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Subdivision Algorithms for Generalized Ball Curves and Its Applications

Author: YuHongJie
Tutor: ZuoHongYi
School: Hefei University of Technology
Course: Computational Mathematics
Keywords: The B De zier curve Said-Ball curve Wang-Ball curve SBGB curve WSGB curve Dual basis Subdivision algorithm Combinatorial identities Subdivision transform Similarity
CLC: O241
Type: Master's thesis
Year: 2004
Downloads: 35
Quote: 0
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This paper is divided into five chapters . The first chapter introduces the definition and properties of Said-Ball curve . Of Said-Ball basis functions duality ( Functional ) base , power basis function Said-Ball base Marsden identity , and the conversion from the the Bézier Curve to Said-Ball curve and gives the Said-Ball curve subdivision algorithm. The second chapter describes the Wang-Ball curve definition and nature , as well as the Wang-Ball curve recursive evaluation algorithm , Wang-Ball basis functions the dual functional Wang-Ball curve is given here explicitly subdivision algorithm and derived several calculation combinatorial identities . The third chapter describes Said-Bézier type generalized Ball curves ( referred to as SBGB type curve ) defined such curves including Said-Ball curve , Bézier curve and certain ranged between middle curve . Given their recursive algorithm , SBGB basis function dual functional , and thus get SBGB basis functions Bernstein basis functions conversion formula . In addition, it also discussed the envelope curve SBGB and segmentation algorithm . The fourth chapter describes the Wang-Said type the generalized Ball the curve (WSGB curve) defined such curves Wang-Ball curve , Said-Ball curve and certain intermediate curve , and their recursive algorithms . Of WSGB curve is given here for the first time subdivision algorithm , and several interesting calculations derived combinatorial identities . The fifth chapter describes the generalized Ball curve subdivision algorithm , and thus derive generalized Ball curve segments is converted to similarity transformation .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis
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