Bounding sphere
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In computer graphics and computational geometry, a bounding sphere is a bounding volume in the form of a sphere surrounding an object.
In statistics and operations research a bounding sphere is an n-dimensional sphere containing a specific set of n-dimensional data points. In general, the sphere of interest for a given set of points is the minimal bounding sphere (the unique sphere with minimal radius among all spheres containing the points). Such spheres are useful in clustering, where groups of similar data points are classified together. In the statistical analysis the scattering of data points within a sphere may be attributed to measurement error or natural (usually thermal) processes, in which case the cluster represents a perturbation of an ideal point. In some circumstances this ideal point may be used as a substitute for the points in the cluster, advantageous in reducing calculation time. In operations research the clustering of values to an ideal point may also be used to reduce the number if inputs in order to obtain approximate values for NP-hard problems in a reasonable time. The point chosen is not usually the center of the sphere, as this can be biased by outliers, but instead some form of average location such as a least squares point is computed to represent the cluster.
Software for computing the minimal bounding sphere
- Miniball software (http://www.inf.ethz.ch/personal/gaertner/miniball.html) — C++ software to compute the minimal bounding sphere of a pointset in dimensions up to 30 (distributed under the GPL license)
- Computational Geometry Algorithms Library CGAL (http://www.cgal.org) — a C++ library with a package, Min_sphere_of_spheres_d (http://www.cgal.org/Manual/doc_html/cgal_manual/Optimisation/Chapter_main.html), to compute the minimal bounding sphere of a set of balls in dimensions up to 30 (distributed under the GPL license)