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Updated Intersection Matrix Calculation (markdown)
authored
Feb 15, 2017
by
eswiss
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Intersection-Matrix-Calculation.md
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@@ -121,12 +121,24 @@ I ∩ I = 0, if line segments from each geometry intersect at the interior of bo
I ∩ B = 0, .false
I ∩ E = 1, if part of one line segment of the LineString lies outside of the LinearRing, else .false (Note this value cannot be 0.)
B ∩ I = 0, if at least one of the endpoints of the LineString intersects the LinearRing, else .false
B ∩ B =
0,
.false
B ∩ B = .false
B ∩ E = 0, if the two endpoints of the LineString do not both lie on the LinearRing, else .false
E ∩ I = 1 (Note part of the LinearRing must lie outside of the LineString)
E ∩ B = .false
E ∩ E = 2
If the order of the two geometries is reversed, the intersection matrix would be the transpose of the above.
If the order of the two geometries is reversed, the intersection matrix would be the transpose of the above.
The IM for a MultilineString (not LinearRing?) and a LineString, in that order, is
I ∩ I = 0, if line segments from each geometry intersect at the interior of both, else .false
I ∩ B = 0, if the interior of one line segment of the MultilineString intersects an endpoint of the LineString, else .false
I ∩ E = 1, if part of one line segment of the MultilineString lies outside of the LineString, else .false (Note this value cannot be 0.)
B ∩ I = 0, if at least one of the endpoints of the MultilineString intersects the LineString, else .false
B ∩ B = 0, if at least one of the endpoints of the MultilineString intersects one of the endpoints of the LineString, else .false
B ∩ E = 0, if all the endpoints of the MultilineString do not lie on the LineString, else .false
E ∩ I = 1, if part of the LineString lies outside of the MultilineString, else .false (Note this value cannot be 0.)
E ∩ B = 0, if the two endpoints of the LineString do not lie on the MultilineString, else .false
E ∩ E = 2
If the order of the two geometries is reversed, the intersection matrix would be the transpose of the above.
**The dimension of the intersection of two geometries, one of which is dimension .one and the other dimension .two, is either .zero, .one, or .false**
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