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- Arrangement_(space_partition) abstract "In discrete geometry, an arrangement is the decomposition of the d-dimesional linear, affine, or projective space into connected open cells of lower dimensions, induced by a finite collection of geometric objects. Sometimes these objects are of the same type, such as hyperplanes or spheres. An interest in the study of arrangements was driven by advances in computational geometry, where the arrangements were unifying structures for many problems. Advances in study of more complicated objects, such as algebraic surfaces, contributed to "real-world" applications, such as motion planning and computer vision.".
- Arrangement_(space_partition) thumbnail Complete-quads.svg?width=300.
- Arrangement_(space_partition) wikiPageID "43167897".
- Arrangement_(space_partition) wikiPageLength "4398".
- Arrangement_(space_partition) wikiPageOutDegree "34".
- Arrangement_(space_partition) wikiPageRevisionID "653801867".
- Arrangement_(space_partition) wikiPageWikiLink Abstract_cell_complex.
- Arrangement_(space_partition) wikiPageWikiLink Affine_geometry.
- Arrangement_(space_partition) wikiPageWikiLink Algebraic_surface.
- Arrangement_(space_partition) wikiPageWikiLink Arrangement_of_hyperplanes.
- Arrangement_(space_partition) wikiPageWikiLink Arrangement_of_lines.
- Arrangement_(space_partition) wikiPageWikiLink Arrangements_of_hyperplanes.
- Arrangement_(space_partition) wikiPageWikiLink Arrangements_of_lines.
- Arrangement_(space_partition) wikiPageWikiLink Beltrami–Klein_model.
- Arrangement_(space_partition) wikiPageWikiLink Category:Computational_geometry.
- Arrangement_(space_partition) wikiPageWikiLink Category:Discrete_geometry.
- Arrangement_(space_partition) wikiPageWikiLink Circle_graph.
- Arrangement_(space_partition) wikiPageWikiLink Complete_(complexity).
- Arrangement_(space_partition) wikiPageWikiLink Complex_number.
- Arrangement_(space_partition) wikiPageWikiLink Computational_geometry.
- Arrangement_(space_partition) wikiPageWikiLink Computer_vision.
- Arrangement_(space_partition) wikiPageWikiLink Curve.
- Arrangement_(space_partition) wikiPageWikiLink Discrete_geometry.
- Arrangement_(space_partition) wikiPageWikiLink Existential_theory_of_the_reals.
- Arrangement_(space_partition) wikiPageWikiLink Graph_coloring.
- Arrangement_(space_partition) wikiPageWikiLink Hyperbolic_space.
- Arrangement_(space_partition) wikiPageWikiLink Hyperplane.
- Arrangement_(space_partition) wikiPageWikiLink Intersection_graph.
- Arrangement_(space_partition) wikiPageWikiLink Jordan_curve_theorem.
- Arrangement_(space_partition) wikiPageWikiLink Klein_model.
- Arrangement_(space_partition) wikiPageWikiLink Linear_space.
- Arrangement_(space_partition) wikiPageWikiLink Motion_planning.
- Arrangement_(space_partition) wikiPageWikiLink Open_set.
- Arrangement_(space_partition) wikiPageWikiLink Pappuss_hexagon_theorem.
- Arrangement_(space_partition) wikiPageWikiLink Projective_geometry.
- Arrangement_(space_partition) wikiPageWikiLink Projective_plane.
- Arrangement_(space_partition) wikiPageWikiLink Simple_closed_curve.
- Arrangement_(space_partition) wikiPageWikiLink Sphere.
- Arrangement_(space_partition) wikiPageWikiLink Topology.
- Arrangement_(space_partition) wikiPageWikiLink Triangle-free_graph.
- Arrangement_(space_partition) wikiPageWikiLink Vector_space.
- Arrangement_(space_partition) wikiPageWikiLink File:Complete-quads.svg.
- Arrangement_(space_partition) wikiPageWikiLinkText "Arrangement (space partition)".
- Arrangement_(space_partition) wikiPageWikiLinkText "arrangement".
- Arrangement_(space_partition) align "center".
- Arrangement_(space_partition) caption "A hyperbolic line arrangement combinatorially equivalent to a chord diagram used by to show that triangle-free circle graphs may sometimes need 5 colors.".
- Arrangement_(space_partition) caption "A non-stretchable pseudoline arrangement of nine pseudolines. Per Pappus's hexagon theorem, this arrangement cannot be realized in a projective plane over any field.".
- Arrangement_(space_partition) direction "horizontal".
- Arrangement_(space_partition) hasPhotoCollection Arrangement_(space_partition).
- Arrangement_(space_partition) image "Ageev 5X circle graph.svg".
- Arrangement_(space_partition) image "Pappos_pseudo.svg".
- Arrangement_(space_partition) width "300".
- Arrangement_(space_partition) width "383".
- Arrangement_(space_partition) wikiPageUsesTemplate Template:Multiple_images.
- Arrangement_(space_partition) wikiPageUsesTemplate Template:Reflist.
- Arrangement_(space_partition) subject Category:Computational_geometry.
- Arrangement_(space_partition) subject Category:Discrete_geometry.
- Arrangement_(space_partition) hypernym Decomposition.
- Arrangement_(space_partition) comment "In discrete geometry, an arrangement is the decomposition of the d-dimesional linear, affine, or projective space into connected open cells of lower dimensions, induced by a finite collection of geometric objects. Sometimes these objects are of the same type, such as hyperplanes or spheres. An interest in the study of arrangements was driven by advances in computational geometry, where the arrangements were unifying structures for many problems.".
- Arrangement_(space_partition) label "Arrangement (space partition)".
- Arrangement_(space_partition) sameAs m.0113_b4w.
- Arrangement_(space_partition) sameAs Q18209559.
- Arrangement_(space_partition) sameAs Q18209559.
- Arrangement_(space_partition) wasDerivedFrom Arrangement_(space_partition)?oldid=653801867.
- Arrangement_(space_partition) depiction Complete-quads.svg.
- Arrangement_(space_partition) isPrimaryTopicOf Arrangement_(space_partition).