Delaunay simplexes - Revision history

Nice and Tidy: Corrected spelling.

2008-12-11T18:28:32Z

Corrected spelling.

← Older revision		Revision as of 20:28, 11 December 2008
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	A '''Delaunay simplex''' is the [[dual lattice \| dual]] of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.		A '''Delaunay simplex''' is the [[dual lattice \| dual]] of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.

	A Delaunay triangulation ~~fulfills~~ the ''empty circle property'' (also called ''Delaunay property''): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.		A Delaunay triangulation fulfils the ''empty circle property'' (also called ''Delaunay property''): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.
	==References==		==References==
	#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.		#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.

Nice and Tidy: Placed external links at foot of page.

2008-12-11T18:28:07Z

Placed external links at foot of page.

← Older revision		Revision as of 20:28, 11 December 2008
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	A Delaunay triangulation fulfills the ''empty circle property'' (also called ''Delaunay property''): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.		A Delaunay triangulation fulfills the ''empty circle property'' (also called ''Delaunay property''): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.

	~~==External links==~~
	*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_VIII The CGAL project on computational geometry]
	==References==		==References==
	#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.		#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
	#[http://dx.doi.org/10.1007/11424758_84 A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science '''3480''' pp. 816-826 (2005)]		#[http://dx.doi.org/10.1007/11424758_84 A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science '''3480''' pp. 816-826 (2005)]
			==External links==
			*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_VIII The CGAL project on computational geometry]
	[[category: mathematics]]		[[category: mathematics]]

Dduque: Fixed DOI

2008-02-28T13:31:47Z

Fixed DOI

← Older revision		Revision as of 15:31, 28 February 2008
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	==References==		==References==
	#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.		#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
	#[http://dx.doi.org/10.1007/~~b136266~~ A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science '''3480''' pp. 816-826 (2005)]		#[http://dx.doi.org/10.1007/11424758_84 A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science '''3480''' pp. 816-826 (2005)]
	[[category: mathematics]]		[[category: mathematics]]

Carl McBride: /* References */ Added a Ref.

2008-02-21T15:49:55Z

References: Added a Ref.

← Older revision		Revision as of 17:49, 21 February 2008
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	==References==		==References==
	#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.		#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
			#[http://dx.doi.org/10.1007/b136266 A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science '''3480''' pp. 816-826 (2005)]
	[[category: mathematics]]		[[category: mathematics]]

Dduque at 13:15, 30 October 2007

2007-10-30T13:15:51Z

← Older revision		Revision as of 15:15, 30 October 2007
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	[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]		[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]
	A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.		A '''Delaunay simplex''' is the [[dual lattice \| dual]] of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.

	A Delaunay triangulation fulfills the ''empty circle property'' (also called ''Delaunay property''): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.		A Delaunay triangulation fulfills the ''empty circle property'' (also called ''Delaunay property''): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.

Dduque at 09:23, 9 October 2007

2007-10-09T09:23:25Z

← Older revision		Revision as of 11:23, 9 October 2007
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	[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]		[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]
	A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''. Delaunay triangulation ~~fulfils~~ the ~~so called '~~''empty circle property'''~~, i.e.~~		A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.
	the circumscribing circle of ~~each~~ facet ~~of such a triangulation does not contain any other vertex~~ of the triangulation in its interior. A similar property holds for tetrahedralisation in three dimensions.
			A Delaunay triangulation fulfills the ''empty circle property'' (also called ''Delaunay property''): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.

	==External links==		==External links==
	*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_VIII The CGAL project on computational geometry]		*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_VIII The CGAL project on computational geometry]

Nice and Tidy at 14:55, 13 September 2007

2007-09-13T14:55:03Z

← Older revision		Revision as of 16:55, 13 September 2007
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	[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]		[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]
	A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.		A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''. Delaunay triangulation fulfils the so called '''empty circle property''', i.e.
			the circumscribing circle of each facet of such a triangulation does not contain any other vertex of the triangulation in its interior. A similar property holds for tetrahedralisation in three dimensions.
	~~The~~ Delaunay triangulation ~~fulfills~~ the '''empty circle property''':		==External links==
	the circumscribing circle of each facet of such a triangulation does not contain any other vertex of the triangulation in its interior (a similar property holds for ~~the~~ tetrahedralisation).		*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_VIII The CGAL project on computational geometry]
	==References==		==References==
	#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.		#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
	~~==External links==~~		[[category: mathematics]]
	#[~~http~~:~~//www.cgal.org/ The CGAL project on computational geometry~~]

Dduque: Some mor info on these nice structures, plus link to CGAL

2007-09-12T14:14:50Z

Some mor info on these nice structures, plus link to CGAL

← Older revision		Revision as of 16:14, 12 September 2007
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	[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]		[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]
	A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.		A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.

			The Delaunay triangulation fulfills the '''empty circle property''':
			the circumscribing circle of each facet of such a triangulation does not contain any other vertex of the triangulation in its interior (a similar property holds for the tetrahedralisation).
	==References==		==References==
	#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.		#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
			==External links==
			#[http://www.cgal.org/ The CGAL project on computational geometry]

Carl McBride at 13:53, 7 September 2007

2007-09-07T13:53:09Z

← Older revision		Revision as of 15:53, 7 September 2007
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	[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]		[[Image:Delaunay.png\|thumb\|An example of Delaunay triangulation in two-dimensions]]
	A '''Delaunay ~~triangulation~~''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay ~~triangulation was~~ developed by Борис Николаевич Делоне.		A '''Delaunay simplex''' is the dual of the [[Voronoi cells \|Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''.
	==References==		==References==
	#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.		#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.

Carl McBride: Delaunay triangulation moved to Delaunay simplexes

2007-09-07T13:47:54Z

Delaunay triangulation moved to Delaunay simplexes

← Older revision	Revision as of 15:47, 7 September 2007
(No difference)