The Finite Termination Property of an Algorithm for Solving the Minimum Circumscribed Ball Problem

• Authors: Andreas Gläser , Christian Grossman , Ulrich Lunze
• Languages of publication: PL

Abstracts

PL

In this paper basic mathematical tasks of coordinate measurement are briefly described and a modied optimization algorithm is proposed. Coordinate measurement devices generate huge data set and require adapted methods to solve related mathematical problems in real time. The proposed algorithm possesses a simplied step size rule and nds the solution of the minimum circumscribed ball fitting after only a nite number The iteration is of the steepest descent type applied to the related distance function. But, in contrast to standard algorithms it uses a modied step size rule that takes into account the specic properties of the occurring objective function. This small dierence in the code improves the performance of the algorithm and it enables real time use of the proposed method in coordinate measurement machines. The eciency of the prosed algorithm will be illustrated by some typical examples.

Keywords

PL

minimum circumscribed, maximum inscribed, minimum zone, geometrical form elements, coordinate measuring, mini-max problem, steepest descent

• Publisher: [unknown2]
• Journal: Schedae Informaticae
• Year: 2012
• Volume: 21

Dates

published

2012

online

21 - 05 - 2015

Contributors

author

Andreas Gläser

author

Christian Grossman

author

Ulrich Lunze