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Introduction of Computational Geometry:
The Computational geometry is a field of computer science which is dedicated to the study of algorithms that can be stated in terms of geometry. A few geometrical problems occur out of the study of computational geometric algorithms and such problems are also considered to be the part of computational geometry.
The major impetus for the growth of computational geometry as a discipline was progress in computer-aided design and computer graphics and manufacturing (CAD/CAM), but most of the problems in computational geometry are classical in nature, and might come from mathematical visualization.
The other significant applications of computational geometry involve robotics (visibility problems and motion planning), geographic information systems (GIS) (i.e., geometrical position and search, route planning), integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (i.e., mesh generation), and computer vision (i.e., 3D reconstruction).
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Categories of Computational Geometry:
Combinatorial Computational Geometry:
This is also termed as algorithmic geometry which deals with geometric objects as discrete entity. A ground laying book in the subject by Shamos and Preparata dates, first use the word "computational geometry" in this sense by the year 1975.
Numerical Computational Geometry:
The Numerical computational geometry is also termed as geometric modeling machine geometry, or computer-aided geometric design, that deals fundamentally with representing real-world objects in forms appropriate for computer computations in CAD/CAM systems. This field may be view as a further development of descriptive geometry and is frequently considered as a branch of computer graphics or CAD. The word "computational geometry" in this meaning has been used since 1971.
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