Perspective

with centre

A mapping of a plane into a plane under which each point in is put into correspondence with the point of intersection of the straight line with (if is not parallel to , see Fig.).

Figure: p072410a

More generally, let and be proper subspaces of identical dimension in a projective space and let be a subspace of maximal dimension not having points in common with or . Let be a subspace contained in , let be the subspace of minimal dimension containing and and let be the intersection of and .

The correspondence by which each subspace contained in is put into correspondence with the subspace contained in is called a perspective mapping from into with perspective centre .

A perspective is a collineation. If the subspaces and intersect, then each point in the subspace corresponds to itself.

If projective coordinates are introduced into the spaces and , then a perspective correspondence can be specified by a linear mapping.

References

[1]	E. Artin, "Geometric algebra" , Interscience (1957)
[2]	N.A. Glagolev, "Projective geometry" , Moscow (1963) (In Russian)

Comments

Perspective mappings are also called central projections or perspectivities.

References

[a1]	M. Berger, "Geometry" , I , Springer (1987)
[a2]	H. Busemann, P.J. Kelly, "Projective geometry and projective metrics" , Acad. Press (1953)
[a3]	H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)
[a4]	H.S.M. Coxeter, "Projective geometry" , Blaisdell (1964)
[a5]	H.S.M. Coxeter, "The real projective plane" , McGraw-Hill (1949)