在三角域上构造三次多项式插值曲面  

Constructing Cubic Polynomial Interpolation Surfaces on Triangular Domain

作　　者：于谦[1] 张彩明[2] Yu Qian;Zhang Caiming(Big Data Engineering Center, Shandong Women’s University, Ji’nan 250300;College of Computer Science and Technology, Shandong University, Ji’nan 250061)

机构地区：[1]山东女子学院大数据工程中心,济南250300 [2]山东大学计算机科学与技术学院,济南250061

出　　处：《计算机辅助设计与图形学学报》2017年第5期868-873,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：山东省自然科学基金(ZR2011FL005;ZR2012FL05);山东省高等学校科技计划项目(J15LN58);山东女子学院数据挖掘科研创新团队基金

摘　　要：为满足矿山地形的拟合、水流深度的绘制等很多特殊工程数据量大、有一定的光顺要求但又不需要曲面过于凸起饱满这一需求,提出一种C1连续的三次多项式插值曲面,同时有针对性地提出一种一阶偏导数估计算法.首先将空间散乱数据点投影到平面后进行三角划分;其次针对每个三角形,在其每条边上构造一个C1连续的三次多项式曲面片,由这3个曲面片加权平均形成该三角形的曲面片;最后将所有三角形上的曲面片拼合成整体曲面.为使生成的曲面尽可能地贴近数据点所建议的形状,在曲面求解过程中将数据点分成内部点和边界点分别估计偏导数.实验结果表明,该算法计算量小、具有良好的局部性,并给出了新曲面的效果.Many special projects,such as mining shape fitting and water depth render,need large amounts of data and have certain requirement on smoothness of interpolation surfaces while the surfaces can't be too convex.To satisfy these requirements,this paper presents a C1continue cubic polynomial interpolation surface and a target method for estimating partial derivatives.Firstly,projected the spatial scattered data points onto a plane and then triangulated them;Secondly,interpolated three piecewise cubic polynomial patches on each triangle which were C1continue on each edge respectively,and the weighted combination of the three patches constructed surface patch of each triangle.Lastly,all surface patches of all triangles were jointed together to form the whole surface.To make the surface be closed to advised shape as far as possible,different partial derivatives estimation methods were used according to the data point was boundary point or not.New method is simple to compute and has a good local property.The result of new surface is given in experiments.

关 键 词：插值 曲面 多项式 偏导数 C1连续 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]