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Natural homogeneous coordinates
Author(s) -
Wegman Edward J.,
Said Yasmin H.
Publication year - 2010
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.122
Subject(s) - homogeneous coordinates , projective geometry , cartesian coordinate system , homogeneous , duality (order theory) , coordinate system , geometry , euclidean geometry , computer graphics , axiom , spherical coordinate system , mathematics , formalism (music) , computer science , pure mathematics , algebraic geometry , computer graphics (images) , combinatorics , art , musical , visual arts
Abstract The natural homogeneous coordinate system is the analog of the Cartesian coordinate system for projective geometry. Roughly speaking a projective geometry adds an axiom that parallel lines meet at a point at infinity. This removes the impediment to line‐point duality that is found in traditional Euclidean geometry. The natural homogeneous coordinate system is surprisingly useful in a number of applications including computer graphics and statistical data visualization. In this article, we describe the axioms of projective geometry, introduce the formalism of natural homogeneous coordinates, and illustrate their use with four applications. WIREs Comp Stat 2010 2 678–685 DOI: 10.1002/wics.122 This article is categorized under: Applications of Computational Statistics > Computational Mathematics