Algorithms and Applications in Computational Geometry

Algorithms and Applications in Computational Geometry is a textbook that covers the fundamental principles and algorithms of computational geometry. The book is written in a clear and concise style, and it is designed to be accessible to students and researchers with a variety of backgrounds, including computer science, mathematics, and physics.

The book begins with an overview of the field of computational geometry and its applications in areas such as robotics, computer graphics, and geographic information systems. It then discusses the basic principles of computational geometry, such as geometric primitives, data structures, and algorithms for geometric operations such as point location, intersection, and visibility.

The book then applies these principles to a variety of specific computational geometry problems, such as:

Polygon triangulation
Convex hull computation
Voronoi diagrams
Delaunay triangulation
Arrangements of lines and segments
Point cloud processing
Mesh generation

The book also includes a number of chapters on more advanced topics, such as:

Algorithmic motion planning
Spatial range searching
Computational topology
Geometric optimization