Does a Line Intersect a Polygon?

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SUMMARY

To determine if a line intersects a polygon defined by latitude and longitude coordinates, one must check for intersections between the line and each bounding edge of the polygon. If the intersection occurs within the endpoints of an edge, the line intersects the polygon. For polygons on the surface of a sphere, the line and edges correspond to segments of great circles, necessitating the intersection of planes through the sphere's center. This discussion highlights the importance of using intersection tests and refers to common algorithms for implementation.

PREREQUISITES
  • Understanding of polygon geometry and edge definitions
  • Knowledge of great circle calculations on a sphere
  • Familiarity with intersection algorithms in computational geometry
  • Proficiency in handling latitude and longitude coordinates
NEXT STEPS
  • Research algorithms for line-polygon intersection, such as the Liang-Barsky algorithm
  • Study great circle distance calculations and their applications
  • Explore computational geometry libraries like CGAL for practical implementations
  • Learn about spherical geometry and its implications for geographic data
USEFUL FOR

Geospatial analysts, software developers working with geographic information systems (GIS), and anyone involved in computational geometry or geographic data visualization.

sfopeano
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Hello, I'm wondering if anyone has a formula for determining whether a line intersects a polygon. I would define the line with a starting latitude/longitude and ending latitude/longitude, and I would define the polygon with a series of latitude/longitude coordinates. Many thanks in advance.

-Stephan
 
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sfopeano said:
Hello, I'm wondering if anyone has a formula for determining whether a line intersects a polygon. I would define the line with a starting latitude/longitude and ending latitude/longitude, and I would define the polygon with a series of latitude/longitude coordinates. Many thanks in advance.

-Stephan

Hi sfopeano, welcome to MHB!

To intersect a line with a polygon, we need to intersect that line with each of the bounding edges of the polygon.
If the intersection is within the end points of an edge, then that line intersects the polygon.
Otherwise it doesn't.

However, you mention latitude and longitude, which suggest that you are talking about a polygon on the surface of a sphere.
If that is the case, then the line and the edges correspond to segments of so called great circles.
And each such great circle lies in a plane through the center of the sphere.
Instead of intersecting lines, we now have to intersect these planes, and see if the intersecting line is within the associated segment.
 
What you're talking about is intersection tests. Here's a web page talking about some common algorithms.
 

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