Introduction

Basic Techniques, DCEL, Plane sweep and Planarity.

Triabgulations, Art-Gallery Theorem, and an O(n log n) algorithm for triangulating a simple polygon.

Linear Programming.

Range trees and kD-trees

Point Location among a set of segments.

Properties of Voronoi Diagrams.

Delauney Triangulation.

Line Arrangement

Motion Planning

Convex Hull in 3D

Binary Space Partition

We also discussed 2D range trees (from Lecture 5), Interval Trees and Segment trees (see the textbook) and and the basic definition of Quadtrees (see the textbook).