Affine Transformation
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In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis, connected with) is a Transformation (function)|transformation which preserves straight lines (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of distances between points lying on a straight line (e.g., the midpoint of a line segment remains the midpoint after transformation). It does not necessarily preserve angles or lengths, but does have the property that sets of parallel lines will remain parallel to each other after an affine transformation. Examples of affine transformations include translation (geometry)|translation, geometric contraction, expansion (geometry)|expansion, homothety, reflection (mathematics)|reflection, rotation, shear mapping, similarity transformation, and spiral similarities and function composition|compositions of them.An affine transformation is equivalent to a linear transformation followed by a translation...
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