A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints  

作　　者：HE Shitao SHEN Liyong WU Qin YUAN Chunming 

机构地区：[1]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [2]KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Journal of Systems Science & Complexity》2024年第3期1271-1294,共24页系统科学与复杂性学报（英文版）

基　　金：partially supported by the National Key Research and Development Program of China under Grant No. 2020YFA0713703;the National Science Foundation of China under Grant Nos. 11688101, 12371384;12271516;the Fundamental Research Funds for the Central Universities。

摘　　要：Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint;the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation.Experimental results are presented to show the advantages of the proposed algorithms.

关 键 词：Cubic B-spline Hausdorff distance INTERPOLATION tangential direction 

分 类 号：O241.3[理学—计算数学]