Abstract: Given two points and their directional tangent vectors, Femiani et al. proposed a method for obtaining an interpolation elliptic arc with least eccentricity. The elliptic arcs from different positions of a same ellipse have different deviations from a circle. The ratio between the minimum curvature radius and the maximum curvature radius of an elliptic arc can be used to measure the corresponding deviation from a circle, which is called pseudo-eccentricity. This paper presents a new method to achieve an interpolation elliptic arc with least pseudo-eccentricity, which means that the resulting elliptic arc has less deviation from a circle than that of Femiani’s method. Examples illustrate the new method and its effectiveness as well.

Key words: rational quadratic Bézier curve, geometric Hermite interpolation, least eccentricity, pseudo-eccentricity of elliptic arc

摘要： 给定两个点以及相应的两个切向，Femiani等人提出了基于最小离心率椭圆的插值方法。同一椭圆上不同位置的椭圆弧，对应的形状与圆弧的接近程度是不一样的。椭圆弧的最小曲率半径和最大曲率半径之比，可以反映对应的椭圆弧与圆弧的接近程度，称之为椭圆弧的拟离心率。给出了基于拟离心率的新方法，使获取的椭圆弧具有最小拟离心率。与Femiani的方法相比，采用新方法得到的插值椭圆弧更加接近于圆弧。最后举例说明了新方法及其效果。

关键词: 有理二次曲线, 几何Hermite插值, 最小离心率, 椭圆弧拟离心率