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一种带约束限制的三次B样条曲线矢量数据压缩算法
冯峰,蒋维
作者单位
冯峰 武汉大学数学与统计学院, 湖北 武汉 430072 
蒋维 武汉大学数学与统计学院, 湖北 武汉 430072 
摘要:
为了便于大型矢量数据高效的检索分析,存储和传输,事先对矢量数据进行压缩是极为必要的.本文基于B样条良好的局部性和光滑性,利用带约束条件限制的三次B样条拟合方法对曲线矢量数据进行压缩.为了验证所提出算法的高效性,本文给出了9种不同的曲线矢量数据压缩算例,并同时与传统的Douglas-Peucker矢量压缩算法进行对比.数值算例表明,本文所提出的曲线矢量数据压缩算法明显优于传统的Douglas-Peucker压缩算法.该算法不仅能够保证曲线整体的二阶光滑性,还能够显著地降低数据的压缩率,因而具有广泛的应用前景(例如自动驾驶).
关键词:  曲线矢量数据压缩  三次B样条  整体C2-连续  Douglas-Peucker算法  约束条件
DOI:
分类号:O241.5
基金项目:湖北省自然科学基金面上项目资助(2018CFB466).
A CUBIC B-SPLINE-BASED VECTOR DATA COMPRESSION ALGORITHM WITH BOUNDARY CONSTRAINTS
FENG Feng,JIANG Wei
Abstract:
In order to efficiently retrieve, analyze, store and transmit large amount of vector data, it is extremely necessary to compress these vector data in advance. Based on elegant properties of the B-spline (e.g., locality and smoothness), we propose a cubic B-spline-based algorithm to compress the vector data with boundary constraints. The proposed cubic B-spline vector data compression algorithm is tested on nine examples with curve vector data. We also compare numerical results produced by the proposed algorithm with these of the classical Douglas-Peucker compression algorithm. Numerical results show that the proposed cubic B-spline-based vector compression algorithm not only can significantly reduce the compression rate, but also can produce highly accurate compression curve with C2-smoothness. Therefore, the algorithm has many important potential applications (e.g., automatic drive).
Key words:  curve vector data compression  cubic B-spline  C2-smoothness  Douglas-Peucker algorithm  boundary constraints

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