Computational Geometry

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.

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), 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.
  • 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.

Read more about Computational Geometry:  Combinatorial Computational Geometry, Numerical Computational Geometry

Other articles related to "computational geometry, computational":

List Of Books In Computational Geometry - Numerical Computational Geometry (geometric Modelling, Computer-aided Geometric Design) - Monographs
... Computational Geometry for Design and Manufacture (Mathematics Its Applications) ... An Introduction to Computational Geometry for Curves and Surfaces ... Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization Series ed.) ...
List Of Books In Computational Geometry
... This is a list of books in computational geometry ... There are two major, largely nonoverlapping categories Combinatorial computational geometry, which deals with collections of discrete objects or defined in discrete terms points, lines, polygons ... and algorithms of discrete/combinatorial character are used Numerical computational geometry, also known as geometric modeling and computer-aided geometric design (CAGD), which deals with ...
List Of Books In Computational Geometry - Combinatorial Computational Geometry - References
... Handbook of Discrete and Computational Geometry ... Algorithms, in its comprehensiveness, only restricted to discrete and computational geometry, computational topology, as well as a broad range of their applications ... Handbook of Computational Geometry ...
Numerical Computational Geometry
... Core problems are curve and surface modelling and representation ... The most important instruments here are parametric curves and parametric surfaces, such as Bezier curves, spline curves and surfaces ...
List Of Books In Computational Geometry - Conferences
... Annual Symposium on Computational Geometry (SoCG) Canadian Conference on Computational Geometry (CCCG) Japanese Conference on Discrete and Computational Geometry (JCDCG) The conferences ...

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