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图学学报

• 可视化/可视分析 • 上一篇    下一篇

平面隐式曲线的Hermite 插值逼近

  

  1. 南京师范大学教育信息工程研究所,江苏 南京 210097
  • 出版日期:2018-08-31 发布日期:2018-08-21
  • 基金资助:
    全国教育科学“十三五”规划2017年教育部重点课题(DCA170302)

Approximating Planar Implicit Curves with Hermite Interpolation

  1. Institute of Educational Information Engineering, Nanjing Normal University, Nanjing Jiangsu 210097, China
  • Online:2018-08-31 Published:2018-08-21

摘要: 隐式曲线在医学图像处理、地理信息系统、数值场可视化等领域中有着重要应用。
在分析点采样和曲线逼近理论的基础上,提出一种运用Hermite 插值方法逼近平面隐式曲线的
算法。首先将曲线绘制区域网格化,在网格单元各边中通过线性插值计算曲线采样点;其次通
过计算采样点精简前后构成的曲线段之间产生的误差优化采样点;最后通过Hermite 插值法逼
近隐函数曲线。实验表明,通过该算法绘制出的曲线在采样点数量较少的情况下,其光滑度和
准确度仍较高。

关键词: 图形绘制, 隐式曲线, Hermite 插值, 采样点优化

Abstract: Implicit curves play an important role in medical image processing, geographic information
system, and numerical field visualization. On the basis of sampling point analysis and curve
approximation method, we introduce an algorithm for approximating planar implicit curves by means
of Hermite interpolation. The sampling points were firstly obtained by linearly interpolating each
edge of the grid cells distributed uniformly in the grid region. Then, we calculated the error between
curve segments before and after optimizing. Once the error meets the optimizing requirements, the
sampling points are consequently optimized. Finally, the algorithm approximated the implicit curves
by the Hermite interpolation method. Experiments have shown that even when the number of
sampling points is small, the curves drawn by the algorithm still have relatively higher smoothness
and accuracy.

Key words: graph plotting, implicit curve, Hermite interpolation, optimizing sampling point