Camera resectioning - Revision history

93.194.154.145: /* Parameters of camera model */

2014-12-28T10:03:21Z

Parameters of camera model

← Older revision		Revision as of 12:03, 28 December 2014
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	~~Hello and welcome~~. ~~My name~~ is ~~Irwin and I totally dig that name~~. ~~Minnesota has usually~~ been ~~his house but his spouse desires them to move. He utilized to be unemployed but now~~ he ~~is a meter reader~~. ~~One of the extremely very best issues in the globe for~~ me is ~~to do aerobics and~~ I've been ~~doing it for quite a whilst~~.<br><br>~~Also visit~~ my ~~weblog ...~~ [http://~~www~~.~~youporntime~~.~~com~~/~~blog~~/~~12800 home std test~~]		The author's title is Christy. Invoicing is my profession. For years he's been residing in Mississippi and he doesn't strategy on altering it. What me and my family members love is bungee leaping but I've been using on new issues recently.<br><br>Take a look at my page: [http://help.ksu.edu.sa/node/65129 real psychic readings]

en>Avi.nehemiah: /* External links */

2014-02-05T20:44:08Z

External links

← Older revision		Revision as of 22:44, 5 February 2014
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	~~[[Image:LegendreRational1.png\|thumb\|300px\|Plot of the Legendre rational functions for n=0,1,2~~ and ~~3 for ''x'' between 0~~.01 and ~~100~~.]]		Hello and welcome. My name is Irwin and I totally dig that name. Minnesota has usually been his house but his spouse desires them to move. He utilized to be unemployed but now he is a meter reader. One of the extremely very best issues in the globe for me is to do aerobics and I've been doing it for quite a whilst.<br><br>Also visit my weblog ... [http://www.youporntime.com/blog/12800 home std test]
	~~In [[mathematics]] the '''Legendre rational functions''' are a sequence of functions which are both [[rational functions\|rational]] and [[orthogonal functions\|orthogonal]]~~. ~~A rational Legendre function of degree ''n'' is defined as:~~

	~~:<math>R_n(x) = \frac{\sqrt{2}}{x+1}\,L_n\left(\frac{x-1}{x+1}\right)</math>~~

	~~where <math>L_n(x)</math>~~ is a ~~[[Legendre polynomial]]~~. ~~These functions are [[eigenfunction]]s~~ of the ~~singular [[Sturm-Liouville problem]]:~~

	~~:<math>(x+1)\partial_x(x\partial_x((x+1)v(x)))+\lambda v(x)=0</math>~~

	~~with eigenvalues~~

	~~:<math>\lambda_n=n(n+1)\,</math>~~

	~~== Properties==~~

	~~Many properties can be derived from~~ the ~~properties of the Legendre polynomials of the first kind. Other properties are unique~~ to ~~the functions themselves.~~

	~~=== Recursion ===~~

	~~:<math>R_{n+1}(x)=\frac{2n+1}{n+1}\,\frac{x-1}{x+1}\,R_n(x)-\frac{n}{n+1}\,R_{n-1}(x)\quad\mathrm{for\,n\ge 1}</math>~~

	and

	~~:<math>2(2n+1)R_n(x)=(x+1)^2(\partial_x R_{n+1}(x)-\partial_x R_{n-1}(x))+(x+1)(R_{n+1}(x)-R_{n-1}(x))</math>~~

	~~=== Limiting behavior ===~~
	~~[[Image:LegendreRational2.png\|thumb\|300px\|Plot of the seventh order (''n=7'') Legendre rational function multiplied by ''1+x'~~' for ~~''x'' between 0.01 and 100. Note that there are ''n'' zeroes arranged symmetrically about ''x=1'' and if ''x''<sub>0</sub> is~~ a ~~zero, then ''1/x''<sub>0</sub> is a zero as well. These properties hold for all orders~~.]]
	~~It can be shown that~~

	:<~~math~~>~~\lim_{x\rightarrow \infty}(x+1)R_n(x)=\sqrt{2}~~<~~/math~~>

	~~and~~

	~~:<math>\lim_{x\rightarrow \infty}x\partial_x((x+1)R_n(x))=0</math>~~

	~~=== Orthogonality ===~~

	~~:<math>\int_{0}^\infty R_m(x)\,R_n(x)\,dx=\frac{2}{2n+1}\delta_{nm}</math>~~

	~~where <math>\delta_{nm}</math> is the [[Kronecker delta]] function.~~

	~~== Particular values ==~~

	~~:<math>R_0(x)=1\,</math>~~
	~~:<math>R_1(x)=\frac{x-1}{x+1}\,</math>~~
	~~:<math>R_2(x)=\frac{x^2-4x+1}{(x+1)^2}\,</math>~~
	~~:<math>R_3(x)=\frac{x^3-9x^2+9x-1}{(x+1)^3}\,</math>~~
	~~:<math>R_4(x)=\frac{x^4-16x^3+36x^2-16x+1}{(x+1)^4}\,</math>~~

