Conversion and evaluation for two types of parametric surfaces constructed by NTP bases

Authors:
Su-Rong Jiang;Guo-Jin Wang
Affiliations:
Department of Mathematics and State Key Laboratory of CAD and CG Zhejiang University, Hangzhou 310027, P.R. China and Department of Mathematics, China Institute of Metrology Hangzhou 310018, P.R. ...;Department of Mathematics and State Key Laboratory of CAD and CG Zhejiang University, Hangzhou 310027, P.R. China
Venue:
Computers & Mathematics with Applications
Year:
2005

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Erratum: Erratum to: "Conversion and evaluation for two types of parametric surface constructed by NTP bases" [Comput. Math. Appl. 49(2) (2005) 321-329]

Computers & Mathematics with Applications

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Abstract

In this paper, a new generalized Ball basis, normalized totally positive (NTP) basis given by Delgado and Pena, is investigated. The conversion formulae between the basis and the Bernstein basis are derived. We also prove that these formulae not only are valuable for studying the geometric properties, such as subdivision, of the curves and surfaces constructed by this generalized Ball basis, but also can improve the computational speed of the Bezier curves and surfaces. After the Bezier surface (curve) is converted into the generalized Ball surface (curve), the time complexity for evaluation can be reduced from cubic to quadratic, of the degree of the surface (curve). However, the intrinsic property, such as shape-preserving property, is not changed. So, the generalized Ball surface and curve have a great future in application of geometric design.