Projective Space 295 浏览 0关注

In mathematics a projective space is the set of lines through the origin of a vector space V. The cases when V=R2 or V=R3 are the projective line and the projective plane, respectively, where R denotes the field (mathematics)|field of real numbers, R2 denotes pairs of real numbers, and R3 denotes triplets of real numbers. The idea of a projective space relates to perspective (graphical)|perspective, more precisely to the way an eye or a camera projects a 3D scene to a 2D image. All points which lie on a projection line (i.e., a line-of-sight), intersecting with the pinhole camera model|entrance pupil of the camera, are projected onto a common image point. In this case the vector space is R3 with the camera entrance pupil at the origin and the projective space corresponds to the image points. Projective spaces can be studied as a separate field in mathematics, but are also used in various applied fields, geometry in particular. Geometric objects, such as points, lines, or planes, can...
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