Interactive Shape Control with Rational Cubic Splines
Interactive Shape Control with Rational Cubic Splines
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DOI：
10.1080/16864360.2004.10738317
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发表时间：
2004
影响因子：
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通讯作者：
Z. Habib;M. Sakai;M. Sarfraz
中科院分区：
文献类型：
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作者：
Z. Habib;M. Sakai;M. Sarfraz
本文讨论了一种带形状参数的有理三次样条，并展望了它在计算机图形学中的应用。它将圆锥曲线和参数三次曲线合并为特例。样条曲线描述中的参数(权重)可用于局部和全局修改曲线的形状。有理三次样条线获得参数C2光滑度，而圆锥线段的缝合在相邻节点处保持视觉上合理的光滑度(C1)。还提出了一种非常简单的基于距离的近似导数方法来计算控制点。该曲线方案是可插补的，可以独立绘制抛物线、双曲线型、椭圆型和圆形样条线以及有理三次样条线的零碎部分。讨论了空间椭圆弧的疑难情况，并介绍了一种中间点插补方案，该方案可以迫使曲线通过任意线段之间的给定点。
AbstractA rational cubic spline, with shape parameters, has been discussed with the view to its application in Computer Graphics. It incorporates both conic sections and parametric cubic curves as special cases. The parameters (weights), in the description of the spline curve can be used to modify the shape of the curve, locally and globally. The rational cubic spline attains parametric C2 smoothness whereas the stitching of the conic segments preserves visually reasonable smoothness (C1) at the neighboring knots. A very simple distance-based approximated derivative scheme is also presented to calculate control points. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as bits and pieces of a rational cubic spline. We discuss difficult cases of elliptic arcs in space and introduce intermediate point interpolation scheme which can force the curve to pass through given point between any segment.