Clifford algebra of points, lines and planes

Journal article

Selig, JM (2000). Clifford algebra of points, lines and planes. Robotica. 18 (5), pp. 545 - 556. https://doi.org/10.1017/S0263574799002568
AuthorsSelig, JM
Abstract

The Clifford algebra for the group of rigid body motions is described. Linear elements, that is points, lines and planes are identified as homogeneous elements in the algebra. In each case the action of the group of rigid motions on the linear elements is found. The relationships between these linear elements are found in terms of operations in the algebra. That is, incidence relations, the conditions for a point to lie on a line for example are found. Distance relations, like the distance between a point and a plane are found. Also the meet and join of linear elements, for example, the line determined by two planes and the plane defined by a line and a point, are found. Finally three examples of the use of the algebra are given: a computer graphics problem on the visibility of the apparent crossing of a pair of lines, an assembly problem concerning a double peg-in-hole assembly, and a problem from computer vision on finding epipolar lines in a stereo vision system.

Year2000
JournalRobotica
Journal citation18 (5), pp. 545 - 556
PublisherCambridge University Press (CUP)
ISSN0263-5747
Digital Object Identifier (DOI)https://doi.org/10.1017/S0263574799002568
Publication dates
Print01 Sep 2000
Publication process dates
Deposited13 Dec 2016
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Open
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