Angular defect: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Entropeter
 
en>Magioladitis
m Removing invisible Unicode character/ Replacing hard spaces See WP:CHECKWIKI error #16 fix + other fixes, replaced: → using AWB (10331)
 
Line 1: Line 1:
[[Image:Bilinear interpolation.png|right|thumb|The four red dots show the data points and the green dot is the point at which we want to interpolate.]]
Hostgator Coupons - [http://roadschola.haja.net/zbxe/?document_srl=3903174 http://roadschola.haja.net/zbxe/?document_srl=3903174]. Hostgator is a huge privately had hosting company running from several state of the art facilities in Dallas, Texas. Hostgator was founded in 2002, since then they have expanded rapidly and presently host over 400,000 internet sites.<br><br><br><br>Hostgator offers many different webhosting packages, and deal with a broad range of consumers. From the first time web designer who requires basic, stress free hosting for their individual site; all the method through to large companies, who require specialist committed hosting services.<br><br>Hostgator's hosting plans can be divided into three groups; conventional shared hosting strategies (ideal for the substantial majority people), reseller hosting plans (these are mainly for individuals and companies that wish to "resell" their account resources to customers of their own), and lastly committed server strategies (these accounts offer customer their own server, so they do not need to share its resources with anyone else). Very few of us will every need a specialized server so this evaluation will focus on the shared hosting strategies that Hostgator offer.<br><br>Functions<br><br>Hostgator's three major shared hosting plans are named: "Hatchling" (the entry level plan priced at $6.95 / month), "Child" (this is the most popular plan, and it is likely to please the requirements of a really broad variety of clients), and "Swamp" (similar as the "Baby" plan, however with increases in bandwidth and disk space, priced at $14.95 / month).<br><br>For a complete list of functions and a side by side comparison of all hosting strategies you ought to visit Hostgator's website below. Below is an evaluation of the most crucial features of the "Baby" plan, this is probably the most ideal package for the majority of users, and it is our favorite strategy.<br><br>Disk space 100GB - This quantity has actually been just recently updated by Hostgator from 5GB to a massive 100GB. All individuals are most likely to find it impossible to tire this amount of disk area.<br><br>Bandwidth 1000GB/month - Also enhanced is the bandwidth allotment, from 75GB to a seemingly extreme 1000GB. Once again quite much no chance of making use of all that, but it's nice to [http://www.Europeana.eu/portal/search.html?query=understand understand] that you definitely won't be dealing with extra charges for reviewing your restriction, even if you have an extremely busy website(s).<br><br>Website Studio website home builder - This is a wonderful complimentary program that enables you to build your internet site from scratch. There is no demand to take my word for it, as Hostgator provides us with a trial version of the software application on their internet site!<br><br>Limitless add-on domains - This truly is the stick out feature of this [https://twitter.com/search?q=hosting+strategy&src=typd hosting strategy] (the "Hatchling" strategy just allows 1 domain), and enables you to host as numerous sites as you such as on a single account, at no additional expense. All your internet sites then share your account resources. This enables you to make complete use of your massive bandwidth and disk area allowances, and host numerous internet sites at a fraction of the normal expense. Wonderful!<br><br>99.9 % Uptime assurance - This basically informs us that Hostgator is a serious host offering a reputable service. If uptime drops below this figure in any given month then you don't pay for that months hosting, it's as simple as that! We would never consider making use of a host that did not offer a solid uptime assurance; this is purely due to the fact that there is just one good reason why a host will not offer an uptime assurance - unreliable uptime!<br><br>30 Day cash back guarantee - This has actually become a quite basic feature in the internet hosting area, though it's good to have actually for added peace of mind.<br><br>Instant setup - The majority of hosting suppliers take 24-48 hours to setup your account however Hostgator guarantees to have you up and running in under 15 minutes (they do not charge a setup fee either)!<br><br>Limitless MySQL data sources - This is really useful since each Fantastico (see below) script requires its own MySQL database.<br><br>Fantastico DeLuxe - This impressive program allows you to instantly install over 50 scripts through your control board. Scripts include blog sites, online forums, galleries, buying carts, and more.<br><br>Unrestricted e-mail accounts - Allows you to have as many, or as few, various email addresses as you like.<br><br>cPanel control board - At the heart of any web hosting experience is the control board, thankfully Hostgator uses one of the very best systems around, a cPanel. It's well laid out and simple to operate. It includes lots of functions and provides excellent efficiency. Most importantly, there is a complete working trial on the Hostgator website, so you can check it out yourself!<br><br>Customer care and technical support<br><br>Hostgator offers us 24/7 phone support, and live online chat. The fact that you are provided 2 options to get immediate technical support at any time of the day is terrific. Our experience has actually always been great when calling Hostgator, their operatives are very polite and most significantly they seem to know their stuff when dealing with technical issues. Nevertheless, we constantly suggest calling them yourself prior to signing up. Ask a question and see if you're made an impression on by their feedback. This constantly informs you a lot about a company!<br><br>Efficiency<br><br>The performance from Hostgator's servers is outstanding! Hostgator location much tighter restrictions on the number of websites sharing the exact same server compared with most other shared hosting providers. This gives greater reliability since less strain is put on the servers; and it also considerably improves the rate at which your internet pages run.<br><br>Server efficiency is an additional one of the essential areas where Hostgator differentiate themselves from the crowd of various other internet hosts.<br><br>Our judgment<br><br>Overall there is so much to like about the means Hostgator does business, they actually do seem to have a great grasp on exactly what the typical consumer requires from a web hosting supplier. Hardly ever do you come across reports of dissatisfied Hostgator clients, and after hosting with them ourselves we now know why! At simply $9.95 / month for the "Child" strategy (which consists of endless domains); anybody looking to host more than one website has a quite simple choice to make.
[[Image:Bilininterp.png|right|thumb|Example of bilinear interpolation on the unit square with the z-values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by color.]]
In [[mathematics]], '''bilinear interpolation''' is an extension of [[linear interpolation]] for [[interpolation|interpolating]] functions of two variables (e.g., <math>x</math> and <math>y</math>) on a [[regular grid|regular 2D grid]].
 
