标题：Discussion on Minimal Curvature Variation in Cubic Hermite Curve Construction
作者：Li, Peipei; Zhang, Caiming; Li, Xuemei; Li, Weitao
作者机构：[Li, Peipei; Zhang, Caiming; Li, Xuemei; Li, Weitao] Shandong Univ, Sch Comp Sci & Technol, Jinan 250101, Peoples R China.; [Zhang, Caiming] Shandon 更多
会议名称：2nd Asian Conference on Design and Digital Engineering (ACDDE)
会议日期：AUG 27-29, 2011
来源：JOURNAL OF ADVANCED MECHANICAL DESIGN SYSTEMS AND MANUFACTURING
关键词：Minimization; Approximation; Numerical Computation; Cubic Hermite Curve;; Curvature Variation
摘要：In the fields of computer aided geometric design, computer graphics and so on, curvature variation minimization has been widely used for constructing curve and surface. This paper investigates the minimal curvature variation in constructing the cubic Hermite curve that interpolates the given positions and unit tangent vectors at two points, while the magnitudes of the tangent vectors are unknown. The computation of this problem is very hard to handle and a very time-consuming task. To reduce the computing cost, simpler models are used to approximate it, but the existing simpler models can't give a good approximation, and hence make the curves constructed have unsatisfactory shapes. So a new model is presented in this paper. In the new model, the magnitude of each tangent vector is expressed as polynomial function of the tangent vector angles, which is easy to compute, and the shapes of constructed curves are visually similar to the ones constructed by minimizing the accurate curvature variation.