For the journal, see Computational Geometry (journal).
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms which 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.
Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(n2) and O(n log n) may be the difference between days and seconds of computation.
The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry are classical in nature, and may come from mathematical visualization.
Other important applications of computational geometry include robotics (motion planning and visibility problems), geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (mesh generation), and computer vision (3D reconstruction).
The main branches of computational geometry are:
Combinatorial computational geometry, also called algorithmic geometry, which deals with geometric objects as discrete entities. A groundlaying book in the subject by Preparata and Shamos dates the first use of the term "computational geometry" in this sense by 1975.[1]
Numerical computational geometry, also called machine geometry, computer-aided geometric design (CAGD), or geometric modeling, which deals primarily with representing real-world objects in forms suitable for computer computations in CAD/CAM systems. This branch may be seen as a further development of descriptive geometry and is often considered a branch of computer graphics or CAD. The term "computational geometry" in this meaning has been in use since 1971.[2]
Although most algorithms of computational geometry have been developed (and are being developed) for electronic computers, some algorithms were developed for unconventional computers (e.g. optical computers [3])
^Franco P. Preparata and Michael Ian Shamos (1985). Computational Geometry - An Introduction. Springer-Verlag. ISBN 0-387-96131-3. 1st edition; 2nd printing, corrected and expanded, 1988.
^A.R. Forrest, "Computational geometry", Proc. Royal Society London, 321, series 4, 187-195 (1971)
^Yevgeny B. Karasik (2019). Optical Computational Geometry. ISBN 979-8511243344.
and 22 Related for: Computational geometry information
computational geometric algorithms, and such problems are also considered to be part of computationalgeometry. While modern computationalgeometry is...
geometry Computational group theory ComputationalgeometryComputational number theory Computational topology Computational statistics Algorithmic information...
theory and computational technique. In the 20th century, algebraic geometry split into several subareas. The mainstream of algebraic geometry is devoted...
The International Symposium on ComputationalGeometry (SoCG) is an academic conference in computationalgeometry. Today its acronym is pronounced "sausage...
game theory, machine learning, computational biology, computational economics, computationalgeometry, and computational number theory and algebra. Work...
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...
kissing numbers. With the emergence of applications of discrete geometry to computationalgeometry, these two fields partially merged and became a separate field...
list of books in computationalgeometry. There are two major, largely nonoverlapping categories: Combinatorial computationalgeometry, which deals with...
Discrete geometry has a large overlap with convex geometry and computationalgeometry, and is closely related to subjects such as finite geometry, combinatorial...
topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computationalgeometry and computational...
communication, data organization, computational devices, the flow of computation, etc. In mathematics, they are useful in geometry and certain parts of topology...
foundation of most modern fields of geometry, including algebraic, differential, discrete and computationalgeometry. Usually the Cartesian coordinate system...
graphics and computationalgeometry address the generation of images. Programming language theory considers different ways to describe computational processes...
In computationalgeometry, numerous algorithms are proposed for computing the convex hull of a finite set of points, with various computational complexities...
journal papers, largely on computationalgeometry, and is the co-author of several books including a widely used computationalgeometry text. Overmars has also...
In computationalgeometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of...
are commonly seen as the input to computationalgeometry problems, including point in polygon testing, area computation, the convex hull of a simple polygon...
An algorithmic paradigm or algorithm design paradigm is a generic model or framework which underlies the design of a class of algorithms. An algorithmic...
line in the previous configuration. In computationalgeometry, this ham sandwich theorem leads to a computational problem, the ham sandwich problem. In...
more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical...
Global Information