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

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