在三角域上构造三次多项式插值曲面

发布时间：2018-03-06 05:11

本文选题：插值　切入点：曲面　出处：《计算机辅助设计与图形学学报》2017年05期 　论文类型：期刊论文

【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.
[Abstract]:In order to meet the requirements of mining terrain fitting, drawing of water depth and so on, many special projects, such as large amount of data, which have certain fairing requirements but do not need the curved surface to be too bulging and full, a C1 continuous cubic polynomial interpolation surface is proposed. At the same time, a first order partial derivative estimation algorithm is proposed. Firstly, the spatial scattered data points are projected to the plane to be triangulated. Secondly, for each triangle, a C 1 continuous cubic polynomial patch is constructed on the edge of each triangle. The three surfaces are weighted to form the triangular patches. Finally, all the surfaces on the triangles are assembled into a global surface. In order to make the generated surface as close as possible to the proposed shape of the data point, In the process of surface solution, the data points are divided into interior points and boundary points to estimate the partial derivatives respectively. The experimental results show that the algorithm has the advantages of small computational complexity and good locality, and the effect of the new surface is given.
【作者单位】：山东女子学院大数据工程中心;山东大学计算机科学与技术学院;
【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
【分类号】：TP391.7

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