Dirichlet process - Revision history

en>Wbm1058: /* Introduction */ disambiguate exchangeable

2014-10-27T03:19:02Z

Introduction: disambiguate exchangeable

← Older revision		Revision as of 05:19, 27 October 2014
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	~~The writer~~ is ~~known as Irwin Wunder but it's not the most masucline~~ name ~~out there~~. ~~My day job is~~ a ~~meter reader~~. ~~One of the things she enjoys most~~ is ~~to read comics~~ and she~~'ll be starting~~ some thing ~~else alongside with it. California is our birth place~~.<br><br>~~Take a look at~~ my ~~webpage;~~ [http://~~dns125~~.~~dolzer~~.at/~~?q=node~~/~~696 http:~~//~~dns125.dolzer.at~~/~~?q=node~~/~~696~~]		Claude is her name and she completely digs that title. She works as a financial officer and she will not alter it whenever soon. Arizona is her birth location and she will by no means move. To perform badminton is some thing he truly enjoys doing.<br><br>Here is my web site - [http://foundation.coachfederation.org/UserProfile/tabid/67/userId/188080/Default.aspx extended auto warranty]

en>LokiClock: /* Applications of the Dirichlet process */ That simplex would be {1}

2014-03-02T16:51:35Z

Applications of the Dirichlet process: That simplex would be {1}

← Older revision		Revision as of 18:51, 2 March 2014
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	~~'''Oriented projective geometry'''~~ is ~~an [[orientability\|oriented]] version of real [[projective geometry]].~~		The writer is known as Irwin Wunder but it's not the most masucline name out there. My day job is a meter reader. One of the things she enjoys most is to read comics and she'll be starting some thing else alongside with it. California is our birth place.<br><br>Take a look at my webpage; [http://dns125.dolzer.at/?q=node/696 http://dns125.dolzer.at/?q=node/696]

	~~Whereas the [[real projective plane]] describes the set of all unoriented lines through the origin in '''R'~~'~~'<sup>3</sup>,~~ the ~~'''oriented projective plane''' describes lines with a given orientation~~. ~~There are applications in [[computer graphics]] and [[computer vision]] where it~~ is ~~necessary to distinguish between rays light being emitted or absorbed by~~ a ~~point.~~

	~~Elements in an oriented projective space are defined using signed [[homogeneous coordinates]]~~. ~~Let <math>\mathbf{R}_{*}^n</math> be the set of elements~~ of ~~<math>\mathbf{R}^n</math> excluding~~ the ~~origin.~~
	~~#'''Oriented projective line''', <math>\mathbf{T}^1</math>: <math>(x,w) \in \mathbf{R}^2_*</math>, with the [[equivalence relation]] <math>(x,w)\sim(a x,a w)\,</math> for all <math>a>0</math>.~~
	~~#'''Oriented projective plane''', <math>\mathbf{T}^2</math>: <math>(x,y,w) \in \mathbf{R}^3_*</math>, with <math>(x,y,w)\sim(a x,a y,a w)\,</math> for all <math>a>0</math>.~~

	~~These spaces can be viewed as extensions of [[euclidean space]]. <math>\mathbf{T}^1</math> can be viewed as the union of two copies of <math>\mathbf{R}</math>, the sets (''x'',1)~~ and ('~~'x'',-1), plus two additional points at infinity, (1,0) and (-1,0). Likewise <math>\mathbf{T}^2</math> can~~ be ~~view two copies of <math>\mathbf{R}^2</math>, (''x'',''y'',1) and (''x'',''y'',-1), plus one copy of <math>\mathbf{T}</math> (''x'',''y'',0)~~.

	~~An alternative way to view the spaces~~ is ~~as points on the circle or sphere, given by the points (''x'',''y'',''w'') with~~

	~~:''x''<sup>2</sup>+''y''<sup>2</sup>+''z''<sup>2</sup>=1~~.

	~~Distances between two points~~

	:<~~math~~>~~p=(p_x,p_y,p_w)</math>~~

	~~and~~

	~~:<math>q=(q_x,q_y,q_w)</math>~~

	in

	~~:<math>\mathbf{T}^2</math>~~

	~~can be defined as elements in <math>\mathbf{T}^1</math>~~
	~~:<math>((p_x q_w-q_x p_w)^2+(p_y q_w-q_y p_w)^2,\mathrm{sign}(p_w q_w)(p_w q_w)^2)\,.</math>~~

	~~==References==~~
	* {{cite book
	~~\| last = Stolfi~~
	~~\| first = Jorge~~
	~~\| title = Oriented Projective Geometry~~
	~~\| publisher = [[Academic Press]]~~
	~~\| date = 1991~~
	~~\| isbn = 978-0-12-672025-9 }}~~<br />~~From original [[Stanford]] Ph.D. dissertation, ''Primitives for Computational Geometry'', available as~~ [http://~~www~~.~~hpl~~.~~hp.com~~/~~techreports/Compaq-DEC/SRC-RR-36.pdf].~~
	* A. G. Oliveira, P. J. de Rezende, F. P. SelmiDei ''An Extension of [[CGAL]] to the Oriented Projective Plane T2 and its Dynamic Visualization System'', 21st Annual ACM Symp. on Computational Geometry, Pisa, Italy, 2005.
	* {{cite book
	~~\| last~~ = ~~Ghali~~
	~~\| first = Sherif~~
	~~\| title = Introduction to Geometric Computing~~
	~~\| publisher = [[Springer Science+Business Media\|Springer]]~~
	~~\| date = 2008~~
	~~\| isbn = 978-1-84800-114-5 }}<br~~ /~~>Nice introduction to oriented projective geometry in chapters 14 and 15. More at authors web-site. [~~http://~~www~~.~~dgp~~.~~toronto.edu~~/~~~ghali~~/ ~~Sherif Ghali].~~

