Computational Geometry

Awesome Computational Geometry

A curated list of awesome computational geometry visualizations, libraries, and resources.

Computational geometry is a topic in computer science that focuses on solving problems in geometry. Applications of computational geometry include computer-aided design, robotics, GIS systems, and computer vision.

Algorithm Visualizations

• Convex Hull - The convex hull of a shape is the smallest convex set that contains it.
• Convex Hull Algorithms - A website with visualizations of many convex hull algorithms, including gift wrapping, Graham's scan, quickhull, divide and conquer, monotone chain, and Chan's algorithm.
• Chan's Algorithm - An optimal output-sensitive algorithm to compute the convex hull of a set of points in 2 or 3 dimensions.
• Kirkpatrick's Point location - A data structure and method for point location with O(n) space and O(log n) query time using triangulation.
• Voronoi Diagrams - A partition of a plane into regions close to a given set of points.
• Fortune's Algorithm - A sweep line algorithm for generating the Voronoi diagram in O(n log n) time and O(n) space.
• Point/Line Duality - A type of mathematical duality frequently used in computational geometry algorithms.
• k-d tree - A method of partitioning k-dimensional space in an efficient way for searches like nearest neighbors.
• Configuration Space - The space of possible configurations of an object like a robot.

Books

• Computational Geometry: Algorithms and Applications - A textbook by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars (2008).
• Computational Geometry in C - A popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design by Joseph O'Rourke (1998).
• Computational Geometry: An Introduction - An introductory textbook by Franco P. Preparata and Michael I. Shamos (1993).
• Algorithmic Geometry - A textbook by Jean-Daniel Boissonnat, Mariette Yvinec, and Herve Bronniman (1998).
• Discrete and Computational Geometry - A comprehensive yet accessible introduction to the intermingling of discrete geometry, a relatively new development in pure mathematics, and computational geometry, an emerging area in applications-driven computer science by Satyan L. Devadoss and Joseph O'Rourke (2011).
• Interactive Computational Geometry - A taxonomic approach - An interactive introduction to some of the fundamental algorithms of computational geometry with Mathematica by Jim Arlow (2014).

Notes

• Lecture Notes - Lecture notes from CMSC 754 Computational Geometry at the University of Maryland by David Mount (2002).
• Handbook of Discrete and Computational Geometry - A handbook by Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth (2017).
• Handbook of Computational Geometry - An overview of key concepts and results in computational geometry by J. R. Sack, and J. Urrutia (1998).
• Computing in Euclidean Geometry - A collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry by Ding-Zhu Du and Frank Hwang (1995).

Libraries

• CGAL - A software project that provides easy access to efficient and reliable geometric algorithms in the form of a C++ library. This website also has explanations of many of these algorithms.
• Wykobi - An extremely efficient, robust, and simple to use C++ 2D/3D oriented computational geometry library.
• geometry3Sharp - Open-Source, Boost-licensed C# library for geometric computing.
• Computational Geometry Software Libraries - UIUC's large collection and library of geometric software by Jeff Erickson.
• The Stony Brook Algorithm Repository - A repository of algorithms based on The Algorithm Design Manual.
• Geometric Tools - A library of source code for computing in the fields of mathematics, graphics, image analysis, and physics that includes some computational geometry algorithms.
• GeoLib - A fast and efficient computational geometry library available in C++, C# and Java.
• hull.js - JavaScript library that builds the convex hull of a set of points.
• S2 Geometry Library - A package for manipulating geometric shapes. Unlike many geometry libraries, S2 is primarily designed to work with spherical geometry, i.e., shapes drawn on a sphere rather than on a planar 2D map. This makes it especially suitable for working with geographic data.
• Computational Geometry Unity Library - A library of computational geometry algorithms for Unity.

Conferences

Strictly Computational Geometry

• Symposium on Computational Geometry - An annual symposium.
• The Canadian Conference on Computational Geometry - An annual international event for the dissemination of new results in the fields of computational and combinatorial geometry. The conference is usually held in a Canadian city sometime in mid-August.
• Japan Conference on Discrete and Computational Geometry, Graphs, and Games - A conference held annually since 1997, except for 2008.

Broader

• Symposium on Discrete Algorithms - ACM-SIAM, held annually.
• Annual ACM Symposium on Theory of Computing - STOC covers all areas of research within Algorithms and Computation Theory.
• IEEE Symposium on Foundations of Computer Science - The flagship conference sponsored by the IEEE Computer Society Technical Committee on the Mathematical Foundations of Computing (TCMF) and covers a broad range of theoretical computer science.
• Annual Allerton Conference on Communications, Control and Computing - Draws some of the brightest minds from industry, academia, and government to discuss innovation in the fields of communication, control, and computing.

Journals

• arXiv - Recent submissions to arXiv about computational geometry.
• Elsevier - A forum for research in theoretical and applied aspects of computational geometry.
• Journal of Computational Geometry - An international open access journal devoted to publishing original research of the highest quality in all aspects of computational geometry.

Competitive Programming

• HackerEarth - A set of articles on computational geometry.
• TopCoder - A set of articles on computational geometry.
• HackerRank - A set of programming problems using computational geometry.
• GeeksforGeeks - Implementations and explanations for a large number of commonly asked questions and common topics in geometric algorithms.

Courses

Open Courses

• MIT OCW - A course taught by Nicholas Patrikalakis and Takashi Maekawa in 2013.
• Udemy - A course about implementing computational geometry algorithms in C++.
• edX - A course in computational geometry.
• Brilliant - Practice problems for basic concepts in computational geometry.

University Courses

• Brown University - A course taught by Roberto Tamassia in 2005.
• Washington University in St. Louis - A course taught by Tao Ju in 2017.
• The University of Maryland - A course taught by Dave Mount in 2002.
• UC Santa Barbara - A course taught by Subhash Suri in 2021.
• UIUC - A course taught by Jeff Erickson in 2022.
• UC Berkeley - A course taught by Jonathan Shewchuk in 2019.
• Tufts - A course taught by Diane Souvaine in 2022.
• KIT - A course taught by Tamara Mchedlidze and Chih-Hung Liu in 2018.

Miscellaneous

• The Open Problems Project - A project aimed to record important open problems in computational geometry and related fields.
• Wolfram - Documentation for computational geometry algorithms implemented in the Wolfram language.
• Matlab - Documentation for computational geometry algorithms implemented in the Matlab.

Contributing

Contributions are welcome! See the contribution guidelines.