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Updated Intersection Matrix Calculation (markdown) authored by eswiss's avatar eswiss
...@@ -173,12 +173,25 @@ The IM for a Polygon and a LineString (not LinearRing), in that order, that do i ...@@ -173,12 +173,25 @@ The IM for a Polygon and a LineString (not LinearRing), in that order, that do i
I ∩ I = 1, if at least one line segment of the LineString enters the interior of the Polygon, else .false (Note this value cannot be 0.) I ∩ I = 1, if at least one line segment of the LineString enters the interior of the Polygon, else .false (Note this value cannot be 0.)
I ∩ B = 0, if the interior of one line segment of the LineString is inside the polygon, else .false I ∩ B = 0, if the interior of one line segment of the LineString is inside the polygon, else .false
I ∩ E = 2 I ∩ E = 2
B ∩ I = 1, if one line segment of the boundary of the Polygon overlaps one line segment from the LineString, else 0, if the interior of the LineString segments touch the Polygon at most a set of points, else .false B ∩ I = 1, if one line segment of the boundary of the Polygon overlaps one line segment from the LineString, else 0, if the interior of the LineString touches the Polygon at most at a set of points, else .false
B ∩ B = 0, if the endpoints of the LineString touch the line segments of the boundary at one or more points, else .false B ∩ B = 0, if the endpoints of the LineString touch the line segments of the boundary at one or more points, else .false
B ∩ E = 1 B ∩ E = 1
E ∩ I = 1, if part of one line segment of the LineString lies outside of the Polygon, else .false (Note this value cannot be 0.) E ∩ I = 1, if part of one line segment of the LineString lies outside of the Polygon, else .false (Note this value cannot be 0.)
E ∩ B = 0, if at least one endpoint of the LineString lies outside of the Polygon, else .false E ∩ B = 0, if at least one endpoint of the LineString lies outside of the Polygon, else .false
E ∩ E = 2 E ∩ E = 2
If the order of the two geometries is reversed, the intersection matrix would be the transpose of the above.
The IM for a Polygon and a LinearRing, in that order, that do intersect is
I ∩ I = 1, if at least one line segment of the LinearRing enters the interior of the Polygon, else .false (Note this value cannot be 0.)
I ∩ B = .false
I ∩ E = 2
B ∩ I = 1, if one line segment of the boundary of the Polygon overlaps one line segment from the LinearRing, else 0, if the interior of the LinearRing touches the Polygon at most at a set of points, else .false
B ∩ B = .false
B ∩ E = 1, if the boundary of the Polygon is not the same as the LinearRing, else .false
E ∩ I = 1, if part of one line segment of the LinearRing lies outside of the Polygon, else .false (Note this value cannot be 0.)
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.
**The dimension of the intersection of two geometries, both of which are dimension .two, is either .zero,.one, .two., or .false** **The dimension of the intersection of two geometries, both of which are dimension .two, is either .zero,.one, .two., or .false**
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