	~~{{geometry-stub}}~~
	~~[[Category:Projective geometry]~~]

122.58.180.208: changed the more computer science-oriented 'returns' to 'a sample from', which is more statistics-friendly

2013-11-22T05:18:21Z

changed the more computer science-oriented 'returns' to 'a sample from', which is more statistics-friendly

← Older revision		Revision as of 07:18, 22 November 2013
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	~~Hi there~~. Let ~~me start~~ by ~~introducing~~ [http://www.~~youporntime~~.com/~~user~~/~~KBiaggini over the counter std test~~] ~~author~~, ~~her name is Myrtle Cleary~~. ~~My working day job is a librarian~~. ~~Doing ceramics is what my family members~~ and ~~I appreciate~~. ~~For a whilst she's been~~ in ~~South Dakota~~.		'''Oriented projective geometry''' is an [[orientability\|oriented]] version of real [[projective geometry]].

			Whereas the [[real projective plane]] describes the set of all unoriented lines through the origin in '''R'''<sup>3</sup>, the '''oriented projective plane''' describes lines with a given orientation. There are applications in [[computer graphics]] and [[computer vision]] where it is necessary to distinguish between rays light being emitted or absorbed by a point.

			Elements in an oriented projective space are defined using signed [[homogeneous coordinates]]. Let <math>\mathbf{R}_{*}^n</math> be the set of elements of <math>\mathbf{R}^n</math> excluding the origin.
			#'''Oriented projective line''', <math>\mathbf{T}^1</math>: <math>(x,w) \in \mathbf{R}^2_*</math>, with the [[equivalence relation]] <math>(x,w)\sim(a x,a w)\,</math> for all <math>a>0</math>.
			#'''Oriented projective plane''', <math>\mathbf{T}^2</math>: <math>(x,y,w) \in \mathbf{R}^3_*</math>, with <math>(x,y,w)\sim(a x,a y,a w)\,</math> for all <math>a>0</math>.

			These spaces can be viewed as extensions of [[euclidean space]]. <math>\mathbf{T}^1</math> can be viewed as the union of two copies of <math>\mathbf{R}</math>, the sets (''x'',1) and (''x'',-1), plus two additional points at infinity, (1,0) and (-1,0). Likewise <math>\mathbf{T}^2</math> can be view two copies of <math>\mathbf{R}^2</math>, (''x'',''y'',1) and (''x'',''y'',-1), plus one copy of <math>\mathbf{T}</math> (''x'',''y'',0).

			An alternative way to view the spaces is as points on the circle or sphere, given by the points (''x'',''y'',''w'') with

			:''x''<sup>2</sup>+''y''<sup>2</sup>+''z''<sup>2</sup>=1.

			Distances between two points

			:<math>p=(p_x,p_y,p_w)</math>

			and

			:<math>q=(q_x,q_y,q_w)</math>

			in

			:<math>\mathbf{T}^2</math>

			can be defined as elements in <math>\mathbf{T}^1</math>
			:<math>((p_x q_w-q_x p_w)^2+(p_y q_w-q_y p_w)^2,\mathrm{sign}(p_w q_w)(p_w q_w)^2)\,.</math>

			==References==
			* {{cite book
			\| last = Stolfi
			\| first = Jorge
			\| title = Oriented Projective Geometry
			\| publisher = [[Academic Press]]
			\| date = 1991
			\| isbn = 978-0-12-672025-9 }}<br />From original [[Stanford]] Ph.D. dissertation, ''Primitives for Computational Geometry'', available as [http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-36.pdf].
			* A. G. Oliveira, P. J. de Rezende, F. P. SelmiDei ''An Extension of [[CGAL]] to the Oriented Projective Plane T2 and its Dynamic Visualization System'', 21st Annual ACM Symp. on Computational Geometry, Pisa, Italy, 2005.
			* {{cite book
			\| last = Ghali
			\| first = Sherif
			\| title = Introduction to Geometric Computing
			\| publisher = [[Springer Science+Business Media\|Springer]]
			\| date = 2008
			\| isbn = 978-1-84800-114-5 }}<br />Nice introduction to oriented projective geometry in chapters 14 and 15. More at authors web-site. [http://www.dgp.toronto.edu/~ghali/ Sherif Ghali].

			{{geometry-stub}}
			[[Category:Projective geometry]]

en>AnomieBOT: Dating maintenance tags: {{Technical}}

2012-08-14T02:59:06Z

Dating maintenance tags: {{Technical}}

New page

Hi there. Let me start by introducing [http://www.youporntime.com/user/KBiaggini over the counter std test] author, her name is Myrtle Cleary. My working day job is a librarian. Doing ceramics is what my family members and I appreciate. For a whilst she's been in South Dakota.