We present a multiresolution morphing algorithm using ``as-rigid-as-possible'' shape interpolation combined with an angle-length based multiresolution decomposition of simple 2D piecewise curves. This novel multiresolution representation is defined intrinsically and has the advantage that the details' orientation follows any deformation naturally. The multiresolution morphing algorithm consists of transforming separately the coarse and detail coefficients of the multiresolution decomposition. Thus all LoD (level of detail) applications like LoD display, compression, LoD editing etc. can be applied directly to all morphs without any extra computation. Furthermore, the algorithm can robustly morph between very large size polygons with many local details as illustrated in numerous figures. The intermediate morphs behave natural and least-distorting due to the particular intrinsic multiresolution representation.
AMS Subject Classifications68U07 68U05 65D05 65D08 65D17
KeywordsGeometric modeling curves multiresolution analysis morphing interpolation vertex correspondence
Unable to display preview. Download preview PDF.
- Alexa, M., Cohen-Or, D., Levin, D.: As-rigid-as-possible shape interpolation. In: SIGGRAPH '00: Proc. 27th Annual Conf. on Computer Graphics and Interactive Techniques. New York: ACM Press/Addison-Wesley 2000, pp. 157–164.Google Scholar
- Carmo, M. D.: Differential geometry of curves and surfaces. Prentice Hall 1976.Google Scholar
- Chui, C., Quak, E. 1992Wavelets on a bounded intervalBraess, D.Schumaker, L. eds. Numerical methods of approximation theoryBirkhäuser Basel124Google Scholar
- Elber, G., Gotsman, C.: Multiresolution control for nonuniform bspline curve editing. In: 3rd Pacific Graphics Conf. on Computer Graphics and Applications, Seoul, Korea, pp. 267–278, August 1995.Google Scholar
- Finkelstein, A., Salesin, D. H.: Multiresolution curves. Computer Graphics Proc. (SIGGRAPH 94), pp. 261–268 (1994).Google Scholar
- Goldstein, E., Gotsman, C.: Polygon morphing using a multiresolution representation. In: Graphics Interface '95. Canadian Inf. Process. Soc., pp. 247–254 (1995).Google Scholar
- Lee, A. W. F., Dobkin, D., Sweldens, W., Schröder, P.: Multiresolution mesh morphing. Computer Graphics Proc. (SIGGRAPH 99), 343–350, (1999).Google Scholar
- Stollnitz, E., DeRose, T., Salesin, D.: Wavelets for computer graphics: Theory and applications. Morgan Kaufmann 1996.Google Scholar