Computational Geometry
Computational geometry is a branch of mathematics and computer science that deals with the design and analysis of algorithms for manipulating geometric objects, such as points, lines, polygons, polyhedra, and curves. It combines techniques from discrete mathematics, algorithm design, data structures, and computational complexity to solve problems in areas such as computer graphics, image processing, robotics, geographic information systems, and computer-aided design. Researchers in this field study both the theoretical properties of geometric algorithms and their practical implementation on real-world datasets. They aim to develop efficient and robust methods for solving geometric problems, taking into account various constraints such as numerical accuracy, memory usage, and parallelism. In the context of combinatorics, computational geometry focuses on the combinatorial aspects of geometric structures, such as planar graphs, triangulations, and visibility graphs, and their applications in algorithm design and optimization.
External Links
- [Tilings.org] Tilings, Geometry and Automorphisms of Surfaces | Tilings, Automorphisms, Hyperbolic Geometry and Computational Group Theory
- [cgal.org] The Computational Geometry Algorithms Library