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- Pseudotriangle abstract "In Euclidean plane geometry, a pseudotriangle (pseudo-triangle) is the simply connected subset of the plane that lies between any three mutually tangent convex sets. A pseudotriangulation (pseudo-triangulations) is a partition of a region of the plane into pseudotriangles, and a pointed pseudotriangulation is a pseudotriangulation in which at each vertex the incident edges span an angle of less than π.Although the words "pseudotriangle" and "pseudotriangulation" have been used with various meanings in mathematics for much longer, the terms as used here were introduced in 1993 by Pocchiola and Vegter in connection with the computation of visibility relations and bitangents among convex obstacles in the plane. Pointed pseudotriangulations were first considered by Streinu (2000, 2005) as part of her solution to the carpenter's ruler problem, a proof that any simple polygonal path in the plane can be straightened out by a sequence of continuous motions. Pseudotriangulations have also been used for collision detection among moving objects and for dynamic graph drawing and shape morphing. Pointed pseudotriangulations arise in rigidity theory as examples of minimally rigid planar graphs, and in methods for placing guards in connection with the art gallery theorem. The shelling antimatroid of a planar point set gives rise to pointed pseudotriangulations, although not all pointed pseudotriangulations can arise in this way.For a detailed survey of much of the material discussed here, see Rote et al. (2006).".
- Pseudotriangle thumbnail Pseudotriangles.svg?width=300.
- Pseudotriangle wikiPageExternalLink ptriang.
- Pseudotriangle wikiPageExternalLink On_constrained_minimum_pseudotriangulations.pdf.
- Pseudotriangle wikiPageExternalLink motion.ps.
- Pseudotriangle wikiPageExternalLink citation.cfm?id=160985.161159.
- Pseudotriangle wikiPageExternalLink 03.ps.
- Pseudotriangle wikiPageExternalLink pv-ptta-96.ps.gz.
- Pseudotriangle wikiPageExternalLink pv-vc-93.ps.
- Pseudotriangle wikiPageExternalLink FSTTCS04.pdf.
- Pseudotriangle wikiPageID "10609147".
- Pseudotriangle wikiPageLength "17297".
- Pseudotriangle wikiPageOutDegree "31".
- Pseudotriangle wikiPageRevisionID "672075256".
- Pseudotriangle wikiPageWikiLink Antimatroid.
- Pseudotriangle wikiPageWikiLink Art_gallery_problem.
- Pseudotriangle wikiPageWikiLink Art_gallery_theorem.
- Pseudotriangle wikiPageWikiLink Bitangent.
- Pseudotriangle wikiPageWikiLink Carpenters_rule_problem.
- Pseudotriangle wikiPageWikiLink Carpenters_ruler_problem.
- Pseudotriangle wikiPageWikiLink Catalan_number.
- Pseudotriangle wikiPageWikiLink Category:Euclidean_plane_geometry.
- Pseudotriangle wikiPageWikiLink Category:Mathematics_of_rigidity.
- Pseudotriangle wikiPageWikiLink Category:Polygons.
- Pseudotriangle wikiPageWikiLink Category:Triangulation_(geometry).
- Pseudotriangle wikiPageWikiLink Convex_hull.
- Pseudotriangle wikiPageWikiLink Convex_set.
- Pseudotriangle wikiPageWikiLink Double_counting_(proof_technique).
- Pseudotriangle wikiPageWikiLink Euclidean_geometry.
- Pseudotriangle wikiPageWikiLink Euler_characteristic.
- Pseudotriangle wikiPageWikiLink International_Journal_of_Computational_Geometry_and_Applications.
- Pseudotriangle wikiPageWikiLink International_Symposium_on_Graph_Drawing.
- Pseudotriangle wikiPageWikiLink Laman_graph.
- Pseudotriangle wikiPageWikiLink Minimally_rigid_graph.
- Pseudotriangle wikiPageWikiLink Polygon.
- Pseudotriangle wikiPageWikiLink Polygonal_chain.
- Pseudotriangle wikiPageWikiLink Quadrilateral.
- Pseudotriangle wikiPageWikiLink Rigidity_theory_(structural).
- Pseudotriangle wikiPageWikiLink SIAM_Journal_on_Computing.
- Pseudotriangle wikiPageWikiLink Simple_polygonal_path.
- Pseudotriangle wikiPageWikiLink Simultaneous_linear_equations.
- Pseudotriangle wikiPageWikiLink Structural_rigidity.
- Pseudotriangle wikiPageWikiLink System_of_linear_equations.
- Pseudotriangle wikiPageWikiLink Triangle.
- Pseudotriangle wikiPageWikiLink Triangulation_(geometry).
- Pseudotriangle wikiPageWikiLink File:Convex_shelling.svg.
- Pseudotriangle wikiPageWikiLink File:Pseudotriangles.svg.
- Pseudotriangle wikiPageWikiLinkText "Pseudotriangle".
- Pseudotriangle wikiPageWikiLinkText "pointed pseudotriangulation".
- Pseudotriangle wikiPageWikiLinkText "pseudotriangle".
- Pseudotriangle hasPhotoCollection Pseudotriangle.
- Pseudotriangle wikiPageUsesTemplate Template:Citation.
- Pseudotriangle wikiPageUsesTemplate Template:Refbegin.
- Pseudotriangle wikiPageUsesTemplate Template:Refend.
- Pseudotriangle wikiPageUsesTemplate Template:Reflist.
- Pseudotriangle subject Category:Euclidean_plane_geometry.
- Pseudotriangle subject Category:Mathematics_of_rigidity.
- Pseudotriangle subject Category:Polygons.
- Pseudotriangle subject Category:Triangulation_(geometry).
- Pseudotriangle type Article.
- Pseudotriangle type Article.
- Pseudotriangle type Mechanic.
- Pseudotriangle type Polytope.
- Pseudotriangle comment "In Euclidean plane geometry, a pseudotriangle (pseudo-triangle) is the simply connected subset of the plane that lies between any three mutually tangent convex sets.".
- Pseudotriangle label "Pseudotriangle".
- Pseudotriangle sameAs m.02qk2f6.
- Pseudotriangle sameAs Q7255664.
- Pseudotriangle sameAs Q7255664.
- Pseudotriangle wasDerivedFrom Pseudotriangle?oldid=672075256.
- Pseudotriangle depiction Pseudotriangles.svg.
- Pseudotriangle isPrimaryTopicOf Pseudotriangle.