collineation


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Related to collineation: Homography, projective geometry

collineation

[kə‚lin·ē′ā·shən]
(mathematics)
A mapping which transforms points into points, lines into lines, and planes into planes. Also known as collineatory transformation.
References in periodicals archive ?
If the collineation has a fixed point z and a fixed line A, so that all lines through z and all points of A also remain fixed, then this collineation is called (z, A)-collineation, with centre z and axis A.
This f is a collineation, because if a point (a, c) lies on the line y = x x m + t, then c = a x m + t, and thus
To prove the remaining three requirements, let a (Y, A)-collineation be considered, whose axis A is the line x = 0, going through the centre Y (in such a case this collineation is called an elation, according to [40], [sections] 20.
Any one-to-one map f of a betweenness plane onto itself is said to be a collineation if (abc) [?
B8: For any two flags F and F0 there exists one and only one collineation f so that F' = f(F).
In [18] coordinates were introduced, algebraic extension to ordered projective geometry was given, and collineations were investigated.
Among collineations movements can be introduced in betweenness geometry, following [10] and [13].