Want to divide
the plane into easily manageable sections.6.838, Computational Geometry; Fall 2001
Point Location
Sergi Elizalde & David Pritchard
Want to divide
the plane into easily manageable sections.
Idea: Divide
the graph into slabs. Draw a veritcal line through every vertex of the graph:
Each slab contains no vertices, so the regions within are nicely ordered from
top to bottom
We take advantage
of this fact by storing the segments that each slab intersects in an array
Algorithm for Point Location
- Do a binary search by x-coordinate of q against the x-coordinates of the vertices of S to determine which slab q lies in
- Do a binary search of q against the segments intersecting this slab
- The label of the edge just below q tells us which face the trapezoid, and thus q, lies in