Joo-Haeng Lee
ABSTRACT
We propose novel methods to generate a sequence of shapes that represents the pattern of morphological development or transformation of a Bézier curve. The methods utilize the intrinsic geometric structures of a Bézier curve that are derived from rib and fan decomposition (RFD) [Lee and Park 2005].
Morphological development based on RFD shows a characteristic pattern of structural growth of a Bézier curve, which is the direct consequence of development path defined using fans. Morphological transformation based RFD utilizes development patterns of given curves inspired by the theory of evolutionary developmental biology: although two mature curves are quite different in shapes, we can easily find similarities in their younger shapes, which makes it easier to set up feature correspondences for blending. Further controls on base transformation and extrapolation ratio can determine the dominance of features and compensate the immaturity that may occur during the transformation.
The development and transformation patterns generated with the methods have smooth and unique geometric style that cannot be generated using conventional methods based on multi-linear blending.
- Aguado, A. S., Montiel, E., and Zaluska, E. 1999. Modeling generalized cylinders via fourier morphing, ACM Transactions on Graphics 18, 4, 293--315. Google Scholar
Digital Library
- Bai, X., Latecki, L. J., and Liu, W.-Y. 2007. Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution, IEEE Trans. Pattern Analysis and Machine Intelligence 29, 3, 449--462. Google ScholarDigital Library
- Blanding, R. L., Turkiyyah, G. M., Storti, D. W., and Ganter, M. A. 2000. Skeleton-based three-dimensional geometric morphing, Computational Geometry: Theory and Applications 15, 1--3, 129--148. Google ScholarDigital Library
- Che, W., Yang, X., and Wang, G. 2004. Skeleton-driven 2D distance field metamorphosis using intrinsic shape parameters, Graphical Models 66, 2, 102--126. Google ScholarDigital Library
- Chuang, G. C. H. and Kuo, C. C. J. 1997. Cartoon Animation and Morphing with Wavelet Curve Descriptor, Multidimensional Systems and Signal Processing 8, 4, 423--447. Google ScholarDigital Library
- Farin, G. E. 2001. Curves and Surfaces for CAGD: a Practical Guide. Morgan Kaufmann. Google ScholarDigital Library
- Forbes, N. 2004. Imitation of Life: How Biology is Inspiring Computing. MIT Press. Google ScholarDigital Library
- Gielis, J. 2003. A generic geometric transformation that unifies a wide range of natural and abstract shapes, American Journal of Botany 90, 3, 333--338.Google ScholarCross Ref
- Gomes, J., Darsa, L., Costa, B., and Velho, L. 1999. Warping and morphing of graphical objects. Morgan Kaufmann Publishers. Google ScholarDigital Library
- Hui, K. C. and Li, Y. 1998. A feature-based shape blending technique for industrial design, Computer-Aided Design 30, 10, 823--834.Google ScholarCross Ref
- Latecki, L. J. and Lakaemper, R. 1999. Polygon Evolution by Vertex Deletion, In Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision (LNCS 1682). Springer-Verlag. Google ScholarDigital Library
- Lee, J.-H., Lee, J. Y., Kim, H., and Kim, H.-S. 2002. Interactive control of geometric shape morphing based on Minkowski sum, Transactions for the Society of CAD/CAM Engineers 7, 4, 317--326.Google Scholar
- Lee, J.-H., Kim, H., and Kim, H.-S. 2003. Efficient computation and control of geometric shape morphing based on direction map, Transactions for the Society of CAD/CAM Engineers 8, 4, 243--253.Google Scholar
- Lee, J.-H. 2005. Modeling generalized cylinders using direction map representation, Computer-Aided Design 37, 8, 837--846. Google ScholarDigital Library
- Lee, J.-H. and Park, H. 2005. Ribs and fans of Bézier curves and surfaces, Computer-Aided Design and Applications 2, 1--4, 125--134.Google ScholarCross Ref
- Lee, J.-H. and Park, H. 2006. Geometric properties of ribs and fans of a Bézier curve, Journal of Computer Science and Technology 21, 2, 279--283.Google ScholarCross Ref
- Lu, L., and Wang, G. 2006. Optimal multi-degree reduction of Bézier curves with G2-continuity, Computer Aided Geometric Design 23, 9, 673--683. Google ScholarDigital Library
- Miyashita, S., Sawada, Y., Okada, T., Murata, O., and Kumai, H. 2001. Morphological development and growth of laboratory-reared larval and juvenile Thunnus Thynnus (Pisces: Scombridae), Fishery Bulletin 99, 4, 601--616.Google Scholar
- Purves, W. K., Orians, G. H., Heller, H. C., and Sadava, D. 2004. Life: the Science of Biology. Sinauer Associates.Google Scholar
- Rossignac, J., and Kaul, A. 1994. Agrels and BIPs: Metamorphosis as a Bézier curve in the space of polyhedra, In Proceedings of EUROGRAPHICS 1994, Blackwell Publishers. M. Dæhlen and L. Kjelldhal, Ed., C179--C184.Google Scholar
- Samoilov, T. and Elber, E. 1998. Self-intersection elimination in metamorphosis of two-dimensional curves, The Visual Computer 14, 8--9, 415--428.Google ScholarCross Ref
- Sederberg, T. W. and Greenwood, E 1992. Physically based approach to 2-D shape blending, ACM Transactions on Graphics 26, 2, 25--34. Google ScholarDigital Library
- Shapira, M. and Rappoport, A. 1995. Shape blending using the star-skeleton representation, IEEE Computer Graphics and Applications 15, 2, 44--50. Google ScholarDigital Library
- Sun, Y. M., Wang, W., and Chin, F. Y. L. 1997. Interpolating Polyhedral Models Using Intrinsic Shape Parameters, Journal of Visualization and Computer Animation 8, 2, 81--96.Google ScholarCross Ref
- Surazhsky, T. and Elber, G. 2002. Metamorphosis of Planar Parametric Curves via Curvature Interpolation, International Journal of Shape Modeling 8, 2, 201--216.Google ScholarCross Ref
- Thom, R. 1989. Structural stability and morphogenesis: an outline of a general theory of models. Addison-Wesley.Google Scholar
- Thompson, D. A. W. 1992. On growth and form. Dover.Google Scholar
- Weng, Y. X. 2004. Growth and Form in Biology: Generation of the Plant Morphology by Spontaneous Symmetry Breaking Based on a Pressure Field, Chinese Physics Letters 21, 1, 211--214.Google ScholarCross Ref
- Wolberg, G. 1989. Skeleton based image warping. The Visual Computer 5, 1--2, 95--108Google ScholarCross Ref
Index Terms
- A note on morphological development and transformation of Bézier curves based on ribs and fans
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