Computing the Hausdorff distance between two B-spline curves

Authors:
Xiao-Diao Chen;Weiyin Ma;Gang Xu;Jean-Claude Paul
Affiliations:
Hangzhou Dianzi University, Hangzhou, 310018, China and Department of MEEM, City University of Hong Kong, Hong Kong, China;Department of MEEM, City University of Hong Kong, Hong Kong, China;Hangzhou Dianzi University, Hangzhou, 310018, China;School of Software, Tsinghua University, Beijing 100084, China and INRIA, France
Venue:
Computer-Aided Design
Year:
2010

Citing 10
Cited 3

Combining binary search and Newton's method to compute real roots for a class of real functions

Journal of Complexity
Shape Interrogation for Computer Aided Design and Manufacturing

Shape Interrogation for Computer Aided Design and Manufacturing
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants

IEEE Computer Graphics and Applications
Point inversion and projection for NURBS curve and surface: control polygon approach

Computer Aided Geometric Design
A second order algorithm for orthogonal projection onto curves and surfaces

Computer Aided Geometric Design
A counterexample on point inversion and projection for NURBS curve

Computer Aided Geometric Design
Geometric accuracy analysis for discrete surface approximation

Computer Aided Geometric Design
Computing the minimum distance between a point and a NURBS curve

Computer-Aided Design
Computing the minimum distance between two Bézier curves

Journal of Computational and Applied Mathematics
Hausdorff and minimal distances between parametric freeforms in R2and R3

GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing

Polyline approach for approximating Hausdorff distance between planar free-form curves

Computer-Aided Design
GPU-accelerated Hausdorff distance computation between dynamic deformable NURBS surfaces

Computer-Aided Design
Efficient Hausdorff Distance computation for freeform geometric models in close proximity

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a geometric pruning method for computing the Hausdorff distance between two B-spline curves. It presents a heuristic method for obtaining the one-sided Hausdorff distance in some interval as a lower bound of the Hausdorff distance, which is also possibly the exact Hausdorff distance. Then, an estimation of the upper bound of the Hausdorff distance in an sub-interval is given, which is used to eliminate the sub-intervals whose upper bounds are smaller than the present lower bound. The conditions whether the Hausdorff distance occurs at an end point of the two curves are also provided. These conditions are used to turn the Hausdorff distance computation problem between two curves into a minimum or maximum distance computation problem between a point and a curve, which can be solved well. A pruning technique based on several other elimination criteria is utilized to improve the efficiency of the new method. Numerical examples illustrate the efficiency and the robustness of the new method.