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

✍ Scribed by Su-Rong Jiang; Guo-Jin Wang

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 435 KB
Volume: 49
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2004.06.031

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✦ Synopsis

In this paper, a new generalized Ball basis, normalized totally positive (NTP) basis given by Delgado and Pefia, 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 B6zier curves and surfaces. After the Bdzier 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.

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