Bounding Sphere

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:

    I fell her finger light
    Laid pausefully upon life’s headlong train;—
    The foot less prompt to meet the morning dew,
    The heart less bounding at emotion new,
    And hope, once crush’d, less quick to spring again.
    Matthew Arnold (1822–1888)

    Everything goes, everything comes back; eternally rolls the wheel of being. Everything dies, everything blossoms again; eternally runs the year of being. Everything breaks, everything is joined anew; eternally the same house of being is built. Everything parts, everything greets every other thing again; eternally the ring of being remains faithful to itself. In every Now, being begins; round every Here rolls the sphere There. The center is everywhere. Bent is the path of eternity.
    Friedrich Nietzsche (1844–1900)