Class MinimumClearance
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.
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

If G has only a single vertex (i.e. is a
Point
), the value of the minimum clearance
is Double.MAX_VALUE
.
If G is a Puntal
or Lineal
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 STRtree.nearestNeighbour(ItemDistance)
method to provide good performance even for
large inputs.
An interesting note is that for the case of MultiPoint
s,
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
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionprivate static class
Implements the MinimumClearance distance function: dist(p1, p2) = p1 != p2 : p1.distance(p2) p1 == p2 : Double.MAX dist(p, seg) = p != seq.p1 invalid input: '&'invalid input: '&' p != seg.p2 : seg.distance(p) ELSE : Double.MAX Also computes the values of the nearest points, if any. -
Field Summary
Fields -
Constructor Summary
ConstructorsConstructorDescriptionMinimumClearance
(Geometry geom) Creates an object to compute the Minimum Clearance for the given Geometry -
Method Summary
Modifier and TypeMethodDescriptionprivate void
compute()
double
Gets the Minimum Clearance distance.static double
Computes the Minimum Clearance distance for the given Geometry.getLine()
Gets a LineString containing two points which are at the Minimum Clearance distance.static Geometry
Gets a LineString containing two points which are at the Minimum Clearance distance for the given Geometry.
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Field Details
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inputGeom
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minClearance
private double minClearance -
minClearancePts
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Constructor Details
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MinimumClearance
Creates an object to compute the Minimum Clearance for the given Geometry- Parameters:
geom
- the input geometry
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Method Details
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getDistance
Computes the Minimum Clearance distance for the given Geometry.- Parameters:
g
- the input geometry- Returns:
- the Minimum Clearance distance
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getLine
Gets a LineString containing two points which are at the Minimum Clearance distance for the given Geometry.- Parameters:
g
- the input geometry- Returns:
- the value of the minimum clearance distance or LINESTRING EMPTY if no Minimum Clearance distance exists
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getDistance
public double getDistance()Gets the Minimum Clearance distance.If no distance exists (e.g. in the case of two identical points) Double.MAX_VALUE is returned.
- Returns:
- the value of the minimum clearance distance or Double.MAX_VALUE if no Minimum Clearance distance exists
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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.
- Returns:
- the value of the minimum clearance distance or LINESTRING EMPTY if no Minimum Clearance distance exists
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compute
private void compute()
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