Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Conformal_geometric_algebra> ?p ?o }
Showing triples 1 to 85 of
85
with 100 triples per page.
- Conformal_geometric_algebra abstract "In mathematics, with application in computational geometry, conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a projective map from an n-dimensional Euclidean or pseudo-Euclidean base space ℝp,q into ℝp+1,q+1. This allows operations on the n-dimensional space, including rotations, translations and reflections to be represented using versors of the geometric algebra; and it is found that points, lines, planes, circles and spheres gain particularly natural and computationally amenable representations.The effect of the mapping is that generalized (i.e. including zero curvature) k-spheres in the base space map onto (k+2)-blades, and so that the effect of a translation (or any conformal mapping) of the base space corresponds to a rotation in the higher-dimensional space. In the algebra of this space, based on the geometric product of vectors, such transformations correspond to the algebra's characteristic sandwich operations, similar to the use of quaternions for spatial rotation in 3D, which combine very efficiently. A consequence of rotors representing transformations is that the representations of spheres, planes, circles and other geometrical objects, and equations connecting them, all transform covariantly. A geometric object (a k-sphere) can be synthesized as the wedge product of k+2 linearly independent vectors representing points on the object; conversely, the object can be decomposed as the repeated wedge product of vectors representing k+2 points in its surface. Some intersection operations also acquire a very tidy algebraic form: for example, for the Euclidean base space ℝ3, applying the wedge product to the dual of the tetravectors representing two spheres produces the dual of the trivector representation of their circle of intersection.As this algebraic structure lends itself directly to effective computation, it facilitates exploration of the classical methods of projective geometry and inversive geometry in a concrete, easy-to-manipulate setting. It has also been used as an efficient structure to represent and facilitate calculations in screw theory. CGA has particularly been applied in connection with the projective mapping of the everyday Euclidean space ℝ3 into a five-dimensional space ℝ4,1, which has been investigated for applications in robotics and computer vision. It can be applied generally to any Euclidean or pseudo-Euclidean space, and the mapping of Minkowski space ℝ3,1 to the space ℝ4,2 is being investigated for applications to relativistic physics.".
- Conformal_geometric_algebra wikiPageExternalLink books?id=A_f3ADC-h2wC.
- Conformal_geometric_algebra wikiPageExternalLink books?id=GVqz9-_fiLEC.
- Conformal_geometric_algebra wikiPageExternalLink books?id=oDrCziWyGo0C.
- Conformal_geometric_algebra wikiPageExternalLink Geometric_computing_with_Clifford_algebr.html?id=DD5QcR6t3h8C.
- Conformal_geometric_algebra wikiPageExternalLink GA&GC.pdf.
- Conformal_geometric_algebra wikiPageExternalLink UAFCG.html.
- Conformal_geometric_algebra wikiPageExternalLink CompGeom-ch1.pdf.
- Conformal_geometric_algebra wikiPageExternalLink CompGeom-ch2.pdf.
- Conformal_geometric_algebra wikiPageExternalLink CompGeom-ch3.pdf.
- Conformal_geometric_algebra wikiPageExternalLink CompGeom-ch4.pdf.
- Conformal_geometric_algebra wikiPageExternalLink New_Tools_for_Comp_Geom.pdf.
- Conformal_geometric_algebra wikiPageExternalLink OldWine.pdf.
- Conformal_geometric_algebra wikiPageExternalLink Journal_2008_DA.pdf.
- Conformal_geometric_algebra wikiPageExternalLink CFgeom5-15-2008.pdf.
- Conformal_geometric_algebra wikiPageExternalLink 9781849961073-c2.pdf?SGWID=0-0-45-938847-0.
- Conformal_geometric_algebra wikiPageExternalLink colapinto_masters_final_02.pdf.
- Conformal_geometric_algebra wikiPageExternalLink r_wareham_pdh_thesis.pdf.
- Conformal_geometric_algebra wikiPageID "34629138".
- Conformal_geometric_algebra wikiPageLength "23221".
- Conformal_geometric_algebra wikiPageOutDegree "34".
- Conformal_geometric_algebra wikiPageRevisionID "644686708".
- Conformal_geometric_algebra wikiPageWikiLink Affine_space.
- Conformal_geometric_algebra wikiPageWikiLink Blade_(geometry).
- Conformal_geometric_algebra wikiPageWikiLink Category:Computational_geometry.
