应用CatMull-Rom样条曲线描述道路透视图中心线特征的方法研究  

Methods about Using Cat Mull-Rom Spline to Describe Characteristics of Road Centerline in Perspective View

作　　者：陈雨人[1] 王瑞云[1] 董永杰[1] 贺思虹[1] 

机构地区：[1]同济大学交通运输工程学院,上海201804

出　　处：《重庆交通大学学报（自然科学版）》2015年第4期45-51,112,共8页Journal of Chongqing Jiaotong University(Natural Science)

基　　金：国家自然科学基金项目(51078270;51238008);高等学校博士学科点专项科研基金项目(20120072110019)

摘　　要：采用三次Bezier曲线、三次B样条曲线和Cat Mull-Rom样条曲线分别拟合道路透视图中心线,并进行对比研究,分析了各自描述道路透视图中心线时控制点确定和拟合产生残差的情况,结果显示,在描述道路透视图中心线特征方面,Cat Mull-Rom样条曲线更为高效和精准,可以适应绝大部分道路几何设计形成的透视图中心线特征描述的需要。将道路透视图划分为"近景"、"中景"和"远景"3个不同功能区域,提出视曲线长和视曲率概念和相应的计算方法,将视曲线长和视曲率作为描述透视图中心线特征的形状参数,并结合运行车速进行了相关性分析。研究表明形状参数和运行车速密切相关。Cubic Bezier spline,cubic B-spline and Cat Mull-Rom spline were used to fit road centerline in perspective view in this paper. The control points and fitting residuals from the three kinds of splines were analyzed by comparative studies.The results show that Cat Mull-Rom spline is more efficient and precise than the others in describing road centerline features in perspective view. It can meet the needs of describing features of perspective view from the vast maiority of road geometric design. The perspective view is divided into＂near-scene＂,＂middle scene＂and＂far scene＂as three different functional regions,and the concept and calculation method of the visual curve length and the visual curve curvature were proposed as shape parameters of road centerline in perspective view,combined the correlation analysis with operating speed. The shape parameters and operating speed are closely related.

关 键 词：道路工程 Cat Mull-Rom样条曲线 道路透视图中心线 视曲线长 视曲率 

分 类 号：U491.254[交通运输工程—交通运输规划与管理]