Class MinimumClearance

Namespace

NetTopologySuite.Precision

Assembly

NetTopologySuite.dll

Computes the Minimum Clearance of a Geometry.

The Minimum Clearance is a measure of what magnitude of perturbation of the vertices of a geometry can be tolerated before the geometry becomes topologically invalid. The smaller the Minimum Clearance distance, the less vertex perturbation the geometry can tolerate before becoming invalid.

public class MinimumClearance

Inheritance

object

MinimumClearance

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The concept was introduced by Thompson and Van Oosterom [TV06], based on earlier work by Milenkovic [Mi88].

The Minimum Clearance of a geometry G is defined to be the value r such that "the movement of all points by a distance of r in any direction will guarantee to leave the geometry valid" [TV06]. An equivalent constructive definition [Mi88] is that r is the largest value such:

• No two distinct vertices of G are closer than r.
• No vertex of G is closer than r to an edge of G of which the vertex is not an endpoint

The following image shows an example of the Minimum Clearance of a simple polygon.

If G has only a single vertex (i.e. is a Point), the value of the minimum clearance is MaxValue.

If G is a IPuntal or ILineal geometry, then in fact no amount of perturbation will render the geometry invalid. In this case a Minimum Clearance is still computed based on the vertex and segment distances according to the constructive definition.

It is possible for no Minimum Clearance to exist. For instance, a MultiPoint with all members identical has no Minimum Clearance (i.e. no amount of perturbation will cause the member points to become non-identical). Empty geometries also have no such distance. The lack of a meaningful MinimumClearance distance is detected and suitable values are returned by GetDistance() and GetLine().

The computation of Minimum Clearance utilizes the NearestNeighbour(IItemDistance<Envelope, TItem>) method to provide good performance even for large inputs.

An interesting note is that for the case of MultiPoints, the computed Minimum Clearance line effectively determines the Nearest Neighbours in the collection.

References

• [Mi88] Milenkovic, V. J., Verifiable implementations of geometric algorithms using finite precision arithmetic. in Artificial Intelligence, 377-401. 1988
• [TV06] Thompson, Rod and van Oosterom, Peter, Interchange of Spatial Data-Inhibiting Factors, Agile 2006, Visegrad, Hungary. 2006

Constructors

MinimumClearance(Geometry)

Creates an object to compute the Minimum Clearance for the given Geometry

public MinimumClearance(Geometry geom)

Parameters

geom Geometry

The input geometry

Methods

GetDistance()

Gets the Minimum Clearance distance.

If no distance exists (e.g. in the case of two identical points) MaxValue is returned.

public double GetDistance()

Returns

double

The value of the minimum clearance distance
or MaxValue if no Minimum Clearance distance exists

GetDistance(Geometry)

Computes the Minimum Clearance distance for the given Geometry.

public static double GetDistance(Geometry g)

Parameters

g Geometry

The input geometry

Returns

double

The minimum clearance

GetLine()

Gets a LineString containing two points which are at the Minimum Clearance distance.

If no distance could be found (e.g. in the case of two identical points) LINESTRING EMPTY is returned.

public LineString GetLine()

Returns

LineString

The value of the minimum clearance distance,
or LINESTRING EMPTY if no minimum clearance distance exists.

GetLine(Geometry)

Gets a LineString containing two points which are at the Minimum Clearance distance for the given Geometry.

public static Geometry GetLine(Geometry g)

Parameters

g Geometry

The input geometry

Returns

Geometry

The value of the minimum clearance distance
or LINESTRING EMPTY if no minimum clearance distance exists.