compound biorthogonal wavelets on quadrilaterals and polar structures复合双正交的小波对四边形和极地的结构.pdfVIP

Algorithms 2009, 2, 1263 - 1280; doi:10.3390/a2041263 OPEN ACCESS algorithms ISSN 1999-4893 /journal/algorithms Article Compound Biorthogonal Wavelets on Quadrilaterals and Polar Structures Chong Zhao , Hanqiu Sun , Huawei Wang and Kaihuai Qin Department of Computer Science Engineering, The Chinese University of Hong Kong, The Chinese University of Hong Kong, Shatin N.T., Hong Kong; E-Mail: hanqiu@.hk (H.Q.S.) Department of MEEM, The City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong; E-Mail: hwwang@.hk (H.W.W.) Department of Computer Science and Technology, East Main Building, Tsinghua University, Beijing 100084, China; E-Mail: qkh-dcs@ (K.H.Q.) Author to whom correspondence should be addressed; E-Mail:czhao@.hk; Tel.: +852 Received: 31 July 2009; in revised form: 19 September 2009 / Accepted: 24 September 2009 / Published: 28 September 2009 Abstract: 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, espe- cially suitable to mod