The Biarc Approximation of Planar NURBS Curve and Its Offset
平面NURBS曲线及其Offset的双圆弧逼近

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.