Discrete and Computational Geometry
Joseph O'Rourke, Satyan L. Devadoss
Naturwissenschaften, Medizin, Informatik, Technik / Geometrie
Beschreibung
An essential introduction to discrete and computational geometry
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.
- The essential introduction to discrete and computational geometry
- Covers traditional topics as well as new and advanced material
- Features numerous full-color illustrations, exercises, and unsolved problems
- Suitable for sophomores in mathematics, computer science, engineering, or physics
- Rigorous but accessible
- An online solutions manual is available (for teachers only)
Kundenbewertungen
Associahedron, Diagram (category theory), Three-dimensional space (mathematics), Dimension, NP-hardness, Subset, Configuration space, Polytope, Convex set, Collinearity, Motion planning, Theorem, Computer science, Computational geometry, Cut locus (Riemannian manifold), Graham scan, Heptagon, Quadrilateral, Regular polygon, Discrete geometry, Formal proof, Polyhedron, Convex hull, General position, Voronoi diagram, Discrete mathematics, Simple polygon, Bisection, Conjecture, Diagonal, Tetrahedron, Time complexity, Upper and lower bounds, Addition, Euler's formula, Diameter, Mathematical induction, Notation, Mathematics, Degeneracy (mathematics), Big O notation, Equation, Scientific notation, Dual graph, Rectangle, Geometry, Exterior (topology), Intersection (set theory), Topology, Medial axis, Polygonal chain, Jordan curve theorem, NP-completeness, Algorithm, Bijection, Delaunay triangulation, Homeomorphism, Summation, Computation, Two-dimensional space, Parity (mathematics), Tangent space, Convex polygon, Inequality (mathematics), Special case, Line segment, Planar graph, Right angle, Circumscribed circle, Mathematician