曲率单调Bézier曲线G1插值算法及应用  

G1 interpolation algorithm and application of Bézier curves with monotone curvature

作　　者：何川 赵罡[1,2] 王伟[1] 王爱增[1,2] HE Chuan;ZHAO Gang;WANG Wei;WANG Ai-zeng(School of Mechanical Engineering&Automation,Beihang University,Beijing 100191,China;State Key Laboratory of Virtual Reality Technology&Systems,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学机械工程及自动化学院,北京100191 [2]北京航空航天大学虚拟现实技术与系统国家重点实验室,北京100191

出　　处：《图学学报》2021年第4期644-650,共7页Journal of Graphics

基　　金：国家自然科学基金项目(61572056,61972011);浙江大学CAD&CG国家重点实验室开放课题(A2024)。

摘　　要：基于曲率单调的Bézier曲线,提出了一种精确而高效的满足G1约束的样条曲线插值算法。给定首尾插值数据点位置及方向角,利用曲率单调Bézier曲线的几何设计准则,求解非线性方程组,构造满足G1插值条件的曲率单调Bézier曲线。与基于欧拉螺旋线的插值算法相比,本文方法构造简单、插值精确,与现有的NURBS方法兼容。基于分段拼接,该算法能够处理给定点列及首尾切线方向的插值问题,具有较强的适应性与通用性。Based on the Bézier curve with monotone curvature,this paper presented an accurate and efficient spline interpolation algorithm satisfying G1 constraint.With the given two point-orientation pairs,the construction was to solve the nonlinear equations using the geometric design criteria of monotone curvature,so as to obtain the Bézier curve satisfying the G1 interpolation condition.Compared with the interpolation algorithm based on Euler spiral,the advantages of the proposed method are as follows:simple construction,accurate calculation,and compatibility with the existing NURBS.Based on the idea of piecewise,this algorithm can deal with the interpolation problems of a given sequence of points and the direction of head and tail tangents,manifesting stronger adaptability and universality.

关 键 词：曲率单调 BÉZIER曲线 G1插值 欧拉螺旋线 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]