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图学学报

图学学报 ›› 2021, Vol. 42 ›› Issue (4): 644-650.DOI: 10.11996/JG.j.2095-302X.2021040644

• 计算机图形学与虚拟现实 • 上一篇    下一篇

曲率单调 Bézier 曲线 G1 插值算法及应用

  

  1. 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
  • 出版日期:2021-08-31 发布日期:2021-08-05
  • 基金资助:
    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)

G1 interpolation algorithm and application of Bézier curves with monotone curvature

  1. 1. School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China;
    2. State Key Laboratory of Virtual Reality Technology & Systems, Beihang University, Beijing 100191, China
  • Online:2021-08-31 Published:2021-08-05
  • Supported by:
    National Natural Science Foundation of China (61572056; 61972011); Open Project Program of the State Key Lab of CAD & CG
    Zhejiang University (A2024)

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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。

关键词: 曲率单调, Bézier 曲线, G1 插值, 欧拉螺旋线

Abstract: 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.

Key words: monotone curvature, Bézier curve, G1 interpolation, Euler spiral

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