平面隐式曲线的Hermite插值逼近  

Approximating Planar Implicit Curves with Hermite Interpolation

作　　者：魏利 赵晶洁 黄慧敏 WEI Li;ZHAO Jingjie;HUANG Huimin(Institute of Educational Information Engineering,Nanjing Normal University,Nanjing Jiangsu 210097,China)

机构地区：[1]南京师范大学教育信息工程研究所,江苏南京210097

出　　处：《图学学报》2018年第4期752-756,共5页Journal of Graphics

基　　金：全国教育科学"十三五"规划2017年教育部重点课题(DCA170302)

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。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.

关 键 词：图形绘制 隐式曲线 HERMITE插值 采样点优化 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]