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A parallel projection is a particular case of projection in mathematics and graphical projection in technical drawing. Parallel projections can be seen as the limit of a central or perspective projection, in which the rays pass through a fixed point called the center or viewpoint, as this point is moved towards
Because a parallel projection and a scaling preserves ratios one can map an arbitrary point = (,,) by the axonometric procedure below. Pohlke's theorem can be stated in terms of linear algebra as: Any affine mapping of the 3-dimensional space onto a plane can be considered as the composition of a similarity and a parallel projection.
General solutions are a class of solutions within descriptive geometry that contain all possible solutions to a problem. The general solution is represented by a single, three-dimensional object, usually a cone, the directions of the elements of which are the desired direction of viewing (projection) for any of an infinite number of solution views.
In an affine space such as the Euclidean plane a similar statement is true, but only if one lists various exceptions involving parallel lines. Desargues's theorem is therefore one of the simplest geometric theorems whose natural home is in projective rather than affine space.
A projective plane of order N is a Steiner S(2, N + 1, N 2 + N + 1) system (see Steiner system). Conversely, one can prove that all Steiner systems of this form (λ = 2) are projective planes. The number of mutually orthogonal Latin squares of order N is at most N − 1. N − 1 exist if and only if there is a projective plane of order N.
Classification of Axonometric projection and some 3D projections "Axonometry" means "to measure along the axes". In German literature, axonometry is based on Pohlke's theorem, such that the scope of axonometric projection could encompass every type of parallel projection, including not only orthographic projection (and multiview projection), but also oblique projection.
Mathematically, the center of projection is a point O of the space (the intersection of the axes in the figure); the projection plane (P 2, in blue on the figure) is a plane not passing through O, which is often chosen to be the plane of equation z = 1, when Cartesian coordinates are considered.
1. Projections of two sets of parallel lines lying in some plane π A appear to converge, i.e. the vanishing point associated with that pair, on a horizon line, or vanishing line H formed by the intersection of the image plane with the plane parallel to π A and passing through the pinhole.