四次间接PH曲线的几何特征
Geometric Characteristics of Quartic Indirect PH Curves
摘要: 四次间接PH曲线根据其导数的表示可以分为两类，本文介绍了两类四次间接PH曲线的几何特征。主要方法是用Bernstein形式的复多项式表示平面Bézier曲线并且通过引入辅助控制顶点将几何特征转化为非线性方程求解问题，使得四次平面曲线成为间接PH曲线的条件可以用控制多边形上的几何约束来描述。
Abstract: Quadric indirect PH curves can be divided into two types according to the expression of their derivatives. This paper introduces the geometric characteristics of two kinds of quadric indirect PH curves. The plane Bézier curves are represented by using the Bernstein form of complex polynomials. The geometric features are transformed into nonlinear equations by introducing auxiliary control vertices. Then the conditions of quartic plane curves to be indirect PH curves can be described by the geometric constraints on the control polygon.
文章引用：沈洋, 秦凌云, 杨雪, 段卓, 彭兴璇. 四次间接PH曲线的几何特征[J]. 应用数学进展, 2022, 11(4): 1588-1593. https://doi.org/10.12677/AAM.2022.114173

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