Class LargestEmptyCircle

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.

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, Geometry, double)

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.

Declaration

public LargestEmptyCircle(Geometry obstacles, Geometry boundary, double tolerance)

Parameters

Type	Name	Description
Geometry	obstacles	A non-empty geometry representing the obstacles (points and lines)
Geometry	boundary	A polygonal geometry to contain the LEC center (may be null or empty)
double	tolerance	The distance tolerance for computing the center point (a positive value)

LargestEmptyCircle(Geometry, double)

Creates a new instance of a Largest Empty Circle construction.

Declaration

[Obsolete("Will be removed in a future version")]
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, Geometry, double)

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.

Declaration

public static Point GetCenter(Geometry obstacles, Geometry boundary, double tolerance)

Parameters

Type	Name	Description
Geometry	obstacles	A geometry representing the obstacles
Geometry	boundary	A polygonal geometry to contain the LEC center
double	tolerance	The distance tolerance for computing the center point

Returns

Type	Description
Point	The center point of the Largest Empty Circle

GetCenter(Geometry, double)

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.

Declaration

public static Point GetCenter(Geometry obstacles, double tolerance)

Parameters

Type	Name	Description
Geometry	obstacles	A geometry representing the obstacles
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, Geometry, double)

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.

Declaration

public static LineString GetRadiusLine(Geometry obstacles, Geometry boundary, double tolerance)

Parameters

Type	Name	Description
Geometry	obstacles	A geometry representing the obstacles (points and lines)
Geometry	boundary	A polygonal geometry to contain the LEC center
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

GetRadiusLine(Geometry, double)

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.

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