	~~== References ==~~

	~~{{cite journal~~
	~~\| last = Zhong-Qing~~
	~~\| first = Wang~~
	~~\| authorlink =~~
	~~\| coauthors = Ben-Yu, Guo~~
	~~\| year = 2005~~
	~~\| month =~~
	~~\| title = A mixed spectral method for incompressible viscous fluid flow in an infinite strip~~
	~~\| journal = Mat~~. ~~apl~~. ~~comput~~.
	~~\| volume = 24~~
	~~\| issue = 3~~
	~~\| pages =~~
	~~\| doi = 10.1590/S0101-82052005000300002~~
	~~\| id =~~
	~~\| url =~~ http://www.~~scielo~~.br/~~scielo.php?script=sci_arttext&pid=S0101-82052005000300002&lng=en&nrm=iso~~
	~~\| format = PDF~~
	~~\| accessdate = 2006-08-08~~
	}}

	~~[[Category:Rational functions]~~]

en>AnomieBOT: Dating maintenance tags: {{Citation needed}}

2013-10-21T16:30:24Z

Dating maintenance tags: {{Citation needed}}

← Older revision		Revision as of 18:30, 21 October 2013
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	~~I would like to introduce myself to you~~, ~~I am Andrew~~ and ~~my spouse doesn~~'~~t like it at all~~. ~~North Carolina~~ is the ~~place he loves most but now he is considering other choices~~. ~~To perform lacross is~~ the ~~thing I adore most~~ of all. He is ~~an info officer~~.<br><br>~~My homepage~~: ~~[https~~://~~www~~-~~ocl~~.~~gist~~.ac.kr/~~work~~/xe/?~~document_srl~~=~~605236 clairvoyants~~]		[[Image:LegendreRational1.png\|thumb\|300px\|Plot of the Legendre rational functions for n=0,1,2 and 3 for ''x'' between 0.01 and 100.]]
			In [[mathematics]] the '''Legendre rational functions''' are a sequence of functions which are both [[rational functions\|rational]] and [[orthogonal functions\|orthogonal]]. A rational Legendre function of degree ''n'' is defined as:

			:<math>R_n(x) = \frac{\sqrt{2}}{x+1}\,L_n\left(\frac{x-1}{x+1}\right)</math>

			where <math>L_n(x)</math> is a [[Legendre polynomial]]. These functions are [[eigenfunction]]s of the singular [[Sturm-Liouville problem]]:

			:<math>(x+1)\partial_x(x\partial_x((x+1)v(x)))+\lambda v(x)=0</math>

			with eigenvalues

			:<math>\lambda_n=n(n+1)\,</math>

			== Properties==

			Many properties can be derived from the properties of the Legendre polynomials of the first kind. Other properties are unique to the functions themselves.

			=== Recursion ===

			:<math>R_{n+1}(x)=\frac{2n+1}{n+1}\,\frac{x-1}{x+1}\,R_n(x)-\frac{n}{n+1}\,R_{n-1}(x)\quad\mathrm{for\,n\ge 1}</math>

			and

			:<math>2(2n+1)R_n(x)=(x+1)^2(\partial_x R_{n+1}(x)-\partial_x R_{n-1}(x))+(x+1)(R_{n+1}(x)-R_{n-1}(x))</math>

			=== Limiting behavior ===
			[[Image:LegendreRational2.png\|thumb\|300px\|Plot of the seventh order (''n=7'') Legendre rational function multiplied by ''1+x'' for ''x'' between 0.01 and 100. Note that there are ''n'' zeroes arranged symmetrically about ''x=1'' and if ''x''<sub>0</sub> is a zero, then ''1/x''<sub>0</sub> is a zero as well. These properties hold for all orders.]]
			It can be shown that

			:<math>\lim_{x\rightarrow \infty}(x+1)R_n(x)=\sqrt{2}</math>

			and

			:<math>\lim_{x\rightarrow \infty}x\partial_x((x+1)R_n(x))=0</math>

			=== Orthogonality ===

			:<math>\int_{0}^\infty R_m(x)\,R_n(x)\,dx=\frac{2}{2n+1}\delta_{nm}</math>

			where <math>\delta_{nm}</math> is the [[Kronecker delta]] function.

			== Particular values ==

			:<math>R_0(x)=1\,</math>
			:<math>R_1(x)=\frac{x-1}{x+1}\,</math>
			:<math>R_2(x)=\frac{x^2-4x+1}{(x+1)^2}\,</math>
			:<math>R_3(x)=\frac{x^3-9x^2+9x-1}{(x+1)^3}\,</math>
			:<math>R_4(x)=\frac{x^4-16x^3+36x^2-16x+1}{(x+1)^4}\,</math>

			== References ==

			{{cite journal
			\| last = Zhong-Qing
			\| first = Wang
			\| authorlink =
			\| coauthors = Ben-Yu, Guo
			\| year = 2005
			\| month =
			\| title = A mixed spectral method for incompressible viscous fluid flow in an infinite strip
			\| journal = Mat. apl. comput.
			\| volume = 24
			\| issue = 3
			\| pages =
			\| doi = 10.1590/S0101-82052005000300002
			\| id =
			\| url = http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-82052005000300002&lng=en&nrm=iso
			\| format = PDF
			\| accessdate = 2006-08-08
			}}

			[[Category:Rational functions]]

en>Supadog: /* Parameters of camera model */ added space after full-stop

2012-01-24T23:02:20Z

Parameters of camera model: added space after full-stop

New page

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