This book introduces fundamental geometric concepts and tools essential for solving geometric problems computationally. It bridges the gap between purely theoretical geometry texts and applied computer graphics, vision, or robotics books by detailing the underlying geometric principles. The author, Jean Gallier, provides an introduction to affine, projective, and Euclidean geometry, along with basics of differential geometry, Lie groups, and computational geometry concepts like convex sets and triangulations. The text explores numerous practical applications, including camera calibration, efficient communication, error-correcting codes, cryptography, motion interpolation, and robot kinematics, making it relevant for researchers in computer graphics, geometric modeling, computer vision, and robotics.

The book is designed to serve as a comprehensive resource for individuals needing a strong geometric foundation for research in fields such as computer graphics, geometric modeling, computer vision, and robotics. Its approach aims to provide the necessary theoretical depth often missing in purely applied texts, while also demonstrating practical relevance through numerous examples. The breadth of topics covered, from fundamental geometries to advanced computational and differential concepts, suggests a text suitable for advanced students and professionals in computer science, mathematics, and engineering.