能量约束下的Bézier曲线构造  

Construction of Bézier Curves by Energy Constraints

作　　者：韩志红 朱春钢[1] Han Zhihong;Zhu Chungang(School of Mathematical Science,Dalian University of Technology,Dalian 116024)

机构地区：[1]大连理工大学数学科学学院

出　　处：《计算机辅助设计与图形学学报》2020年第2期213-221,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11671068,11271060)

摘　　要：Bézier曲线是计算机辅助几何设计中应用广泛的曲线造型工具,构造具有能量约束的曲线也是曲线造型研究的重要内容之一.构造给定首末控制顶点与初始切方向的Bézier曲线,当其满足jerk能量极小时,其余控制顶点可以由已知条件与参数α确定;其中α与初始切向量长度有关.当曲线满足弯曲能量约束时,参数α唯一确定,从而对有序点集,可以显式地构造满足jerk能量极小与弯曲能量约束的G^1拼接组合Bézier曲线.最后,通过具体实例构造通过给定有序点集且满足能量约束的组合Bézier曲线,并与其他方法所得结果进行对比,验证了方法的有效性与可行性.Bézier curve is a widely used modeling tool in Computer Aided Geometric Design.Construction of Bézier curves with energy constraints is one of the important topics in curve design.For design of Bézier curve with given ending control points and initial tangent vector,the remaining control points can be determined by known conditions and a parameterαwith minimal jerk energy.The parameterαcan be uniquely determined by bending energy constraints.For the ordered set of points,a combined Bézier curve with G^1 continuity can be constructed by minimal jerk energy and bending energy constraints.Finally,the combined Bézier curves of given ordered set of points and satisfying energy constraints are constructed by several examples,verifying the effectiveness and feasibility of the proposed method when compared with other methods.

关 键 词：BÉZIER曲线 能量约束 曲线构造 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]