A GENERALIZED BALL CURVE AND ITS RECURSIVE ALGORITHM
A GENERALIZED BALL CURVE AND ITS RECURSIVE ALGORITHM
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DOI：
10.1145/77269.77275
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发表时间：
1989-10-01
影响因子：
6.2
通讯作者：
SAID, HB
中科院分区：
文献类型：
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作者：
SAID, HB
使用伯恩斯坦多项式作为Bézier的UNISURF中的基函数是众所周知的。这些基函数具有设计自由曲线和曲面所需的形状保持特性。使用de Casteljau算法有效地计算这些曲线和曲面。Ball在他的CONSURF程序中使用类似的方法定义三次曲线和双三次曲面。所采用的基函数与伯恩斯坦多项式略有不同。然而，它们也具有相同的形状保持特性。本文将Ball的三次基函数推广到高阶曲线曲面，并给出了生成广义曲线曲面的递归算法。该算法可以扩展到生成一个广义曲面，其方式与de Casteljau算法可以用于生成Bézier曲面的方式大致相同。
The use of Bernstein polynomials as the basis functions in Bézier's UNISURF is well known. These basis functions possess the shape-preserving properties that are required in designing free form curves and surfaces. These curves and surfaces are computed efficiently using the de Casteljau Algorithm. Ball uses a similar approach in defining cubic curves and bicubic surfaces in his CONSURF program. The basis functions employed are slightly different from the Bernstein polynomials. However, they also possess the same shape-preserving properties. A generalization of these cubic basis functions of Ball, such that higher order curves and surfaces can be defined and a recursive algorithm for generating the generalized curve are presented. The algorithm could be extended to generate a generalized surface in much the same way that the de Casteljau Algorithm could be used to generate a Bézier surface.