- Conformal_geometric_algebra wikiPageWikiLink Category:Conformal_geometry.
- Conformal_geometric_algebra wikiPageWikiLink Category:Geometric_algebra.
- Conformal_geometric_algebra wikiPageWikiLink Category:Inversive_geometry.
- Conformal_geometric_algebra wikiPageWikiLink Chasles_theorem.
- Conformal_geometric_algebra wikiPageWikiLink Computational_geometry.
- Conformal_geometric_algebra wikiPageWikiLink Conformal_map.
- Conformal_geometric_algebra wikiPageWikiLink Conformal_mapping.
- Conformal_geometric_algebra wikiPageWikiLink David_Hestenes.
- Conformal_geometric_algebra wikiPageWikiLink Dilation_(metric_space).
- Conformal_geometric_algebra wikiPageWikiLink Euclidean_space.
- Conformal_geometric_algebra wikiPageWikiLink Euclidean_transformation.
- Conformal_geometric_algebra wikiPageWikiLink Exterior_algebra.
- Conformal_geometric_algebra wikiPageWikiLink Geometric_algebra.
- Conformal_geometric_algebra wikiPageWikiLink Geometric_product.
- Conformal_geometric_algebra wikiPageWikiLink Inner_automorphism.
- Conformal_geometric_algebra wikiPageWikiLink Inversion_transformation.
- Conformal_geometric_algebra wikiPageWikiLink Inversive_geometry.
- Conformal_geometric_algebra wikiPageWikiLink Liouvilles_theorem_(conformal_mappings).
- Conformal_geometric_algebra wikiPageWikiLink Mathematics.
- Conformal_geometric_algebra wikiPageWikiLink Minkowski_space.
- Conformal_geometric_algebra wikiPageWikiLink N-sphere.
- Conformal_geometric_algebra wikiPageWikiLink Point_at_infinity.
- Conformal_geometric_algebra wikiPageWikiLink Projective_geometry.
- Conformal_geometric_algebra wikiPageWikiLink Pseudo-Euclidean_space.
- Conformal_geometric_algebra wikiPageWikiLink Quaternions_and_spatial_rotation.
- Conformal_geometric_algebra wikiPageWikiLink Rigid_transformation.
- Conformal_geometric_algebra wikiPageWikiLink Screw_theory.
- Conformal_geometric_algebra wikiPageWikiLink Versor.
- Conformal_geometric_algebra wikiPageWikiLink Wedge_product.
- Conformal_geometric_algebra wikiPageWikiLink File:Conformal_Embedding.svg.
- Conformal_geometric_algebra wikiPageWikiLinkText "Conformal geometric algebra".
- Conformal_geometric_algebra wikiPageWikiLinkText "conformal Clifford algebra".
- Conformal_geometric_algebra wikiPageWikiLinkText "conformal geometric algebra".
- Conformal_geometric_algebra wikiPageWikiLinkText "conformal".
- Conformal_geometric_algebra hasPhotoCollection Conformal_geometric_algebra.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Cite_book.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Clarify.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Cleanup-remainder.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Math.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Refbegin.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Refend.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Reflist.
- Conformal_geometric_algebra wikiPageUsesTemplate Template:Refn.
- Conformal_geometric_algebra subject Category:Computational_geometry.
- Conformal_geometric_algebra subject Category:Conformal_geometry.
- Conformal_geometric_algebra subject Category:Geometric_algebra.
- Conformal_geometric_algebra subject Category:Inversive_geometry.
- Conformal_geometric_algebra hypernym Algebra.
- Conformal_geometric_algebra type Article.
- Conformal_geometric_algebra type Algebra.
- Conformal_geometric_algebra type Algorithm.
- Conformal_geometric_algebra type Article.
- Conformal_geometric_algebra type Page.
- Conformal_geometric_algebra comment "In mathematics, with application in computational geometry, conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a projective map from an n-dimensional Euclidean or pseudo-Euclidean base space ℝp,q into ℝp+1,q+1.".
- Conformal_geometric_algebra label "Conformal geometric algebra".
- Conformal_geometric_algebra sameAs m.0jt02nj.
- Conformal_geometric_algebra sameAs Q5160252.
- Conformal_geometric_algebra sameAs Q5160252.
- Conformal_geometric_algebra wasDerivedFrom Conformal_geometric_algebra?oldid=644686708.
- Conformal_geometric_algebra isPrimaryTopicOf Conformal_geometric_algebra.