A class of generalized B-spline quaternion curves

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• 作者：Yan Xing ; ^{xy1128@126.com" class="auth_mail" title="E-mail the corresponding author} ; ^{yanxing28@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Ren-zheng Xu¹ ; ^{1291359929@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Jie-qing Tan ; ^{jieqingtan@hfut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Wen Fan ; Ling Hong
• 关键词：Quaternion ; SO(3)(3D rotation group) ; S3(Unit 3-sphere) ; Generalized B-spline ; Ck-continuity
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：15 November 2015
• 年：2015
• 卷：271
• 期：Complete
• 页码：288-300
• 全文大小：2853 K

文摘

Unit quaternion curves have gained considerable attention in the fields of robot control and computer animation. Kim et al. proposed a general construction method of unit quaternion curves which can transform the closed form equation for kth order B-spline basis functions in R³ into its unit quaternion analogue in SO  (3) while preserving the mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300315012436&_mathId=si18.gif&_user=111111111&_pii=S0096300315012436&_rdoc=1&_issn=00963003&md5=d641e9288f3ceec2b88003ff96a17ca7" title="Click to view the MathML source">Ck−2mathContainer hidden">mathCode"><math altimg="si18.gif" overflow="scroll">Ck−2math>-continuity. Juhász and Róth generalized the classical B-spline functions by means of monotone increasing continuously differentiable core functions based on the recurrence formula of B-spline functions. In order to extend the applications of the generalized B-spline functions in computer animation, the definition and construction scheme of generalized B-spline quaternion curves in S³ are put forward in this paper. The introduced nonlinear core functions are not only theoretically interesting, but also offer a large variety of shapes. Some properties of this class of unit quaternion curves, such as continuity and local controllability are also discussed. Experimental results show the effectiveness and usefulness of our construction methods of generalized B-spline quaternion curves.