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Computational Geometry

Computational Geometry. Instructor: Prof. Pankaj Aggarwal, Department of Computer Science and Engineering, IIT Delhi. This course covers lessons in Introduction using Basic Visibility Problems, The Maximal Points Problem, The Plane Sweep Technique and applications, Convex Hull Different Paradigms and Quickhull, Dual Transformation and Applications, Lower Bounds on Algebraic Tree Model, Point Location and Triangulation, Voronoi Diagram and Delaunay Triangulation, Randomized Incremental Construction and Random Sampling, Arrangements and Levels, Range Searching, Clustering Point Sets using Quadtrees and Applications, Epsilon-Nets VC Dimension and Applications, Shape Analysis and Shape Comparison. (from nptel.ac.in)

Lecture 11 - Insertion of Half Planes and Duality

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Introduction using Basic Visibility Problems

Lecture 01 - Introduction

Lecture 02 - Visibility Problems

The Maximal Points Problem

Lecture 03 - 2D Maxima

The Plane Sweep Technique and Applications

Lecture 04 - Line Sweep Method

Lecture 05 - Segment Intersection Problem

Lecture 06 - Line Sweep: Rectangle Union

Convex Hull Different Paradigms and Quickhull

Lecture 07 - Convex Hull

Lecture 08 - Convex Hull (cont.)

Lecture 09 - Quick Hull

Lecture 10 - More Convex Hull Algorithms

Dual Transformation and Applications

Lecture 11 - Insertion of Half Planes and Duality

Lecture 12 - Insertion of Half Planes and Duality (cont.)

Lower Bounds on Algebraic Tree Model

Lecture 13 - Lower Bounds

Point Location and Triangulation

Lecture 14 - Planar Point Location

Lecture 15 - Point Location and Triangulation (cont.)

Lecture 16 - Triangulation of Arbitrary Polygon

Voronoi Diagram and Delaunay Triangulation

Lecture 17 - Voronoi Diagram: Properties

Lecture 18 - Voronoi Diagram Construction

Lecture 19 - Delaunay Triangulation

Randomized Incremental Construction and Random Sampling

Lecture 20 - Quick Sort and Backward Analysis

Lecture 21 - Generalized RIC (Randomized Incremental Construction)

Lecture 22 - Randomized Incremental Construction (cont.)

Arrangements and Levels

Lecture 23 - Arrangements

Lecture 24 - Applications of Zone Theorem and Arrangements

Lecture 25 - Arrangements (cont.)

Range Searching

Lecture 26 - Range Searching: Introduction

Lecture 27 - Orthogonal Range Searching

Lecture 28 - Priority Search Trees

Lecture 29 - Non-Orthogonal Range Searching

Lecture 30 - Range Searching: Half Plane Range Counting

Clustering Point Sets using Quadtrees and Applications

Lecture 31 - Well Separated Partitioning

Lecture 32 - Quadtrees Epsilon-WSPD (Well Separated Pair Decomposition)

Lecture 33 - Construction of Epsilon-WSPD

Lecture 34 - Construction of Epsilon-WSPD (cont.)

Epsilon-Nets, VC Dimension and Applications

Lecture 35 - Epsilon-Nets and VC Dimension

Lecture 36 - Epsilon-Nets and VC Dimension (cont.)

Lecture 37 - Geometric Set Cover

Lecture 38 - Geometric Set Cover (with Bounded VC Dimension)

Shape Analysis and Shape Comparison

Lecture 39 - Shape Representation

Lecture 40 - Shape Comparison