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

# Natural homogeneous coordinates

Advanced Review

Published Online: Aug 25 2010

DOI: 10.1002/wics.122

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