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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 of a convex polygon 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 motion.ps.
- Pseudotriangle wikiPageExternalLink citation.cfm?id=160985.161159.
- Pseudotriangle wikiPageExternalLink ptriang.
- Pseudotriangle wikiPageExternalLink 03.ps.
- Pseudotriangle wikiPageExternalLink pv-ptta-96.ps.gz.
- Pseudotriangle wikiPageExternalLink pv-vc-93.ps.
- Pseudotriangle wikiPageExternalLink On_constrained_minimum_pseudotriangulations.pdf.
- Pseudotriangle wikiPageExternalLink FSTTCS04.pdf.
- Pseudotriangle wikiPageID "10609147".
- Pseudotriangle wikiPageRevisionID "584285366".
- Pseudotriangle hasPhotoCollection Pseudotriangle.
- Pseudotriangle subject Category:Euclidean_plane_geometry.
- Pseudotriangle subject Category:Mathematics_of_rigidity.
- Pseudotriangle subject Category:Polygons.
- Pseudotriangle subject Category:Triangulation_(geometry).
- Pseudotriangle type Abstraction100002137.
- Pseudotriangle type Attribute100024264.
- Pseudotriangle type Figure113862780.
- Pseudotriangle type PlaneFigure113863186.
- Pseudotriangle type Polygon113866144.
- Pseudotriangle type Polygons.
- Pseudotriangle type Shape100027807.
- 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 sameAs Pseudotriangle.
- Pseudotriangle wasDerivedFrom Pseudotriangle?oldid=584285366.
- Pseudotriangle depiction Pseudotriangles.svg.
- Pseudotriangle isPrimaryTopicOf Pseudotriangle.
