Certified Efficient Global Roundness Evaluation

We propose and analyze a global search algorithm for the computation of the minimum zone sphericity (circularity) error of a given set. The formulation is valid in any dimension and covers both finite sets of data points as well as infinite sets like polygonal chains or triangulations of surfaces. We derive theoretical estimates for the cost to reach a desired accuracy, and validate the performance of the algorithm with various numerical experiments.

[1]  Theodore J. Rivlin.  Approximation by circles , 2005, Computing.

[2]  K. Kim,et al.  Assessing Roundness Errors Using Discrete Voronoi Diagrams , 2000 .

[3]  Olivier Devillers,et al.  Computing Roundness is Easy if the Set is Almost Round , 2002, Int. J. Comput. Geom. Appl..

[4]  Michiel H. M. Smid,et al.  On the width and roundness of a set of points in the plane , 1999, Int. J. Comput. Geom. Appl..

[5]  I. D. Coope,et al.  Circle fitting by linear and nonlinear least squares , 1993 .

[6]  Reiner Horst,et al.  Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems , 1988, Math. Program..

[7]  P. Agarwal,et al.  Approximation Algorithms for Minimum-Width Annuli and Shells , 2000 .

[8]  Jyunping Huang.  An exact minimum zone solution for sphericity evaluation , 1999, Comput. Aided Des..

[9]  Jack Snoeyink,et al.  Fitting a Set of Points by a Circle , 1998, Discret. Comput. Geom..

[10]  G. A. Watson,et al.  On a sequential linear programming approach to finding the smallest circumscribed, largest inscribed, and minimum zone circle or sphere , 2001 .

[11]  Jose Mathew,et al.  Comparative study of roundness evaluation algorithms for coordinate measurement and form data , 2018 .

[12]  Jyunping Huang,et al.  An exact solution for the roundness evaluation problems , 1999 .

[13]  Timothy M. Chan.  Approximating the Diameter, Width, Smallest Enclosing Cylinder, and Minimum-Width Annulus , 2002, Int. J. Comput. Geom. Appl..

[14]  Micha Sharir,et al.  Efficient randomized algorithms for some geometric optimization problems , 1996, Discret. Comput. Geom..

[15]  Utpal Roy,et al.  Development and application of Voronoi diagrams in the assessment of roundness error in an industrial environment , 1994 .

[16]  D. T. Lee,et al.  An Optimal Algorithm for Roundness Determination on Convex Polygons , 1995, Comput. Geom..