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单词 ProjectionOfPoint
释义

projection of point


Let a line l be given in a Euclidean planeMathworldPlanetmath or space. The (orthogonalMathworldPlanetmathPlanetmath) projection of a P onto the line l is the point P of l at which the normal line of l passing through P intersects l. One says that P has been (orthogonally) projected onto the line l.

..PPl

The projection of a set S of points onto the line l is defined to be the set of projection points of all points of S on l.

Especially, the projection of a PQ onto l is the line segmentMathworldPlanetmath PQ determined by the projection points P and Q of P and Q. If the length of PQ is a and the angle between the lines (http://planetmath.org/AngleBetweenTwoLines) PQ and l is α, then the length p of its projection is

p=acosα.(1)
..αPPQQl

Remark.  As one speaks of the projections onto a line l, one can speak in the Euclidean space also of projections onto a plane τ.

Titleprojection of point
Canonical nameProjectionOfPoint
Date of creation2013-03-22 17:09:50
Last modified on2013-03-22 17:09:50
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id21
Authorpahio (2872)
Entry typeDefinition
Classificationmsc 51N99
Synonymorthogonal projection
Related topicProjection
Related topicCompassAndStraightedgeConstructionOfPerpendicular
Related topicMeusniersTheorem
Definesproject
Definesprojection of line segment
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