I have a line and polygon in this image.
If i find the intersection of line exterior and polygon boundry, what will be the graphical representation of both objects intersection..
its my concept..
If the line just crosses the border of the polygon as in your image the intersection of the boundary of the polygon and the exterior of the line will be the boundary of the polygon. But because of the intersections the boundary will go from LINESTRING to MULTILINESTRING and be interrupted by the intersections at least according to PostGIS (GEOS->JTS).
This is because
The intersection between the exterior of the line and the boundary of the polygon is the same as the difference between the line and the boundary of the polygon.
You can try it by running the queries below on http://postgisonline.org/map.php:
first: to see the geometries run:
by copying it into the terminal in the link and press "map1"
Then, since it is not possible to make a geometry of the exterior we use the difference between the boundary of the polygon and the line instead:
If you run this as "map2" instead of "map1" you will get the difference on top of the previous ran query.
To see the resulting coordinates and how they have been divided in three parts of the MULTILINESTRING, try:
Is this what you were thinking about?
How about a red cross? It's really your choice.