Projective transformations of space
Overview
Important
A projective transformation of space is a special way to map points, lines, and planes in projective space to other points, lines, and planes, so that straight lines remain straight and incidences (like points lying on a line) are preserved. These transformations are also called projectivities or collineations.
Important properties
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Projective transformations map lines to lines and planes to planes.
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They preserve incidence: if a point lies on a line before the transformation, it will still lie on the image of that line after the transformation.
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Parallelism and distances are not preserved, but cross-ratios of four collinear points are preserved.
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Any projective transformation can be represented using matrices and homogeneous coordinates.