点击次数：

论文类型：期刊论文

发表时间：2016-09-01

发表刊物：VISUAL COMPUTER

收录刊物：SCIE、EI、Scopus

卷号：32

期号：9

页面范围：1071-1084

ISSN号：0178-2789

关键字：Generalized rational Bezier curves; Generalized rational de Casteljau algorithm; Hermite interpolation; Geometrical continuity; Rigid body motion

摘要：In this paper, we present a new method for the smooth interpolation of the orientations of a rigid body motion. The method is based on the geometrical Hermite interpolation in a hypersphere. However, the non-Euclidean structure of a sphere brings a great challenge to the interpolation problem. For this consideration and the requirements for practical application, we construct the spherical analogue of classical rational B,zier curves, called generalized rational B,zier curves. The new spherical curves are obtained using the generalized rational de Casteljau algorithm, which is a generalization of the classical rational de Casteljau algorithm to a hypersphere. Then, Hermite interpolation problem in hypersphere is solved analytically using the generalized rational B,zier curve of degree 5. The new method offers residual free parameters including shape parameters and weights, which guarantee the existence of the interpolant to arbitrary motion data and offer great flexibility for the shape design of the motion. Numerical examples show that our method is far better behaved according to the energy functional which is regarded as a measure of the motion shape.