样条曲线的保形性
Shape preservation behavior of spline curves
摘要：
样条曲线的保形性包括保凸性、保拐性、保共线性、保挠性和保共面性的条件。我们提出了我们的结果，作为一个改进的定义，并提供几何洞察到上述形状保持标准。我们还调查了各种结果的影响，从文献上的各种形状保存标准。这些结果没有被早先提到的背景下，样条的形状保持行为。我们指出，每个曲线段需要满足一个以上的形状保持标准。我们研究了不同的形状保持标准之间的冲突1）在每个曲线段和2）相邻的曲线段。推导了三次曲线段保形准则的简化公式。我们研究了三次Catmull-Rom样条的保形性，发现它虽然是一条非常简单的样条曲线，但它确实满足所有的保形准则。
英文摘要：
Shape preservation behavior of a spline consists of criterial conditions for preserving convexity, inflection, collinearity, torsion and coplanarity shapes of data polgonal arc. We present our results which acts as an improvement in the definitions of and provide geometrical insight into each of the above shape preservation criteria. We also investigate the effect of various results from the literature on various shape preservation criteria. These results have not been earlier refered in the context of shape preservation behaviour of splines. We point out that each curve segment need to satisfy more than one shape preservation criteria. We investigate the conflict between different shape preservation criteria 1)on each curve segment and 2)of adjacent curve segments. We derive simplified formula for shape preservation criteria for cubic curve segments. We study the shape preservation behavior of cubic Catmull-Rom splines and see that, though being very simple spline curve, it indeed satisfy all the shape preservation criteria.
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