On the circle closest to a set of points

Authors:
Zvi Drezner;Stefan Steiner;George O. Wesolowsky
Affiliations:
Department of Management Science/Information Systems, California State University, Fullerton, CA;Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ont., Canada;Faculty of Business, McMaster University, Hamilton, Ont., Canada
Venue:
Computers and Operations Research - Location analysis
Year:
2002

Citing 5
Cited 12

Layout of facilities with some fixed points

Computers and Operations Research
Out-of-Roundness Problem Revisited

IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatial tessellations: concepts and applications of Voronoi diagrams

Spatial tessellations: concepts and applications of Voronoi diagrams
Circle fitting by linear and nonlinear least squares

Journal of Optimization Theory and Applications
Development and application of Voronoi diagrams in the assessment of roundness error in an industrial environment

Computers and Industrial Engineering

On an approximate minimax circle closest to a set of points

Computers and Operations Research
Majorization Algorithms for Inspecting Circles, Ellipses, Squares, Rectangles, and Rhombi

Operations Research
Locating a minisum circle in the plane

Discrete Applied Mathematics
The big cube small cube solution method for multidimensional facility location problems

Computers and Operations Research
Measure of circularity for parts of digital boundaries and its fast computation

Pattern Recognition
Locating Objects in the Plane Using Global Optimization Techniques

Mathematics of Operations Research
Robust Fitting of Circle Arcs

Journal of Mathematical Imaging and Vision
Geometric fit of a point set by generalized circles

Journal of Global Optimization
Minsum hyperspheres in normed spaces

Discrete Applied Mathematics
Fitting cylinders to data

Journal of Computational and Applied Mathematics
An exact method to find a circle passing through two points and minimizing the maximal weighted distance to a set of points

Computers and Operations Research
Algorithms for projecting points onto conics

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The objective of this paper is to find a circle whose circumference is as close as possible to a given set of points. Three objectives are considered: minimizing the sum of squares of distances, minimizing the maximum distance, and minimizing the sum of distances. We prove that these problems are equivalent to minimizing the variance, minimizing the range, and minimizing the mean absolute deviation, respectively. These problems are formulated and heuristically solved as mathematical programs. Special efficient heuristic algorithms are designed for two cases: the sum of squares, and the minimax. Computational experience is reported.