Almost strictly total positivity of NUAT B-spline basis

• Published in: Science China. Information sciences Vol. 56; no. 9; pp. 46 - 51
• Main Authors: Wei, WeiLi, Wang, GuoZhao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2013; Springer Nature B.V
• Subjects: Algorithms; B spline functions; B样条函数; B样条基; CAD; China; Coefficient of variation; Collection; Computer aided design; Computer Science; Information Systems and Communication Service; Knot insertion; Mathematical analysis; Mathematical models; Research Paper; Splines; 几何方法; 变异系数; 插入算法; 未成年人; 计算机辅助几何设计; 阳性; ASTP; NUAT B-spline basis; knot insertion algorithm; coefficient variation
• ISSN: 1674-733X; 1869-1919
• DOI: 10.1007/s11432-013-4995-2

Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometrical approach is proposed to prove the collection matrices of NUAT B-spline basis are almost strictly totally positive. In this paper, knot insertion algorithm combined with coefficient variation of NUAT B-spline function, we put forward an intuitive and geometrical method.