Intersection-Matrix-Calculation.md

@@ -34,7 +34,7 @@ The IM for the two disjoint geometries of dimension .zero is FF0FFF0F2.  The IM
 To determine if two geometries, one of size .one and the other of size .zero, intersect, each point must be checked to see if it lies on any of the line segments for the geometry of size .one.  As soon as a point is found that does lie on a line segment, return a dimension of .zero, else return a dimension of .false.
 
 The IM for the two disjoint geometries of dimensions .one and .zero, in that order, is FF1FF00F2.  
-The IM for a LineString (not a LinearRing) and a geometry of dimension .zero, in that order, are  
+The IM for a LineString (not a LinearRing) and a geometry of dimension .zero, in that order, is  
 I ∩ I = 0, if a point intersects the interior of the LineString, else .false  
 I ∩ B = .false  
 I ∩ E = 1  
@@ -46,7 +46,7 @@ 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 IM for a LinearRing and a geometry of dimension .zero, in that order, are  
+The IM for a LinearRing and a geometry of dimension .zero, in that order, is  
 I ∩ I = 0, if a point intersects the LinearRing, else .false  
 I ∩ B = .false  
 I ∩ E = 1  
@@ -60,7 +60,7 @@ If the order of the two geometries is reversed, the intersection matrix would be
  
 The boundary of a MultilineString is those points that are in the boundaries of an odd number of its elements (curves).
 The interior of a MultilineString is those points that are left when the boundary points are removed.
-The IM for a MultilineString and a geometry of dimension .zero, in that order, are  
+The IM for a MultilineString and a geometry of dimension .zero, in that order, is  
 I ∩ I = 0, if a point intersects the interior of the MultilineString, else .false  
 I ∩ B = .false  
 I ∩ E = 1  
@@ -75,7 +75,7 @@ If the order of the two geometries is reversed, the intersection matrix would be
 To determine if two geometries, one of size .two and the other of size .zero, intersect, each point must be checked to see if it inside or on the boundary of each polygon, making sure to check if it is inside a hole within the polygon.  If a single point is inside a polygon, not a hole, return .zero, else return .false.
 
 The IM for the two disjoint geometries of dimensions .two and .zero, in that order, is FF2FF10F2.  
-The IM for a Polygon and a geometry of dimension .zero, in that order, are  
+The IM for a Polygon and a geometry of dimension .zero, in that order, is  
 I ∩ I = 0, if a point intersects the interior of the Polygon, else .false  
 I ∩ B = .false  
 I ∩ E = 2  
@@ -87,7 +87,7 @@ 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 IM for a MultiPolygon and a geometry of dimension .zero, in that order, are  
+The IM for a MultiPolygon and a geometry of dimension .zero, in that order, is  
 I ∩ I = 0, if a point intersects the interior of the MultiPolygon, else .false  
 I ∩ B = .false  
 I ∩ E = 2  
@@ -105,6 +105,16 @@ Use the SweepLineIntersector algorithm.  If two segments overlap on any sub-segm
 
 The IM for the two disjoint geometries of dimension .one is (1) FF1FF0102, if both geometries are not LinearRings, or (2) FF1FFF102, if the first geometry is a LinearRing, (3) FF1FF01F2, if the second geometry is a LinearRing, or (4) FF1FFF1F2, if both geometries are LinearRings.
 
+The IM for two LineStrings (not LinearRings) is  
+I ∩ I = 0, if two line segments intersect at the interior of both LineStrings, else .false  
+I ∩ B = 0, if the interior of one line segment intersects an endpoint of another line segment, else .false  
+I ∩ E = 1, if part of one line segment of the first LineString lies outside of the second line String, else .false (Note this value cannot be 0.)  
+B ∩ I = 0, if the interior of one line segment intersects an endpoint of another line segment, else .false    
+B ∩ B = 0, if the endpoints of the LineStrings meet at one more points, else. false   
+B ∩ E = 0, if the two endpoints of the first LineString do not both lie on the second LineString, else .false    
+E ∩ I = 0, if part of one line segment of the second LineString lies outside of the first line String, else .false (Note this value cannot be 0.)    
+E ∩ B = 0, if the two endpoints of the second LineString do not both lie on the first LineString, else .false     
+E ∩ E = 2  
 
 **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**