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In this viewpoint, an affine transformation geometry is a group of projective transformations that do not permute finite points with points at infinity.
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A quadrilateral is affine-regular if and only if it is a parallelogram, which includes rectangles and rhombuses as well as squares.
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Here, an "affine set" may be defined as the translation of a vector subspace.
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Note that on the "affine" plane, one might push off to a parallel line, so (thinking geometrically) the number of intersection points depends on the choice of push-off.
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There are many finite and infinite affine planes.
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Once a set of basic primitives have been created, they can easily be combined with one another using operations such as sweep, shrink-wrap and affine transformation.
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In affine geometry, there is no metric structure but the parallel postulate does hold.
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Similarly, a parabola is a concept in affine geometry but not in projective geometry, where a parabola is simply a kind of conic.
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Given a system of parametrized geodesics, one can specify a class of affine connections having those geodesics, but differing by their torsions.
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Archetypical resolvable 2-designs are the finite affine planes.
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