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Algorithms 2009, 2(4), 1263-1280; doi:10.3390/a2041263

Compound Biorthogonal Wavelets on Quadrilaterals and Polar Structures

1,* , 1
1 Department of Computer Science Engineering, The Chinese University of Hong Kong, The Chinese University of Hong Kong, Shatin N.T., Hong Kong 2 Department of MEEM, The City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong 3 Department of Computer Science and Technology, East Main Building, Tsinghua University, Beijing 100084, China
* Author to whom correspondence should be addressed.
Received: 31 July 2009 / Revised: 19 September 2009 / Accepted: 24 September 2009 / Published: 28 September 2009
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In geometric models with high-valence vertices, current subdivision wavelets may not deal with the special cases well for good visual effect of multiresolution surfaces. In this paper, we present the novel biorthogonal polar subdivision wavelets, which can efficiently perform wavelet analysis to the control nets with polar structures. The polar subdivision can generate more natural subdivision surfaces around the high-valence vertices and avoid the ripples and saddle points where Catmull-Clark subdivision may produce. Based on polar subdivision, our wavelet scheme supports special operations on the polar structures, especially suitable to models with many facets joining. For seamless fusing with Catmull-Clark subdivision wavelet, we construct the wavelets in circular and radial layers of polar structures, so can combine the subdivision wavelets smoothly for composite models formed by quadrilaterals and polar structures. The computations of wavelet analysis and synthesis are highly efficient and fully in-place. The experimental results have confirmed the stability of our proposed approach.
Keywords: polar subdivision; Catmull-Clark subdivision; bicubic B-spline; subdivision wavelet; local lifting polar subdivision; Catmull-Clark subdivision; bicubic B-spline; subdivision wavelet; local lifting
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhao, C.; Sun, H.; Wang, H.; Qin, K. Compound Biorthogonal Wavelets on Quadrilaterals and Polar Structures. Algorithms 2009, 2, 1263-1280.

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