具有局部性质的球面插值样条曲线的构造

高维球面样条曲线拟合技术在计算机动画和惯性导航等领域都受到广泛地关注.实际中常需球面曲线插值给定的数据点,并要求曲线具有一定的连续性和良好的局部性质.此前的方法存在一定的局限性.为此,基于球面Bézier曲线,提出了一种仅利用插值点位置信息便可在任意维空间中构造C 2球面插值样条曲线的新方法.首先,通过映射拟合出了插值...

The construction of spherical interpolation splines with local properties

The high dimensional spherical spline curves fitting technology has received wide attention in computer animation and inertial navigation.In practical applications,spline curves are usually required to interpolate the given data points with certain continuity and local properties.Thus,the previous methods are limited in certain regards.For this reason,a new method,based on spherical Bézier curves,of constructing spherical spline in arbitrary dimensional space was proposed.Firstly,the higher order derivative vectors at the interpolation points were fitted by a reflection.Then,necessary and sufficient conditions for C²Hermite interpolation were given.Finally,the C²spherical Bézier spline was constructed,using only interpolation points.The proposed method exhibitslocal properties.The disturbance of some points will not impact other parts of the spline.The splines possess explicit expressions not involving nonlinear equations.Numerical experiments show that the method can be widely applicable and efficient.