Computational geometry and computer graphics

Article Abstract:

Computational geometry and computer graphics consider the geometric phenomena related to computing. While computational geometry provides a theoretical foundation involving the study of algorithms and data structures for doing geometric computations, computer graphics is concerned with the practical development of the hardware, software and algorithms needed to create graphics on the screen. The interaction between them can be explored through spatial subdivisions studied from the viewpoint of computational geometry, and hidden surface removal problems of computer graphics, which have led to sweep-line and area subdivision algorithms in computational geometry. Also discussed are the theories for representing subdivisions of plane and space, and algorithmic paradigms from computer graphics.

Computer science, Computer graphics, Theory

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Computational geometry

Article Abstract:

Computational geometry is concerned with computing geometric properties of sets of geometric objects in space, and with the design and analysis of algorithms for solving geometric problems. It is also the study of the complexity inherent in geometric problems under varying models of computation, in which it presupposes the determination of which geometric properties are computable in the first place. Before the computer age, computational geometry was done with knotted strings, rulers and compasses. Present-day computational geometry includes parallel computational geometry, such as neural-network computational geometry, isothetic computational geometry and numerical computational geometry. The evolution of computational geometry is discussed in detail.

Computer history, History of Computing

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Relative neighborhood graphs and their relatives

Article Abstract:

The relative neighborhood graph (RNG) represents a finite set of points and is a prominent representative of the line of graphs that are defined using a concept of neighborliness. The relative neighborhood graph of V for points in a real space Rd is a graph with vertex set V and edges that are exactly those pairs of points where a symbol denotes the distance between p and q. RNGs are related to other prominent geometric structures. For example, the Delaunay triangulation of a set V is the dual graph of the Voronoi diagram of V. V is a decomposition of Rd into n cells, n being the number of points in V. Also discussed are the size of neighborhood graphs, algorithms, variants and special cases, and applications.

Algorithms, Biology, Algorithm, Clustering (Computers), Server Clustering, Graphs, Size, Nearest-Neighbor

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