6.838, Computational Geometry; Fall 2001

Point Location

Sergi Elizalde & David Pritchard

Incrementing D - General Case

General case: s_i intersects D₀, D₁,...,D_k

To update D:

- Remove the leaves for D₀, D₁,...,D_k

- Create leaves for the new trapezoids

- If D₀ has the left endpoint p of s_i in its interior, replace the leaf for D₀ with a point node for p and a segment node for s_i (similarly with D_k)

- Replace the leaves of the other trapezoids with single segment nodes for s_i

- Make the outgoing edges of the inner nodes point to the correct leaves