The key idea is to perform linear interpolation first in one direction, and then again in the other direction. Although each step is linear in the sampled values and in the position, the interpolation as a whole is not linear but rather quadratic in the sample location (details below).
 
==Algorithm==
 
Suppose that we want to find the value of the unknown function ''f'' at the point ''P'' = (''x'', ''y''). It is assumed that we know the value of ''f'' at the four points ''Q''<sub>11</sub> = (''x''<sub>1</sub>,&nbsp;''y''<sub>1</sub>), ''Q''<sub>12</sub> = (''x''<sub>1</sub>,&nbsp;''y''<sub>2</sub>), ''Q''<sub>21</sub> = (''x''<sub>2</sub>,&nbsp;''y''<sub>1</sub>), and ''Q''<sub>22</sub> = (''x''<sub>2</sub>,&nbsp;''y''<sub>2</sub>).  
 
We first do linear interpolation in the ''x''-direction. This yields
:<math> f(R_1) \approx \frac{x_2-x}{x_2-x_1} f(Q_{11}) + \frac{x-x_1}{x_2-x_1} f(Q_{21})</math>
where <math>R_1 = (x,y_1)</math>,
:<math> f(R_2) \approx \frac{x_2-x}{x_2-x_1} f(Q_{12}) + \frac{x-x_1}{x_2-x_1} f(Q_{22})</math>
where <math>R_2 = (x,y_2). </math>
 
We proceed by interpolating in the ''y''-direction.
:<math> f(P) \approx \frac{y_2-y}{y_2-y_1} f(R_1) + \frac{y-y_1}{y_2-y_1} f(R_2). </math>
 
