Class LargestEmptyCircle

Constructs the Largest Empty Circle for a set of obstacle geometries, up to a specified tolerance. The obstacles are point and line geometries.

The Largest Empty Circle is the largest circle which has its center in the convex hull of the obstacles (the boundary), and whose interior does not intersect with any obstacle. The circle center is the point in the interior of the boundary which has the farthest distance from the obstacles (up to tolerance). The circle is determined by the center point and a point lying on an obstacle indicating the circle radius.

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.

Future Enhancements

• Support polygons as obstacles
• Support a client-defined boundary polygon

Inheritance

Object

LargestEmptyCircle

Inherited Members

Object.Equals(Object)

Object.Equals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Object.ReferenceEquals(Object, Object)

Object.ToString()

Namespace: NetTopologySuite.Algorithm.Construct

Assembly: NetTopologySuite.dll

Syntax

public class LargestEmptyCircle

Constructors

LargestEmptyCircle(Geometry, Double)

Creates a new instance of a Largest Empty Circle construction.

Declaration

public LargestEmptyCircle(Geometry obstacles, double tolerance)

Parameters

Type	Name	Description
Geometry	obstacles	A geometry representing the obstacles (points and lines)
Double	tolerance	The distance tolerance for computing the center point

Methods

GetCenter()

Gets the center point of the Largest Empty Circle (up to the tolerance distance).

Declaration

public Point GetCenter()

Returns

Type	Description
Point	The center point of the Largest Empty Circle

GetCenter(Geometry, Double)

Computes the center point of the Largest Empty Circle within a set of obstacles, up to a given tolerance distance.

Declaration

public static Point GetCenter(Geometry obstacles, double tolerance)

Parameters

Type	Name	Description
Geometry	obstacles	A geometry representing the obstacles (points and lines)
Double	tolerance	The distance tolerance for computing the center point

Returns

Type	Description
Point	The center point of the Largest Empty Circle

GetRadiusLine()

Gets a line representing a radius of the Largest Empty Circle.

Declaration

public LineString GetRadiusLine()

Returns

Type	Description
LineString	A line from the center of the circle to a point on the edge

GetRadiusLine(Geometry, Double)

Computes a radius line of the Largest Empty Circle within a set of obstacles, up to a given distance tolerance.

Declaration

public static LineString GetRadiusLine(Geometry obstacles, double tolerance)

Parameters

Type	Name	Description
Geometry	obstacles	A geometry representing the obstacles (points and lines)
Double	tolerance	The distance tolerance for computing the center point

Returns

Type	Description
LineString	A line from the center of the circle to a point on the edge

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.

Declaration

public Point GetRadiusPoint()

Returns

Type	Description
Point	A point defining the radius of the Largest Empty Circle