Computational geometry is a field of computer science concerned with the derivation and analysis of algorithms to address problems formulated in terms of geometry. Beyond computer graphics, important applications of computational geometry include robotics (motion planning and visibility problems), geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (mesh generation), and computer vision (3D reconstruction), among others. Computational complexity and numerical robustness are central topics in computational geometry, with great practical significance if algorithms are used on arbitrary, possbily very large datasets in real-world applications.
The course introduces core concepts of computational geometry, as well as important problem classes and algorithms, considering both theoretical and practical aspects. Emphasis is placed on fundamental principles of geometry algorithms, such as output size-sensitive and randomized algorithms and the notion of general position.