Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Homogeneous_coordinates> ?p ?o }
- Homogeneous_coordinates abstract "In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix.If the homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infinity, the number of coordinates required to allow this extension is one more than the dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three homogeneous coordinates are required to specify a point in the projective plane.".
- Homogeneous_coordinates thumbnail RationalBezier2D.svg?width=300.
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- Homogeneous_coordinates wikiPageExternalLink HomogeneousCoordinates.html.
- Homogeneous_coordinates wikiPageExternalLink homo-coor.html.
- Homogeneous_coordinates wikiPageExternalLink homog-coords.pdf.
- Homogeneous_coordinates wikiPageID "243316".
- Homogeneous_coordinates wikiPageLength "27010".
- Homogeneous_coordinates wikiPageOutDegree "48".
- Homogeneous_coordinates wikiPageRevisionID "683321831".
- Homogeneous_coordinates wikiPageWikiLink Affine_transformation.
- Homogeneous_coordinates wikiPageWikiLink August_Ferdinand_Möbius.
- Homogeneous_coordinates wikiPageWikiLink Bxc3xa9zouts_theorem.
- Homogeneous_coordinates wikiPageWikiLink Cartesian_coordinate_system.
- Homogeneous_coordinates wikiPageWikiLink Category:Linear_algebra.
- Homogeneous_coordinates wikiPageWikiLink Category:Projective_geometry.
- Homogeneous_coordinates wikiPageWikiLink Center_of_mass.
- Homogeneous_coordinates wikiPageWikiLink Circular_algebraic_curve.
- Homogeneous_coordinates wikiPageWikiLink Circular_points_at_infinity.
- Homogeneous_coordinates wikiPageWikiLink Commutative_property.
- Homogeneous_coordinates wikiPageWikiLink Complex_number.
- Homogeneous_coordinates wikiPageWikiLink Complex_projective_line.
- Homogeneous_coordinates wikiPageWikiLink Complex_projective_space.
- Homogeneous_coordinates wikiPageWikiLink Computer_graphics.
- Homogeneous_coordinates wikiPageWikiLink Computer_vision.
- Homogeneous_coordinates wikiPageWikiLink Direct3D.
- Homogeneous_coordinates wikiPageWikiLink Division_ring.
- Homogeneous_coordinates wikiPageWikiLink Euclidean_geometry.
- Homogeneous_coordinates wikiPageWikiLink Field_(mathematics).
- Homogeneous_coordinates wikiPageWikiLink Finite_field.
- Homogeneous_coordinates wikiPageWikiLink Graphics_card.
- Homogeneous_coordinates wikiPageWikiLink Homogeneous_function.
- Homogeneous_coordinates wikiPageWikiLink Homogeneous_polynomial.
- Homogeneous_coordinates wikiPageWikiLink Homography.
- Homogeneous_coordinates wikiPageWikiLink Julius_Plücker.
- Homogeneous_coordinates wikiPageWikiLink Line_at_infinity.
- Homogeneous_coordinates wikiPageWikiLink Line_coordinates.
- Homogeneous_coordinates wikiPageWikiLink Mathematics.
- Homogeneous_coordinates wikiPageWikiLink Microsoft_Direct3D.
- Homogeneous_coordinates wikiPageWikiLink OpenGL.
- Homogeneous_coordinates wikiPageWikiLink Parametric_equation.
- Homogeneous_coordinates wikiPageWikiLink Perspective_(graphical).
- Homogeneous_coordinates wikiPageWikiLink Perspective_projection.
- Homogeneous_coordinates wikiPageWikiLink Plücker_embedding.
- Homogeneous_coordinates wikiPageWikiLink Point_at_infinity.
- Homogeneous_coordinates wikiPageWikiLink Polynomial.
- Homogeneous_coordinates wikiPageWikiLink Projective_geometry.
- Homogeneous_coordinates wikiPageWikiLink Projective_line.
- Homogeneous_coordinates wikiPageWikiLink Projective_plane.
- Homogeneous_coordinates wikiPageWikiLink Projective_space.
- Homogeneous_coordinates wikiPageWikiLink Projective_transformation.
- Homogeneous_coordinates wikiPageWikiLink Real_number.
- Homogeneous_coordinates wikiPageWikiLink Riemann_sphere.
- Homogeneous_coordinates wikiPageWikiLink Rotation_(mathematics).
- Homogeneous_coordinates wikiPageWikiLink Scaling_(geometry).
- Homogeneous_coordinates wikiPageWikiLink Shader.
- Homogeneous_coordinates wikiPageWikiLink Translation_(geometry).
- Homogeneous_coordinates wikiPageWikiLink Vector_processor.
- Homogeneous_coordinates wikiPageWikiLink Vertex_shader.
- Homogeneous_coordinates wikiPageWikiLink Video_card.
- Homogeneous_coordinates wikiPageWikiLink File:RationalBezier2D.svg.
- Homogeneous_coordinates wikiPageWikiLinkText "Homogeneous coordinates".
- Homogeneous_coordinates wikiPageWikiLinkText "Homogeneous_coordinates".
- Homogeneous_coordinates wikiPageWikiLinkText "affine transformations".
- Homogeneous_coordinates wikiPageWikiLinkText "homogeneous coordinate system".
- Homogeneous_coordinates wikiPageWikiLinkText "homogeneous coordinate vector".
- Homogeneous_coordinates wikiPageWikiLinkText "homogeneous coordinate".
- Homogeneous_coordinates wikiPageWikiLinkText "homogeneous coordinates".
- Homogeneous_coordinates wikiPageWikiLinkText "homogeneous image coordinates".
- Homogeneous_coordinates wikiPageWikiLinkText "homogeneous".
- Homogeneous_coordinates wikiPageWikiLinkText "linear combinations".
- Homogeneous_coordinates date "November 2014".
- Homogeneous_coordinates hasPhotoCollection Homogeneous_coordinates.
- Homogeneous_coordinates reason "Confusing; it must be explicit how this matrix acts on coordinates vectors. Apparently, contrarily to the common convention, the vector is on the left and the matrix on the right in the multiplication matrix vector".
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- Homogeneous_coordinates wikiPageUsesTemplate Template:Cite_book.
- Homogeneous_coordinates wikiPageUsesTemplate Template:Clarify.
- Homogeneous_coordinates wikiPageUsesTemplate Template:Main.
- Homogeneous_coordinates wikiPageUsesTemplate Template:Reflist.
- Homogeneous_coordinates wikiPageUsesTemplate Template:See_also.
- Homogeneous_coordinates subject Category:Linear_algebra.
- Homogeneous_coordinates subject Category:Projective_geometry.
- Homogeneous_coordinates hypernym System.
- Homogeneous_coordinates type Article.
- Homogeneous_coordinates type Article.
- Homogeneous_coordinates type Thing.
- Homogeneous_coordinates comment "In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates.".
- Homogeneous_coordinates label "Homogeneous coordinates".
- Homogeneous_coordinates seeAlso Transformation_matrix.
- Homogeneous_coordinates sameAs إحداثيات_متجانسة.
- Homogeneous_coordinates sameAs Homogene_koordinate.
- Homogeneous_coordinates sameAs Homogene_Koordinaten.
- Homogeneous_coordinates sameAs Homogenaj_koordinatoj.