A physically based approach to 2–D shape blending
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Cartoon Animation and Morphing with Wavelet Curve Descriptor
Multidimensional Systems and Signal Processing
Warping and morphing of graphical objects
Warping and morphing of graphical objects
Modeling generalized cylinders via Fourier morphing
ACM Transactions on Graphics (TOG)
Skeleton-based three-dimensional geometric morphing
Computational Geometry: Theory and Applications - special issue on virtual reality
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Shape Blending Using the Star-Skeleton Representation
IEEE Computer Graphics and Applications
Imitation of Life: How Biology Is Inspiring Computing
Imitation of Life: How Biology Is Inspiring Computing
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modeling generalized cylinders using direction map representation
Computer-Aided Design
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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.