This gives us the desired estimate of ''f''(''x'', ''y'').
:<math>
\begin{align}
f(x,y) \approx & \, \frac{f(Q_{11})}{(x_2-x_1)(y_2-y_1)} (x_2-x)(y_2-y) \, + \\
              & \, \frac{f(Q_{21})}{(x_2-x_1)(y_2-y_1)} (x-x_1)(y_2-y) \, + \\
              & \, \frac{f(Q_{12})}{(x_2-x_1)(y_2-y_1)} (x_2-x)(y-y_1) \, + \\
              & \, \frac{f(Q_{22})}{(x_2-x_1)(y_2-y_1)} (x-x_1)(y-y_1) \\
            = & \, \frac{1}{(x_2-x_1)(y_2-y_1)} \Big(  f(Q_{11})(x_2-x)(y_2-y) \, + \\
              & \, \qquad \qquad \qquad \qquad \; \;    f(Q_{21})(x-x_1)(y_2-y) \, + \\
              & \, \qquad \qquad \qquad \qquad \; \;    f(Q_{12})(x_2-x)(y-y_1) \, + \\
              & \, \qquad \qquad \qquad \qquad \; \;    f(Q_{22})(x-x_1)(y-y_1) \quad \Big)
\end{align}
</math>
 
Note that we will arrive at the same result if the interpolation is done first along the ''y''-direction and then along the ''x''-direction.
===Unit Square===
 
If we choose a coordinate system in which the four points where ''f'' is known are (0,&nbsp;0), (0,&nbsp;1),  (1,&nbsp;0), and (1,&nbsp;1), then the interpolation formula simplifies to
:<math> f(x,y) \approx f(0,0) \, (1-x)(1-y) + f(1,0) \, x(1-y) + f(0,1) \, (1-x)y + f(1,1) xy. </math>
Or equivalently, in matrix operations:
:<math> f(x,y) \approx \begin{bmatrix}
1-x & x \end{bmatrix} \begin{bmatrix}
f(0,0) & f(0,1) \\
f(1,0) & f(1,1) \end{bmatrix} \begin{bmatrix}
1-y \\
y \end{bmatrix}.</math>
 
===Nonlinear===
 
Contrary to what the name suggests, the bilinear interpolant is ''not'' linear; nor is it the product of two [[linear functions]].
 
Alternatively, the interpolant can be written as
:<math> b_1 + b_2 x + b_3 y + b_4 x y \, </math>
where
:<math> b_1 = f(0,0) \,</math>
:<math> b_2 = f(1,0)-f(0,0) \,</math>
:<math> b_3 = f(0,1)-f(0,0) \,</math>
:<math> b_4 = f(0,0)-f(1,0)-f(0,1)+f(1,1). \,</math>
 
[[File:bilinear_interpolation_visualisation.svg|thumb|right|In this geometric visualisation, the value at the black spot is the sum of the value at each coloured spot multiplied by the area of the rectangle of the same colour, divided by the total area of all four rectangles.]]
 
In both cases, the number of constants (four) correspond to the number of data points where ''f'' is given. The interpolant is linear along lines [[Parallel (geometry)|parallel]] to either the <math>x</math> or the <math>y</math> direction, equivalently if <math>x</math> or <math>y</math> is set constant. Along any other straight line, the interpolant is [[Quadratic function|quadratic]].  However, even if the interpolation is ''not'' linear in the position (''x'' and ''y''), it ''is'' linear in the amplitude, as it is apparent from the equations above: all the coefficient ''bj, j=1..4'', are proportional to the value of the function ''f(,)''.
 
The result of bilinear interpolation is independent of which axis is interpolated first and which second. If we had first performed the linear interpolation in the ''y''-direction and then in the ''x''-direction, the resulting approximation would be the same.
 
The obvious extension of bilinear interpolation to three dimensions is called [[trilinear interpolation]].
 
== Application in image processing ==
In [[computer vision]] and [[image processing]], bilinear interpolation is one of the basic [[resampling]] techniques.
 
In [[texture mapping]], it is also known as [[bilinear filtering]] or ''bilinear texture mapping'', and it can be used to produce a reasonably realistic image. An algorithm is used to map a screen pixel location to a corresponding point on the texture map. A weighted average of the attributes (color, alpha, etc.) of the four surrounding texels is computed and applied to the screen pixel. This process is repeated for each pixel forming the object being textured.<ref>[http://www.pcmag.com/encyclopedia_term/0,2542,t=bilinear+interpolation&i=38607,00.asp Bilinear interpolation definition at www.pcmag.com]</ref>
 
When an image needs to be scaled up, each pixel of the original image needs to be moved in a certain direction based on the scale constant. However, when scaling up an image by a non-integral scale factor, there are pixels (i.e., ''holes'') that are not assigned appropriate pixel values. In this case, those ''holes'' should be assigned appropriate [[RGB]] or [[grayscale]] values so that the output image does not have non-valued pixels.
 
