May 1, 2024
Updated May 9, 2025
24 minute read
Computational geometry is a fascinating and vital branch of computer science dedicated to the study of algorithms that can be described in terms of geometry. It involves developing and analyzing algorithms and data structures to solve problems related to geometric shapes and structures. While it might sound abstract, computational geometry is the engine behind many technologies we interact with daily, from the graphics on our screens to the navigation systems in our cars. If you've ever wondered how your GPS finds the best route or how video games create realistic 3D worlds, you've encountered the power of computational geometry.
Working in computational geometry can be incredibly engaging. Imagine designing algorithms that allow a robot to navigate a complex environment, or developing techniques to create stunning visual effects in movies and games. Another exciting aspect is its role in geographic information systems (GIS), where it helps analyze spatial data for urban planning, environmental monitoring, and even disaster response. The field is constantly evolving, offering opportunities to tackle new and challenging problems with creative and efficient solutions.
What is Computational Geometry?
At its core, computational geometry is about finding efficient ways to solve geometric problems using computers. This involves designing algorithms and data structures specifically tailored for geometric data, such as points, lines, polygons, and more complex shapes in two, three, or even higher dimensions.
Think of it as teaching a computer to "see" and "understand" shapes and their relationships in the same way humans do, but with the added power of precise calculation and the ability to handle massive amounts of data. The primary goal is to develop algorithms that are not only correct but also efficient in terms of processing time and memory usage, especially when dealing with very large datasets where a small improvement in an algorithm can mean the difference between days and seconds of computation.
2ocmgq|
Find a path to becoming a Computational Geometry. Learn more at:
OpenCourser.com/topic/2ocmgq/computational
Reading list
We've selected 27 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Computational Geometry.
Is widely considered a standard textbook for introductory and advanced courses in computational geometry. It provides a broad understanding of fundamental concepts and algorithms, making it suitable for high school students with a strong math background, undergraduates, and early-stage graduate students. It is an excellent resource for solidifying understanding and is often used as a primary textbook. The book relates techniques to applications in robotics, graphics, CAD/CAM, and GIS, providing valuable context.
This comprehensive handbook serves as a primary reference for both discrete and computational geometry. It covers a wide range of topics, from fundamental concepts to advanced and contemporary research areas. While not a textbook for a single course, it is an invaluable resource for graduate students and working professionals needing to deepen their understanding or explore specialized topics. Its breadth makes it a key reference tool in the field.
Provides a comprehensive overview of computational geometry, covering both theoretical foundations and practical applications. It is suitable for advanced undergraduates and graduate students in computer science and related fields.
Bridges the gap between discrete geometry and computational geometry, offering an accessible introduction suitable for advanced undergraduates and graduate students. It covers traditional topics while also introducing more recent subjects. It's helpful for gaining a broad understanding and seeing the connections between theoretical and applied aspects of the field.
A translation of a French edition, this book provides a solid foundation in algorithmic geometry. It's a good resource for undergraduates and graduate students seeking a rigorous approach to the algorithmic aspects of computational geometry. It can serve as a textbook or supplementary reading.
Offers a practical introduction to computational geometry with implementations of algorithms in C. It's valuable for students and professionals who want to understand the algorithms and see how they can be translated into code. It good resource for solidifying understanding through practical application and is often used in conjunction with more theoretical texts. It's particularly useful for those with a computer science background.
This specialized monograph provides an in-depth treatment of Voronoi diagrams and Delaunay triangulations, fundamental structures in computational geometry. It's suitable for graduate students and researchers focusing on these specific topics, offering a deeper understanding than general textbooks.
This classic textbook provides a rigorous and in-depth treatment of computational geometry. It is suitable for advanced undergraduates and graduate students in computer science and mathematics.
Provides a theoretical treatment of algorithms in combinatorial geometry. It's suitable for graduate students and researchers with a strong mathematical background interested in the combinatorial aspects of geometric algorithms. It offers depth in the theoretical underpinnings of the field.
Focuses on arrangements within the context of the Computational Geometry Algorithms Library (CGAL). It's highly practical for students and professionals who want to use CGAL for geometric programming and understand the underlying concepts of arrangements. It's a valuable resource for applying theoretical knowledge.
Provides a detailed coverage of visibility algorithms in the plane, a fundamental topic in computational geometry with applications in robotics and graphics. It's suitable for graduate students and researchers focusing on these types of geometric problems.
While focused on computer graphics, this book provides a broad range of 2D and 3D geometry algorithms essential for computational geometry practitioners. It's a useful reference tool for those working in graphics, CAD, or related fields who need practical geometric algorithms. It can supplement more theoretical computational geometry texts.
Provides a comprehensive overview of geometric algorithms and combinatorial optimization. It is suitable for advanced undergraduates and graduate students in computer science and operations research.
Focuses on algorithms for computing Euclidean shortest paths, a specific but important problem in computational geometry with applications in areas like motion planning. It's suitable for graduate students and researchers interested in pathfinding algorithms.
This monograph focuses on geometric spanner networks, a more advanced topic in computational geometry with applications in network design. It's suitable for graduate students and researchers specializing in geometric graph theory and network algorithms.
Explores the computational geometry of folding, a more specialized but fascinating area. It's suitable for graduate students and researchers interested in specific, contemporary topics at the intersection of geometry and algorithms. It provides depth in a niche area.
Delves into Davenport-Schinzel sequences and their applications in computational geometry. It's a specialized topic suitable for advanced graduate students and researchers interested in the combinatorial complexity of geometric problems.
A classic in geometric modeling, this book provides foundational knowledge on curves and surfaces crucial for computational geometry applications in CAD. While older, it's a valuable reference for understanding the mathematical basis of shape representation. It's more valuable as additional reading for historical context and foundational concepts.
Provides a comprehensive overview of convex optimization, which powerful tool for solving a wide range of problems in computational geometry and other fields. It is suitable for advanced undergraduates and graduate students in computer science, optimization, and related fields.
Describes LEDA, a software library for combinatorial and geometric computing. While not a textbook on computational geometry theory, it's a practical resource for those implementing geometric algorithms. It's useful for translating theoretical knowledge into working code and is relevant for students and professionals using LEDA.
A classic text that, while not solely focused on the modern definition of computational geometry, provides foundational ideas related to the computational capabilities of simple geometric structures. is more of historical significance and relevant for understanding the origins of certain computational concepts. It's suitable for graduate students and researchers interested in the history and theoretical underpinnings of computation and geometry.
Provides a comprehensive overview of geometric approximation algorithms. It is suitable for advanced undergraduates and graduate students in computer science and mathematics.
Provides a comprehensive overview of computational geometry, covering both theoretical foundations and practical applications. It is suitable for advanced undergraduates and graduate students in computer science and related fields.
For more information about how these books relate to this course, visit:
OpenCourser.com/topic/2ocmgq/computational
Save
