Editing Bounding sphere (section)

===Ritter's bounding sphere===
In 1990, Jack Ritter proposed a simple algorithm to find a non-minimal bounding sphere.{{r|Ritter1990}} It is widely used in various applications for its simplicity. The algorithm works in this way:

#Pick a point <math>x</math> from <math>P</math>, search a point <math>y</math> in <math>P</math>, which has the largest distance from <math>x</math>;
#Search a point <math>z</math> in <math>P</math>, which has the largest distance from <math>y</math>. Set up an initial ball <math>B</math>, with its centre as the midpoint of <math>y</math> and <math>z</math>, the radius as half of the distance between <math>y</math> and <math>z</math>;
#If all points in <math>P</math> are within ball <math>B</math>, then we get a bounding sphere. Otherwise, let <math>p</math> be a point outside the ball, constructs a new ball covering both point <math>p</math> and previous ball. Repeat this step until all points are covered.

Ritter's algorithm runs in time <math>O(nd)</math> on inputs consisting of <math>n</math> points in <math>d</math>-dimensional space, which makes it very efficient. However, it gives only a coarse result which is usually 5% to 20% larger than the optimum.{{r|Ritter1990}}