Recall the concept
of a planar subdivision from chapter 2:6.838, Computational Geometry; Fall 2001
Point Location
Sergi Elizalde & David Pritchard
Recall the concept
of a planar subdivision from chapter 2:
- Embedding of a normal graph in Cartesian plane
- Composed of vertices, faces and half-edges
- Perimeters of polygons stored in doubly-linked list
- Can determine which face a half-edge lies on, which faces lie within other faces, etc. in O(1) time
In everything
that follows, S refers to this structure, and n refers
to the number of edges. Note that the number of faces, vertices are O(n).