A normalized basis for cubic super spline space on Powell-Sabin triangulation

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• 作者：M. Lamnii^a ; ^{m_lamnii1@yahoo.fr" class="auth_mail} ; H. Mraoui^a ; ^{hamid_mraoui@yahoo.f" class="auth_mail} ; ^{hamid_mraoui@gmail.com" class="auth_mail} ; A. Tijini^a ; ^{tijiniahmed@yahoo.fr" class="auth_mail} ; A. Zidna^b ; ^{zidna@univ-metz.fr" class="auth_mail}
• 关键词：41A05 ; 41A25 ; 41A50 ; 65D05
• 刊名：Mathematics and Computers in Simulation
• 出版年：May, 2014
• 年：2014
• 卷：99
• 期：Complete
• 页码：108-124
• 全文大小：710 K

文摘

In this paper, we describe the construction of a suitable normalized B-spline representation for bivariate cubic super splines defined on triangulations with a Powell-Sabin refinement. The basis functions have local supports, they form a convex partition of unity, and every spline is locally controllable by means of control triangles. As application, discrete and differential quasi-interpolants of optimal approximation order are developed and numerical tests for illustrating theoretical results are presented.