Computational geometry

Definition

Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.

Related concepts

3D reconstruction 4-polytope 5-cell ACM Computing Classification System ACM Computing Surveys ACM Transactions on Graphics Absolute geometry Acta Informatica Advances in Geometry Affine geometry Affine transformation Ahmes Algebra of physical space Algebraic geometry Algebraic structure Algebraic topology Algorithm Algorithm design Algorithmic efficiency Algorithmica Alhazen Altitude (triangle)Amortized analysis Anabelian geometry Analysis of algorithms Analytic geometry Analytical mechanics Angle Antipodal point Apollonius of Perga Application security Applied mathematics Approximation theory Archimedes Area Area of a circle Arithmetic geometry Ars Combinatoria (journal)Artificial intelligence Aryabhata Augmented reality Automata theory Automated planning and scheduling Automated theorem proving Axiomatic system Baudhayana Before Common Era Bentley–Ottmann algorithm Bernhard Riemann Big O notation Blaise Pascal Boolean operations on polygons Bosonic string theory Bowyer–Watson algorithm Brahmagupta Brute-force search Bézier curve Calculus of variations Calculus on Euclidean space Carl Friedrich Gauss Cartesian coordinate system Chan's algorithm Chaos theory Chew's second algorithm Christiaan Huygens Circle Circular triangle Circumference Classical field theory Clifford algebra Clifford analysis Closest pair of points Closest pair problem Coding theory Collision detection Combinatorial topology Combinatorics Communication protocol Communications of the ACM Compiler construction Complex geometry Computability theory Computational Geometry (journal)Computational biology Computational chemistry Computational complexity Computational complexity theory Computational engineering Computational intelligence Computational mathematics Computational number theory Computational physics Computational problem Computational social science Computational statistics Computational topology Computer Computer-aided design Computer-aided engineering Computer-aided geometric design Computer-aided manufacturing Computer Graphics World Computer Graphics and Applications Computer accessibility Computer algebra Computer animation Computer architecture Computer data storage Computer graphics Computer hardware Computer network Computer representation of surfaces Computer science Computer security Computer vision Computing Computing platform Concurrency (computer science)Concurrent computing Cone Cone algorithm Conformal field theory Conformal geometry Congruence (geometry)Constrained Delaunay triangulation Constraint programming Constraint satisfaction problem Constructive geometry Continuum (topology)Control flow Control theory Convex geometry Convex hull Convex hull algorithms Convex polygon Convex set Coordinate system Cross-validation (statistics)Cryptography Cube Cuboid Curve Cyber-physical system Cyberwarfare Cylinder (geometry)Data mining Data pre-processing Data structure Database David Hilbert Decision support system Decision theory Delaunay triangulation Dependability Descriptive geometry Diagonal Diameter Differential equation Differential form Differential geometry Differential topology Digital art Digital geometry Digital library Digital marketing Dimension (geometry)Dimension (mathematics and physics)Diophantine geometry Discrete & Computational Geometry Discrete differential geometry Discrete geometry Discrete mathematics Disk (mathematics)Distance Distributed artificial intelligence Distributed computing Document management system Dodecahedron Domain-specific language Duality (mathematics)Dynamic convex hull Dynamic data structures Dynamic problem (algorithms)Dynamic range searching Dynamical system E-commerce Educational technology Effective field theory Electronic design automation Electronic publishing Electronic voting Elliptic curve Elliptic geometry Embedded system Enterprise information system Enterprise software Euclid Euclid's Elements Euclidean distance map Euclidean geometry Euclidean shortest path Euclidean space European Community on Computational Methods in Applied Sciences Exterior algebra Exterior calculus Fault tolerance Felix Klein Field (mathematics)Field theory (physics)Finite geometry Form factor (design)Formal language Formal methods Fortune's Algorithm Foundations of geometry Four-dimensional space Fourier analysis Fractal Fractal analysis Franco P. Preparata Functional analysis Functional integration Game theory Gauge theory Gauge theory (mathematics)General topology Generalized trigonometry Geographic information system Geombinatorics Geometriae Dedicata Geometric algebra Geometric analysis Geometric calculus Geometric data analysis Geometric group theory Geometric hashing Geometric measure theory Geometric modeling Geometric topology Geometry Geometry of numbers Gift wrapping algorithm Gilbert–Johnson–Keerthi distance algorithm Glossary of Riemannian and metric geometry Glossary of algebraic geometry Glossary of algebraic topology Glossary of arithmetic and diophantine geometry Glossary of classical algebraic geometry Glossary of differential geometry and topology Glossary of general topology Glossary of mathematical symbols Glossary of shapes with metaphorical names Glossary of symplectic geometry Graham scan Graph theory Graphics processing unit Great circle Green computing Group theory Hamiltonian