Class MaximumInscribedCircle

Constructs the Maximum Inscribed Circle for a polygonal Geometry, up to a specified tolerance. The Maximum Inscribed Circle is determined by a point in the interior of the area which has the farthest distance from the area boundary, along with a boundary point at that distance.

In the context of geography the center of the Maximum Inscribed Circle is known as the Pole of Inaccessibility. A cartographic use case is to determine a suitable point to place a map label within a polygon.

The radius length of the Maximum Inscribed Circle is a measure of how "narrow" a polygon is. It is the distance at which the negative buffer becomes empty.

The class supports polygons with holes and multipolygons.

The implementation uses a successive-approximation technique over a grid of square cells covering the area geometry. 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 a polygonal constraint on placement of center

Inheritance

object

MaximumInscribedCircle

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 MaximumInscribedCircle

Constructors

MaximumInscribedCircle(Geometry, double)

Creates a new instance of a Maximum Inscribed Circle computation.

Declaration

public MaximumInscribedCircle(Geometry polygonal, double tolerance)

Parameters

Type	Name	Description
Geometry	polygonal	An areal geometry
double	tolerance	The distance tolerance for computing the centre point (must be positive)

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if the tolerance is non-positive
ArgumentException	Thrown if the input geometry is non-polygonal or empty

Methods

GetCenter()

Gets the center point of the maximum inscribed circle (up to the tolerance distance).

Declaration

public Point GetCenter()

Returns

Type	Description
Point	The center point of the maximum inscribed circle

GetCenter(Geometry, double)

Computes the center point of the Maximum Inscribed Circle of a polygonal geometry, up to a given tolerance distance.

Declaration

public static Point GetCenter(Geometry polygonal, double tolerance)

Parameters

Type	Name	Description
Geometry	polygonal	A polygonal geometry
double	tolerance	The distance tolerance for computing the center point

Returns

Type	Description
Point	The center point of the maximum inscribed 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 Maximum Inscribed Circle of a polygonal geometry, up to a given tolerance distance.

Declaration

public static LineString GetRadiusLine(Geometry polygonal, double tolerance)

Parameters

Type	Name	Description
Geometry	polygonal	A polygonal geometry
double	tolerance	The distance tolerance for computing the center point

Returns

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

GetRadiusPoint()

Gets a point defining the radius of the Maximum Inscribed Circle. This is a point on the boundary which is nearest to the computed center of the Maximum Inscribed 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 Maximum Inscribed Circle