Circle approximation using LN Bézier curves of even degree and its application |
| |
Authors: | Young Joon Ahn Christoph Hoffmann |
| |
Institution: | 1. Department of Mathematics Education, Chosun University, Gwangju 501-759, South Korea;2. Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA |
| |
Abstract: | We present an approximation method of circular arcs using linear-normal (LN) Bézier curves of even degree, four and higher. Our method achieves Gm continuity for endpoint interpolation of a circular arc by a LN Bézier curve of degree 2m , for m=2,3. We also present the exact Hausdorff distance between the circular arc and the approximating LN Bézier curve. We show that the LN curve has an approximation order of 2m+2, for m=2,3. Our approximation method can be applied to offset approximation, so obtaining a rational Bézier curve as an offset approximant. We derive an algorithm for offset approximation based on the LN circle approximation and illustrate our method with some numerical examples. |
| |
Keywords: | Circle approximation Offset approximation LN Bé zier curve Hausdorff distance Curvature continuous interpolation |
本文献已被 ScienceDirect 等数据库收录! |
|