论文标题
立方Bezier曲线和CATMULL-ROM花纹之间的转换
Conversion Between Cubic Bezier Curves and Catmull-Rom Splines
论文作者
论文摘要
花键是数学代表复杂形状的主要方法之一，这些方法已成为计算机图形（CG）和计算机辅助几何设计（CAGD）的主要技术，用于建模复杂表面。其中，Bézier和Catmull-ROM花纹是工程次场中最常见的。在本文中，我们专注于立方Bézier和Catmull-Rom曲线段之间的转换，而不是浏览其属性。通过得出转换方程，我们旨在将CATMULL-ROM或Bézier立方曲线的原始控制点集转换为一组新的控制点，当将其视为另一个曲线的控制点时，它与原始曲线的形状大致相同。由于提供了控制点的简单线性变换，该方法非常简单，高效且易于实现，本文在本文中使用一些数值和视觉示例进行了进一步验证。
Splines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull-Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull-Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull-Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.
