• Algorithms, 4th edition
  • 1.  Fundamentals
    • 1.1  Programming Model
    • 1.2  Data Abstraction
    • 1.3  Stacks and Queues
    • 1.4  Analysis of Algorithms
    • 1.5  Case Study: Union-Find
  • 2.  Sorting
    • 2.1  Elementary Sorts
    • 2.2  Mergesort
    • 2.3  Quicksort
    • 2.4  Priority Queues
    • 2.5  Sorting Applications
  • 3.  Searching
    • 3.1  Symbol Tables
    • 3.2  Binary Search Trees
    • 3.3  Balanced Search Trees
    • 3.4  Hash Tables
    • 3.5  Searching Applications
  • 4.  Graphs
    • 4.1  Undirected Graphs
    • 4.2  Directed Graphs
    • 4.3  Minimum Spanning Trees
    • 4.4  Shortest Paths
  • 5.  Strings
    • 5.1  String Sorts
    • 5.2  Tries
    • 5.3  Substring Search
    • 5.4  Regular Expressions
    • 5.5  Data Compression
  • 6.  Context
    • 6.1  Event-Driven Simulation
    • 6.2  B-trees
    • 6.3  Suffix Arrays
    • 6.4  Maxflow
    • 6.5  Reductions
    • 6.6  Intractability
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    • Algorithms, Part I
    • Algorithms, Part II
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    • Algorithms, Part I
    • Algorithms, Part II
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9.   Geometry

This chapter under major construction.

Given a set of points (which can be preprocessed), the problem of determining which points lie in a given interval generalizes to determining which points lie in a given rectangle. Algorithms to solve this problem are important not just in geometry, but in database search.

Do two polygons intersect? Given N geometric objects, do any two intersect? Intersections problems like these are fundamental geometric algorithms. We consider an important application: design rule checking for integrated circuits.

Another fundamental geometric problem is the nearest neighbor problem. Given a set of points, find the one that is nearest to a given point. A generalization of binary search trees is effective for this problem.

Clarkson's notes on computational geometry

Need some model of physical world. Wireframe model with Eiffel tower.

Hidden line elimination - Warnock's algorithm.

Geometric application from David Eppstein.

Java programs in this chapter.

Below is a list of Java programs in this chapter. Click on the program name to access the Java code; click on the reference number for a brief description; read the textbook for a full discussion.

REF	PROGRAM	DESCRIPTION / JAVADOC