Orthogonal projection
In Euclidean geometry , Orthogonal projection is one whose projecting auxiliary lines are perpendicular to the plane of projection (or projection line), establishing a relationship between all points of the projected projecting element.
In the plane, the orthogonal projection is one whose projecting auxiliary lines are perpendicular to the line of projection L .
Thus, given a segment AB , simply project the points "extreme" segment-by projecting auxiliary lines perpendicular to L - to determine the projection on the line L .
An application of orthogonal projections are the theorems of Foreign the triangle metric by which one can calculate the dimension of the sides of a triangle.
orthogonal projection concept generalizes to Euclidean spaces of dimension arbitrary, even infinite dimension . This generalization plays an important role in many branches of mathematics and physics.
Case orthogonal projection on the plane
Orthogonal projection of a point
The orthogonal projection of a point P on a line L is another item, which is obtained by plotting an auxiliary line perpendicular to L from the point A. Logically, if the point PL, match: P = A. belongs to the line
Orthogonal projection of a segment.
General case: if the segment given AB is not parallel the line L , the orthogonal projection segment PQ obtained by drawing lines perpendicular to L from the endpoints. The magnitude of the projection is always less than the given segment.
If the segment PQ and the line L are parallel, the projection is: AB = PQ, which obtained similarly.
If the segment AB has a common point with the line L , the projection is obtained similarly.
If the segment AB intersects the line L , the projection is obtained similarly.