Bilinear interpolation can be used where perfect image transformation with pixel matching is impossible, so that one can calculate and assign appropriate intensity values to pixels. Unlike other interpolation techniques such as [[nearest neighbor interpolation]] and [[bicubic interpolation]], bilinear interpolation uses only the 4 nearest pixel values which are located in diagonal directions from a given pixel in order to find the appropriate color intensity values of that pixel.
 
Bilinear interpolation considers the closest 2x2 neighborhood of known pixel values surrounding the unknown pixel's computed location. It then takes a weighted average of these 4 pixels to arrive at its final, interpolated value. The weight on each of the 4 pixel values is based on the computed pixel's distance (in 2D space) from each of the known points.<ref>[http://www.cambridgeincolour.com/tutorials/image-interpolation.htm "Digital Image Interpolation"]</ref>
 
[[File:Bilin3.png|thumb|right|alt=Bilinear interpolation|Example of bilinear interpolation in grayscale values.]]
 
As seen in the example on the right, the intensity value at the pixel computed to be at row 20.2, column 14.5 can be calculated by first linearly interpolating between the values at column 14 and 15 on each rows 20 and 21, giving
<br /><math>
\begin{array}{llll}
I_{20, 14.5} & = \tfrac{15 - 14.5}{15 - 14} \cdot 91  \, & + \; \tfrac{14.5 - 14}{15 - 14} \cdot 210 \, & = 150.5 \\
I_{21, 14.5} & = \tfrac{15 - 14.5}{15 - 14} \cdot 162 \, & + \; \tfrac{14.5 - 14}{15 - 14} \cdot 95  \, & = 128.5
\end{array}
</math><br />
and then interpolating linearly between these values, giving
<br /><math>I_{20.2, 14.5} = \tfrac{21 - 20.2}{21 - 20} \cdot 150.5 + \tfrac{20.2 - 20}{21 - 20} \cdot 128.5 = 146.1</math>
 
This algorithm reduces some of the visual distortion caused by resizing an image to a non-integral zoom factor, as opposed to nearest neighbor interpolation, which will make some pixels appear larger than others in the resized image. Bilinear interpolation tends, however, to produce a greater number of interpolation artifacts (such as [[aliasing]], blurring, and edge halos) than more computationally demanding techniques such as bicubic interpolation.<ref>[http://www.optoiq.com/index/machine-vision-imaging-processing/display/vsd-article-display/308929/articles/vision-systems-design/volume-12/issue-10/departments/wilsons-websites/understanding-image-interpolation-techniques.html "Understanding image-interpolation techniques"]</ref>
 
== See also ==
*[[Bicubic interpolation]]
*[[Trilinear interpolation]]
*[[Spline interpolation]]
*[[Lanczos resampling]]
*[[Stairstep interpolation]]
*[[Barycentric coordinate system (mathematics)|Barycentric coordinates - for interpolating within a triangle or tetrahedron]]
 
==References==
<references/>
 
[[Category:Multivariate interpolation]]

Latest revision as of 19:43, 26 July 2014

Hostgator Coupons - http://roadschola.haja.net/zbxe/?document_srl=3903174. Hostgator is a huge privately had hosting company running from several state of the art facilities in Dallas, Texas. Hostgator was founded in 2002, since then they have expanded rapidly and presently host over 400,000 internet sites.



Hostgator offers many different webhosting packages, and deal with a broad range of consumers. From the first time web designer who requires basic, stress free hosting for their individual site; all the method through to large companies, who require specialist committed hosting services.

Hostgator's hosting plans can be divided into three groups; conventional shared hosting strategies (ideal for the substantial majority people), reseller hosting plans (these are mainly for individuals and companies that wish to "resell" their account resources to customers of their own), and lastly committed server strategies (these accounts offer customer their own server, so they do not need to share its resources with anyone else). Very few of us will every need a specialized server so this evaluation will focus on the shared hosting strategies that Hostgator offer.

