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The affine planes which arise from the projective planes PG(2, q) are denoted by AG(2, q). There is a projective plane of order N if and only if there is an affine plane of order N. When there is only one affine plane of order N there is only one projective plane of order N, but the converse is not true. The affine planes formed by the removal ...
In the Cayley plane, lines and points may be defined in a natural way so that it becomes a 2-dimensional projective space, that is, a projective plane. It is a non-Desarguesian plane, where Desargues' theorem does not hold. More precisely, as of 2005, there are two objects called Cayley planes, namely the real and the complex Cayley plane.
The Fano plane is the projective plane with the fewest points and lines. The smallest 2-dimensional projective geometry (that with the fewest points) is the Fano plane, which has 3 points on every line, with 7 points and 7 lines in all, having the following collinearities:
One common model of the real projective plane is the space of lines in three-dimensional Euclidean space which pass through a particular origin point; in this model, lines through the origin are considered to be the "points" of the projective plane, and planes through the origin are considered to be the "lines" in the projective plane.
Fig.5: A second, horizontal plane of projection is added, perpendicular to the first. Fig.6: Projectors emanate parallel from all points of the object perpendicular to the second plane of projection. Fig.7: An image is created thereby. Fig.8: The third plane of projection is added, perpendicular to the previous two.
The centre of projection can be thought of as the location of the observer, while the plane of projection is the surface on which the two dimensional projected image of the scene is recorded or from which it is viewed (e.g., photographic negative, photographic print, computer monitor).
To get a true view (length in the projection is equal to length in 3D space) of one of the lines: SU in this example, projection 3 is drawn with hinge line H 2,3 parallel to S 2 U 2. To get an end view of SU, projection 4 is drawn with hinge line H 3,4 perpendicular to S 3 U 3. The perpendicular distance d gives the shortest distance between PR ...