N次Bezier曲线的多边形快速逼近算法
Fast Approximation Algorithm of N-Degree Bezier Curve via Polygon

作为一种重要的形状表示的数学方法，Bezier曲线在各种CAD/CAM（计算机辅助设计和计算机辅助制造）软件中广泛应用。在复杂曲面的数控加工操作中，CAD/CAM系统最终以直线段代替曲线段进行加工。为了提高以微小直线段逼近Bezier曲线的效率和精度，提出了一种对于N次Bezier曲线较为实用的快速逼近算法。该方法通过对Bezier曲线反复进行定比分割，使其控制多边形逐步收敛于原Bezier曲线，直至逼近误差满足要求。通过MATLAB软件将该算法与已有分割算法进行对比，结果表明与已有分割算法相比，多边形快速逼近算法极大地降低了逼近误差，较好的提高分割效率。最后，通过给出工程实例验证了该算法在工程应用上的实用性。
As an important mathematical method of shape representation, Bezier curve is widely used in CAD/CAM software. In the numerical control machining operation of complex surface, the CAD/CAM (computer-aided design, computer-aided manufacturing) system eventually uses the straight line segments instead of the curve to process a workpiece. In order to improve the efficiency and accuracy of approximation Bezier curve with tiny straight line segments, a fast approximation algorithm for N-degree Bezier curve is proposed. In this method, the Bezier curve is subdivided with an invariable proportion repeatedly to make the control polygon converge gradually to the original Bezier curve until the approximation error meets the requirement. Comparing with the existing segmentation algorithm by using MATLAB software, the results show that the fast approximation algorithm via polygon reduces greatly the approximation error and improves the segmentation efficiency. Finally, the practicality of this algorithm in engineering is verified by giving an example