mechanics Hardware acceleration Hardware security Harmonic analysis Harmonic analysis (mathematics)Harold Scott MacDonald Coxeter Health informatics Henri Poincaré Hermann Minkowski History of geometry Human-centered computing Human–computer interaction Hyperbolic geometry Hyperbolic triangle Hypercube Hypersphere Hypotenuse IEEE Transactions on Computers IEEE Transactions on Graphics IEEE Transactions on Pattern Analysis and Machine Intelligence Ibn al-Yasamin Icosahedron Image compression Incidence geometry Industrial process control Information Processing Letters Information geometry Information retrieval Information security Information system Information theory Integrated circuit Integrated development environment Interaction design International Council for Industrial and Applied Mathematics International Journal of Computational Geometry and Applications Interpreter (computing)Intrusion detection system Japan Society for Industrial and Applied Mathematics Joseph O'Rourke (professor)Journal of Algorithms Journal of Combinatorial Theory Journal of Computational Geometry Journal of Computer and System Sciences Journal of the ACM Jump-and-Walk algorithm Jyeṣṭhadeva János Bolyai Kirkpatrick–Seidel algorithm Kite (geometry)Knot theory Knowledge representation and reasoning Kātyāyana Lagrangian mechanics Laplacian smoothing Largest empty circle Lattice theory Length Leonhard Euler Level-set method Library (computing)Line (geometry)Line segment Line segment intersection Linear programming List of algorithms List of arbitrary-precision arithmetic software List of books in computational geometry List of combinatorial computational geometry topics List of computer size categories List of differential geometry topics List of examples in general topology List of finite element software packages List of formulas in Riemannian geometry List of formulas in elementary geometry List of geometers List of geometry topics List of information graphics software List of interactive geometry software List of knot theory topics List of mathematics topics List of numerical-analysis software List of numerical computational geometry topics List of optimization software List of polygons List of shapes List of statistical software List of topologies List of uniform polyhedra Lists of geometry topics Logic in computer science Low-dimensional topology Machine learning Malliavin calculus Management Science (journal)Manava Marching triangles Mathematical analysis Mathematical and theoretical biology Mathematical chemistry Mathematical economics Mathematical finance Mathematical optimization Mathematical physics Mathematical psychology Mathematical sociology Mathematical software Mathematical visualization Mathematics Mesh generation Metric geometry Michael Atiyah Michael Ian Shamos Middleware Mikhail Leonidovich Gromov Minggatu Minimum bounding box Minimum bounding box algorithms Mobile computing Model of computation Modeling language Motion planning Multi-task learning Multicomplex number Multilinear algebra Multimedia database Multiprocessing Multithreading (computer architecture)Multivariable calculus N-sphere Nasir al-Din al-Tusi Natural language processing Nearest neighbor search Nearest neighbour search Nesting algorithm Network architecture Network performance Network scheduler Network security Network service Networking hardware Nikolai Lobachevsky Non-Archimedean geometry Non-Euclidean geometry Non-Euclidean space Noncommutative algebraic geometry Noncommutative geometry Noncommutative topology Numerical analysis Numerical linear algebra Numerical methods for ordinary differential equations Numerical methods for partial differential equations Octahedron Omar Khayyám One-dimensional space Open source Operating system Operations research Operator algebra Operator theory Ordered geometry Ordinary differential equation Orthogonality Oswald Veblen Outline of computer science Outline of geometry PDF Parallel (geometry)Parallel computing Parallelogram Parameshvara Parametric curve Parametric surface Partial differential equation Particle physics and representation theory Path integral formulation Pattern Recognition (journal)Pattern Recognition Letters Peripheral Perpendicular Perturbation theory Perturbation theory (quantum mechanics)Philosophy of artificial intelligence Photograph manipulation Plane (geometry)Platonic Solid Point (geometry)Point cloud Point in polygon Point location problem Point set registration Pointer (graphical user interfaces)Poisson algebra Polar coordinate system Polygon Polygon triangulation Polyhedron Potential theory Printed circuit board Probability Probability distribution Probability theory Processor (computing)Programming language Programming language theory Programming paradigm Programming team Programming tool Projective geometry Pyramid (geometry)Pythagoras Pythagorean theorem Quadrilateral Quantum computing Quantum field theory Quantum group Quasitriangulation Query (complexity)Quickhull Radius Random variable Randomized algorithm Range searching Ray tracing (graphics)Real-time computing Rectangle Reinforcement learning Rendering (computer graphics)Renormalization group René Descartes Requirements analysis Rhomboid Rhombus Riemannian geometry Ring theory Robotics Robust geometric computation Rotating calipers Ruppert's algorithm SIAM Journal on Computing

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