon morphing using a multiresolution representation. Graphics Interface 1995, 247–254 (1995)
Grayson, M.: The heat equation shrinks embedded plane curves to round points. J. Differential Geometry 26, 285–314 (1987)
Guibas, L.J., Knuth, D., Sharir, M.: Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica 7, 381–413 (1992)
Preparata, F., Shamos, M.: Computational Geometry: An Introduction. Springer, New York (1988)
Sederberg, T., Greenwood, E.: A physically based approach to 2-D shape blending. In: SIGGRAPH 1992, pp. 25–34 (1992)
Shapira, M., Rappoport, A.: Shape blending using the star-skeleton representation. IEEE Computer Graphics and Applications, 44–50 (March 1995)
Shewchuk, J.R.: Delaunay Refinement Algorithms for Triangular Mesh Generation. Computational Geometry: Theory and Applications 22, 21–74 (2002)
Turk, G., O’Brien, J.: Shape transformation using variational implicit functions. In: SIGGRAPH 1999, pp. 335–342 (1999)
Wu, X.: Morphing many polygons across a change in topology. Ph.D. Thesis, Department of Computer and Information Sciences, University of Alabama at Birmingham (2003)
Wu, X., Johnstone, J.: A Visibility-Based Polygonal Decomposition (Manuscript under preparation) (2006)
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© 2006 Springer-Verlag Berlin Heidelberg
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Wu, X., Johnstone, J.K. (2006). Delaunay-Based Polygon Morphing Across a Change in Topology. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751540_53
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DOI: https://doi.org/10.1007/11751540_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34070-6
Online ISBN: 978-3-540-34071-3
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