In mathematics, given a non-empty set of objects of finite extension in n-dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is an n-dimensional solid sphere containing all of these objects.
In the plane the terms bounding or enclosing circle are used.
Used in computer graphics and computational geometry, a bounding sphere is a special type of bounding volume. There are several fast and simple bounding sphere construction algorithms with a high practical value in real-time computer graphics applications.
In statistics and operations research, the objects are typically points, and generally the sphere of interest is the minimal bounding sphere, that is, the sphere with minimal radius among all bounding spheres. It may be proven that such sphere is unique: If there are two of them, then the objects in question lies within their intersection. But an intersection of two non-coinciding spheres of equal radius is contained in a sphere of smaller radius.
The problem of computing the center of a minimal bounding sphere is also known as the "unweighted Euclidean 1-center problem".
Famous quotes containing the words bounding and/or sphere:
“Lame as I am, I take the prey,
Hell, earth, and sin with ease o’ercome;
I leap for joy, pursue my way,
And as a bounding hart fly home,
Through all eternity to prove,
Thy nature, and Thy name is Love.”
—Charles Wesley (1707–1788)
“Don’t feel guilty if you don’t immediately love your stepchildren as you do your own, or as much as you think you should. Everyone needs time to adjust to the new family, adults included. There is no such thing as an “instant parent.”
Actually, no concrete object lies outside of the poetic sphere as long as the poet knows how to use the object properly.”
—Johann Wolfgang Von Goethe (1749–1832)