基于二元混合有理插值的形状渐变方法

为实现多个多边形间的平滑自然渐变，提出基于二元混合向量值有理插值的非线性二维形状渐变方法。将多个多边形的顶点坐标作为平面域上的向量，利用二元Newton-Thiele型向量连分式建立有理插值曲面，通过对插值曲面进行重采样得到一系列渐变中间多边形。实验结果表明，该方法具有计算精度高、适应性强、易于编程实现的特点。

Shape Morphing Method Based on Bivariate Blending Rational Interpolation

In order to realize metamorphosis among series of polygons, this paper presents a non-linear 2D shape morphing method based on bivariate blending vector rational interpolation. It makes the vertex coordinate of series of polygons as vector on plane domain, builds rational interpolation surface by bivariate Newton-Thiele vector continued fraction, and series of metamorphosis polygons are generated by resembling the surface of this interpolation function. Experimental results show that this method has the high precision of calculation, strong adaptation and easiness of programming.