Conversion and evaluation for two types of parametric surfaces constructed by NTP bases
Conversion and evaluation for two types of parametric surfaces constructed by NTP bases
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DOI：
10.1016/j.camwa.2004.06.031
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发表时间：
2005
影响因子：
2.9
通讯作者：
Sun Jiang;Guojin Wang
中科院分区：
文献类型：
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作者：
Sun Jiang;Guojin Wang
本文研究了 Delgado 和 Peña 提出的一种新的广义 Ball 基，即归一化完全正 (NTP) 基。推导了该基与Bernstein基之间的转换公式。我们还证明这些公式不仅对于研究由广义Ball基构造的曲线和曲面的几何性质（例如细分）有价值，而且可以提高Bézier曲线和曲面的计算速度。将Bézier曲面（曲线）转换为广义Ball曲面（曲线）后，评估的时间复杂度可以从曲面（曲线）的次数的三次方降低到二次方。然而，固有属性，例如形状保持属性，并没有改变。因此，广义的球面和曲线在几何设计的应用中具有广阔的前景。
In this paper, a new generalized Ball basis, normalized totally positive (NTP) basis given by Delgado and Peña, 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 Bézier curves and surfaces. After the Bézier 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.