郭明阳,李崇君.基于离散点和法矢的曲线重构算法[J].数学研究及应用,2020,40(1):87~100
基于离散点和法矢的曲线重构算法
Curve Reconstruction Algorithm Based on Discrete Data Points and Normal Vectors
投稿时间:2019-06-17  修订日期:2019-10-26
DOI:10.3770/j.issn:2095-2651.2020.01.008
中文关键词:  曲线重构  曲线拟合  法矢  B样条  主导点
英文关键词:curve reconstruction  curve fitting  normal vector  B-spline  dominant point
基金项目:国家自然科学基金(Grant Nos.11871137; 11572081),辽宁省高等学校创新人才支持计划(Grant No.LCR2018001).
作者单位
郭明阳 大连理工大学数学科学学院, 辽宁 大连 116024 
李崇君 大连理工大学数学科学学院, 辽宁 大连 116024 
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中文摘要:
      本文提出了一个基于离散点及法矢的B样条曲线重构算法.本方法在以下三个步骤做出了改进:基于法矢条件的离散点参数化,基于由法矢信息选取主导点的B样条节点向量确定方法,以及在拟合模型中平衡数据点误差及法矢向量误差的参数选取方法.由此,我们将B样条曲线拟合问题转化为三个相应子问题,并且能够自适应地得到B样条曲线.对比仅由数据点选取主导点的传统拟合方法,本文方法对一些包含较高噪音的数据集仍然能较好地保持原曲线的几何形状.
英文摘要:
      This paper presents a curve reconstruction algorithm based on discrete data points and normal vectors using B-splines. The proposed algorithm has been improved in three steps: parameterization of the discrete data points with tangent vectors, the B-spline knot vector determination by the selected dominant points based on normal vectors, and the determination of the weight to balancing the two errors of the data points and normal vectors in fitting model. Therefore, we transform the B-spline fitting problem into three sub-problems, and can obtain the B-spline curve adaptively. Compared with the usual fitting method which is based on dominant points selected only by data points, the B-spline curves reconstructed by our approach can retain better geometric shape of the original curves when the given data set contains high strength noises.
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