Computational Geometry

“Computational Geometry” is a comprehensive guide to the field of geometry and its applications in computer science. This book covers the fundamentals of computational geometry, including topics such as polygon triangulation, convex hulls, Voronoi diagrams, and geometric search algorithms. The authors delve into advanced topics such as motion planning, robotics, and the design of geometric algorithms. This book provides a solid foundation in the field of computational geometry, making it an essential resource for students, researchers, and professionals alike.

The book begins with an introduction to the basic concepts of computational geometry, including points, lines, and polyggonal shapes. The authors then move on to explore polygon triangulation, which is a process of breaking down a polygon into a set of triangles that can be used to perform various operations. This is followed by a discussion of convex hulls, which are the smallest convex polygons that enclose a set of points. The authors also delve into the concept of Voronoi diagrams, which are used to visualize the distribution of data points in space.

In the latter half of the book, the authors delve into more advanced topics such as motion planning, robotics, and the design of geometric algorithms. Motion planning involves finding the best path for a moving object to follow, while taking into account obstacles and other constraints. Robotics involves the use of computational geometry to control robots, including the design of algorithms for tasks such as object recognition, localization, and navigation. The design of geometric algorithms involves the creation of efficient algorithms to solve geometric problems, including algorithms for sorting, searching, and constructing geometric objects.

Throughout the book, the authors provide clear and concise explanations of complex mathematical concepts, accompanied by numerous illustrations and examples to help readers understand the material. The book also includes a large number of exercises and problems to help reinforce key concepts and develop problem-solving skills. Whether you are a student, researcher, or professional, “Computational Geometry” is a comprehensive resource that provides a solid foundation in the field of computational geometry and its applications.