带有给定切线多边形的曲率连续的有理二次样条曲线

The G^2-Continuous Rational Quadratic Bézier Curve with a Given Tangent Polygon

本文论述了与给定切线多边形相切的有理二次Bézier曲线,构造曲线是曲率连续的,具有局部可调性,且对切线多边形是保形的;跟三次(四次)Bézier曲线或B样条曲线方法相比,具有切点的变动范围更大、曲线次数低、结构简单、计算量少、显示更快的特点。最后,通过实例加以说明。

This paper proposes an approach of constructing rational quadratic Bézier curves with all edges tangent to a given control polygon. The curve is joined by piecewise as G^2-continuity and shape-preserving to the tangent polygon. The rational quadratic Bézier curve is less of computation than the curves with the cubic（quartic） B6zier and cubic（quartic） B- Spline curves. Pinally, two examples show that the method given in this paper is effective for CAGD.