Class MinimumClearance

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.

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:

1. No two distinct vertices of G are closer than r
2. 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 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 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

Authors:

Martin Davis