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Delaunay-Based Polygon Morphing Across a Change in Topology

  • Xiaqing Wu
  • John K. Johnstone
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3980)

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.

Keywords

Delaunay Triangulation Medial Axis Steiner Point Target Shape Intermediate Shape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alexa, M., Cohen-Or, D., Koltun, V. (2001) Object-space morphing. Tutorial notes, Shape Modeling International (2001)Google Scholar
  2. 2.
    Bruckstein, A., Sapiro, G., Shaked, D.: Evolutions of planar polygons. International Journal of Pattern Recognition and Artificial Intelligence 9(6), 991–1014 (1995)CrossRefGoogle Scholar
  3. 3.
    Chew, L.P.: Constrained Delaunay triangulations. In: Proceedings of the third annual symposium on Computational geometry, June 08-10, pp. 215–222 (1987)Google Scholar
  4. 4.
    Cohen-Or, D., Levin, D., Solomovici, A.: Three-dimensional distance field metamorphosis. ACM Transactions on Graphics 17(2), 116–141 (1998)CrossRefGoogle Scholar
  5. 5.
    DeCarlo, D., Gallier, J.: Topological Evolution of Surfaces. Graphics Interface 1996, 194–203 (1996)Google Scholar
  6. 6.
    Gage, M., Hamilton, R.: The heat equation shrinking convex plane curves. J. Differential Geometry 23, 69–96 (1986)MATHMathSciNetGoogle Scholar
  7. 7.
    Gomes, J., Darsa, L., Costa, B., Velho, L.: Warping and morphing of graphical objects. Morgan Kaufmann Publishers, Inc., San Francisco (1998)Google Scholar
  8. 8.
    Goldstein, E., Gotsman, C.: Polygon morphing using a multiresolution representation. Graphics Interface 1995, 247–254 (1995)Google Scholar
  9. 9.
    Grayson, M.: The heat equation shrinks embedded plane curves to round points. J. Differential Geometry 26, 285–314 (1987)MATHMathSciNetGoogle Scholar
  10. 10.
    Guibas, L.J., Knuth, D., Sharir, M.: Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica 7, 381–413 (1992)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Preparata, F., Shamos, M.: Computational Geometry: An Introduction. Springer, New York (1988)Google Scholar
  12. 12.
    Sederberg, T., Greenwood, E.: A physically based approach to 2-D shape blending. In: SIGGRAPH 1992, pp. 25–34 (1992)Google Scholar
  13. 13.
    Shapira, M., Rappoport, A.: Shape blending using the star-skeleton representation. IEEE Computer Graphics and Applications, 44–50 (March 1995)Google Scholar
  14. 14.
    Shewchuk, J.R.: Delaunay Refinement Algorithms for Triangular Mesh Generation. Computational Geometry: Theory and Applications 22, 21–74 (2002)MATHMathSciNetGoogle Scholar
  15. 15.
    Turk, G., O’Brien, J.: Shape transformation using variational implicit functions. In: SIGGRAPH 1999, pp. 335–342 (1999)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Wu, X., Johnstone, J.: A Visibility-Based Polygonal Decomposition (Manuscript under preparation) (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiaqing Wu
    • 1
  • John K. Johnstone
    • 1
  1. 1.CIS DepartmentUniversity of Alabama at BirminghamBirminghamUSA

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