Functions

Hostgator's three major shared hosting plans are named: "Hatchling" (the entry level plan priced at $6.95 / month), "Child" (this is the most popular plan, and it is likely to please the requirements of a really broad variety of clients), and "Swamp" (similar as the "Baby" plan, however with increases in bandwidth and disk space, priced at $14.95 / month).

For a complete list of functions and a side by side comparison of all hosting strategies you ought to visit Hostgator's website below. Below is an evaluation of the most crucial features of the "Baby" plan, this is probably the most ideal package for the majority of users, and it is our favorite strategy.

Disk space 100GB - This quantity has actually been just recently updated by Hostgator from 5GB to a massive 100GB. All individuals are most likely to find it impossible to tire this amount of disk area.

Bandwidth 1000GB/month - Also enhanced is the bandwidth allotment, from 75GB to a seemingly extreme 1000GB. Once again quite much no chance of making use of all that, but it's nice to understand that you definitely won't be dealing with extra charges for reviewing your restriction, even if you have an extremely busy website(s).

Website Studio website home builder - This is a wonderful complimentary program that enables you to build your internet site from scratch. There is no demand to take my word for it, as Hostgator provides us with a trial version of the software application on their internet site!

Limitless add-on domains - This truly is the stick out feature of this hosting strategy (the "Hatchling" strategy just allows 1 domain), and enables you to host as numerous sites as you such as on a single account, at no additional expense. All your internet sites then share your account resources. This enables you to make complete use of your massive bandwidth and disk area allowances, and host numerous internet sites at a fraction of the normal expense. Wonderful!

99.9 % Uptime assurance - This basically informs us that Hostgator is a serious host offering a reputable service. If uptime drops below this figure in any given month then you don't pay for that months hosting, it's as simple as that! We would never consider making use of a host that did not offer a solid uptime assurance; this is purely due to the fact that there is just one good reason why a host will not offer an uptime assurance - unreliable uptime!

30 Day cash back guarantee - This has actually become a quite basic feature in the internet hosting area, though it's good to have actually for added peace of mind.

Instant setup - The majority of hosting suppliers take 24-48 hours to setup your account however Hostgator guarantees to have you up and running in under 15 minutes (they do not charge a setup fee either)!

Limitless MySQL data sources - This is really useful since each Fantastico (see below) script requires its own MySQL database.

Fantastico DeLuxe - This impressive program allows you to instantly install over 50 scripts through your control board. Scripts include blog sites, online forums, galleries, buying carts, and more.

Unrestricted e-mail accounts - Allows you to have as many, or as few, various email addresses as you like.

cPanel control board - At the heart of any web hosting experience is the control board, thankfully Hostgator uses one of the very best systems around, a cPanel. It's well laid out and simple to operate. It includes lots of functions and provides excellent efficiency. Most importantly, there is a complete working trial on the Hostgator website, so you can check it out yourself!

Customer care and technical support

Hostgator offers us 24/7 phone support, and live online chat. The fact that you are provided 2 options to get immediate technical support at any time of the day is terrific. Our experience has actually always been great when calling Hostgator, their operatives are very polite and most significantly they seem to know their stuff when dealing with technical issues. Nevertheless, we constantly suggest calling them yourself prior to signing up. Ask a question and see if you're made an impression on by their feedback. This constantly informs you a lot about a company!

Efficiency

The performance from Hostgator's servers is outstanding! Hostgator location much tighter restrictions on the number of websites sharing the exact same server compared with most other shared hosting providers. This gives greater reliability since less strain is put on the servers; and it also considerably improves the rate at which your internet pages run.

Server efficiency is an additional one of the essential areas where Hostgator differentiate themselves from the crowd of various other internet hosts.

Our judgment

Overall there is so much to like about the means Hostgator does business, they actually do seem to have a great grasp on exactly what the typical consumer requires from a web hosting supplier. Hardly ever do you come across reports of dissatisfied Hostgator clients, and after hosting with them ourselves we now know why! At simply $9.95 / month for the "Child" strategy (which consists of endless domains); anybody looking to host more than one website has a quite simple choice to make.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Angular_defect&oldid=293126"