平面三次交错曲线的刻划
Characterization of Planar Cubic Alternative curve
摘要：
本文通过对平面三次Alternative曲线的分析，确定了凸、环、尖点和拐点的条件。因此，三次曲线由三个控制点和两个形状参数组成的基函数的线性组合来表示。利用代数运算确定形状参数的约束条件，并给出了曲线为严格凸曲线、有环曲线、尖点曲线和拐点曲线的充分条件。我们将结果总结为参数形状图。这种形式的简单性使得表征更直观和有效的计算。
英文摘要：
In this paper, we analyze the planar cubic Alternative curve to determine the conditions for convex, loops, cusps and inflection points. Thus cubic curve is represented by linear combination of three control points and basis function that consist of two shape parameters. By using algebraic manipulation, we can determine the constraint of shape parameters and sufficient conditions are derived which ensure that the curve is a strictly convex, loops, cusps and inflection point. We conclude the result in a shape diagram of parameters. The simplicity of this form makes characterization more intuitive and efficient to compute.
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