6.838, Computational Geometry; Fall 2001
Point Location
Sergi Elizalde & David Pritchard
Introduction / Motivation
Formalization of the Problem
Single Shot Algorithm
Naive Algorithm
Idea
Analysis
An Improved Algorithm
The Trapezoidal Map
Assumptions / Simplifications
Navigating the Map (1)
Navigating the Map (2)
Searching - Idea
An Incremental Randomized Algorithm
Global Description
Finding Intersected Trapezoids
Incrementing T and D - Simple Case
Incrementing T - General Case
Incrementing D - General Case
Analysis
Expected Performance
Proof: Query Time
Proof: Storage Size
Proof: Construction Time
Removing Our Assumptions
Symbolic Transformation
A Tail Estimate
A Tail Estimate (1)
A Tail Estimate (2)
Maximum Search Path Length
Linear Storage, Logarithmic Queries with n log
n Construction Time
Related Problems