Tautological Line Bundle
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High Quality Content by WIKIPEDIA articles! In mathematics a projective space is a set of elements similar to the set P(V) 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. The idea of a projective space relates to 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 focal point of the camera, are projected onto a common image point. In this case the vector space is R3 with…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics a projective space is a set of elements similar to the set P(V) 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. The idea of a projective space relates to 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 focal point of the camera, are projected onto a common image point. In this case the vector space is R3 with the camera focal point 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 be given a representation as elements in projective spaces based on homogeneous coordinates.