Largest empty sphere

(Redirected from Largest empty circle)

In computational geometry, the largest empty sphere problem is the problem of finding a hypersphere of largest radius in d-dimensional space whose interior does not overlap with any given obstacles.

The dashed circle is the outline of the largest empty sphere in the close-packing of spheres. See also Interstitial defect.
Finding the largest empty circle using the Voronoi diagram (two solutions).

Two dimensions

edit

The largest empty circle problem is the problem of finding a circle of largest radius in the plane whose interior does not overlap with any given obstacles.

A common special case is as follows. Given n points in the plane, find a largest circle centered within their convex hull and enclosing none of them. The problem may be solved using Voronoi diagrams in optimal time  .[1][2]

See also

edit

References

edit
  1. ^ G. T. Toussaint, "Computing largest empty circles with location constraints," International Journal of Computer and Information Sciences, vol. 12, No. 5, October, 1983, pp. 347-358.
  2. ^ Megan Schuster, "The Largest Empty Circle Problem"