| 摘要: |
| 除直线、圆弧、速端曲线等少数几种曲线外,平面参数曲线的offset曲线通常不能表示成有 理参数形式,因此在实际应用中,为了方便造型系统中数据结构和几何算法的统一表示,offse t曲线通常用低次曲线逼近来表示.通过用双圆弧逼近表示NURBS(non-uniform rational B -spline)曲线及其offset,并利用双圆弧逼近的特有性质,把offset的双圆弧逼近转化为原 曲线的双圆弧逼近,简化了问题的求解.同时考虑了双圆弧逼近算法中分割点的选取、公切点 的确定以及误差估计等主要问题.具体算 |
| 关键词: NURBS(non-uniform rational B-spline)曲线,offset,逼近,双圆弧,计算机辅助几何设计. |
| DOI： |
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| 基金项目:本文研究得到国家自然科学基金(No.69772019)和国家863高科技项目基金(No.863- 511-842-004)资助. |
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| The Biarc Approximation of Planar NURBS Curve and Its Offset |
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WANG Guo-ping,SUN Jia-guang
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| Abstract: |
| The planar offset curve cannot be expressed as rational parametric curve in gene ral excepta few types of curves such as line, arc, Hodograghs etc. In practice, the offset curve usually is approximated by lower degree rational polynomial cur ve in order to have the unified expression of data structure and geometric algor ithm in the commercial modeling systems. In this paper, an approximation approac h to NURBS (non-uniform rational B-spline) curve and its offset is presented b y using biarc. The biarc approximation of offset curve is simplified to biarc ap proximation to original curve. Some important and key problems, such as the reas onable selection of split points in NURBS curve, the definition of cotangent poi nt of biarc and error estimate method, are discussed. Examples verify the effici ency and reliability of the algorithms, which are implemented in the commercial geometric modeling systems Gems5.0 developed by CAD Center of Tsinghua University. |
| Key words: NURBS (non-uniform rational B-spline) curve, offset, approximation, biarc, CAGD (computer aided geometric design). |
