Class LargestEmptyCircle


  • public class LargestEmptyCircle
    extends Object
    Constructs the Largest Empty Circle for a set of obstacle geometries, up to a given accuracy distance tolerance. The obstacles may be any combination of point, linear and polygonal geometries.

    The Largest Empty Circle (LEC) is the largest circle whose interior does not intersect with any obstacle and whose center lies within a polygonal boundary. The circle center is the point in the interior of the boundary which has the farthest distance from the obstacles (up to the accuracy of the distance tolerance). The circle itself is determined by the center point and a point lying on an obstacle determining the circle radius.

    The polygonal boundary may be supplied explicitly. If it is not specified the convex hull of the obstacles is used as the boundary.

    To compute an LEC which lies wholly within a polygonal boundary, include the boundary of the polygon(s) as a linear obstacle.

    The implementation uses a successive-approximation technique over a grid of square cells covering the obstacles and boundary. The grid is refined using a branch-and-bound algorithm. Point containment and distance are computed in a performant way by using spatial indexes.

    Author:
    Martin Davis
    See Also:
    MaximumInscribedCircle, InteriorPoint, Centroid
    • Constructor Summary

      Constructors 
      Constructor Description
      LargestEmptyCircle​(Geometry obstacles, Geometry boundary, double tolerance)
      Creates a new instance of a Largest Empty Circle construction, interior-disjoint to a set of obstacle geometries and having its center within a polygonal boundary.
    • Constructor Detail

      • LargestEmptyCircle

        public LargestEmptyCircle​(Geometry obstacles,
                                  Geometry boundary,
                                  double tolerance)
        Creates a new instance of a Largest Empty Circle construction, interior-disjoint to a set of obstacle geometries and having its center within a polygonal boundary. The obstacles may be any collection of points, lines and polygons. If the boundary is null or empty the convex hull of the obstacles is used as the boundary.
        Parameters:
        obstacles - a non-empty geometry representing the obstacles
        boundary - a polygonal geometry (may be null or empty)
        tolerance - a distance tolerance for computing the circle center point (a positive value)
    • Method Detail

      • getCenter

        public static Point getCenter​(Geometry obstacles,
                                      double tolerance)
        Computes the center point of the Largest Empty Circle interior-disjoint to a set of obstacles, with accuracy to a given tolerance distance. The obstacles may be any collection of points, lines and polygons. The center of the LEC lies within the convex hull of the obstacles.
        Parameters:
        obstacles - a geometry representing the obstacles
        tolerance - the distance tolerance for computing the center point
        Returns:
        the center point of the Largest Empty Circle
      • getCenter

        public static Point getCenter​(Geometry obstacles,
                                      Geometry boundary,
                                      double tolerance)
        Computes the center point of the Largest Empty Circle interior-disjoint to a set of obstacles and within a polygonal boundary, with accuracy to a given tolerance distance. The obstacles may be any collection of points, lines and polygons. The center of the LEC lies within the given boundary.
        Parameters:
        obstacles - a geometry representing the obstacles
        boundary - a polygonal geometry to contain the LEC center
        tolerance - the distance tolerance for computing the center point
        Returns:
        the center point of the Largest Empty Circle
      • getRadiusLine

        public static LineString getRadiusLine​(Geometry obstacles,
                                               double tolerance)
        Computes a radius line of the Largest Empty Circle interior-disjoint to a set of obstacles, with accuracy to a given tolerance distance. The obstacles may be any collection of points, lines and polygons. The center of the LEC lies within the convex hull of the obstacles.
        Parameters:
        obstacles - a geometry representing the obstacles
        tolerance - the distance tolerance for computing the center point
        Returns:
        a line from the center of the circle to a point on the edge
      • getRadiusLine

        public static LineString getRadiusLine​(Geometry obstacles,
                                               Geometry boundary,
                                               double tolerance)
        Computes a radius line of the Largest Empty Circle interior-disjoint to a set of obstacles and within a polygonal boundary, with accuracy to a given tolerance distance. The obstacles may be any collection of points, lines and polygons. The center of the LEC lies within the given boundary.
        Parameters:
        obstacles - a geometry representing the obstacles
        boundary - a polygonal geometry to contain the LEC center
        tolerance - the distance tolerance for computing the center point
        Returns:
        a line from the center of the circle to a point on the edge
      • getCenter

        public Point getCenter()
        Gets the center point of the Largest Empty Circle (up to the tolerance distance).
        Returns:
        the center point of the Largest Empty Circle
      • getRadiusPoint

        public Point getRadiusPoint()
        Gets a point defining the radius of the Largest Empty Circle. This is a point on the obstacles which is nearest to the computed center of the Largest Empty Circle. The line segment from the center to this point is a radius of the constructed circle, and this point lies on the boundary of the circle.
        Returns:
        a point defining the radius of the Largest Empty Circle
      • getRadiusLine

        public LineString getRadiusLine()
        Gets a line representing a radius of the Largest Empty Circle.
        Returns:
        a line from the center of the circle to a point on the edge