An algorithm for computing a distance metric which is an approximation to the Hausdorff Distance based on a discretization of the input {link Geometry}. The algorithm computes the Hausdorff distance restricted to discrete points for one of the geometries. The points can be either the vertices of the geometries (the default), or the geometries with line segments densified by a given fraction. Also determines two points of the Geometries which are separated by the computed distance.
This algorithm is an approximation to the standard Hausdorff distance. Specifically,
<pre> for all geometries a, b: DHD(a, b) <= HD(a, b) </pre>
The approximation can be made as close as needed by densifying the input geometries. In the limit, this value will approach the true Hausdorff distance:
<pre> DHD(A, B, densifyFactor) -> HD(A, B) as densifyFactor -> 0.0 </pre>
The default approximation is exact or close enough for a large subset of useful cases. Examples of these are:
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computing distance between Linestrings that are roughly parallel to each other, and roughly equal in length. This occurs in matching linear networks.
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Testing similarity of geometries.
An example where the default approximation is not close is:
<pre> A = LINESTRING (0 0, 100 0, 10 100, 10 100) B = LINESTRING (0 100, 0 10, 80 10) DHD(A, B) = 22.360679774997898 HD(A, B) ~= 47.8 </pre>
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