Boundary value problem: Difference between revisions

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<!-- Deleted image removed: [[Image:Serioussam.jpg|thumb|270px|[[Serious Sam]] was one of the first [[First-person shooter|first person shooters]] to use mipmapping in real time.]] -->


In [[3D computer graphics]], '''mipmaps''' (also '''MIP maps''') are pre-calculated, [[Optimization (computer science)|optimized]] collections of images that accompany a main texture, intended to increase rendering speed and reduce [[aliasing]] artifacts. They are widely used in 3D [[computer game]]s, [[flight simulator]]s and other 3D imaging systems for [[texture filtering]]. Their use is known as '''mipmapping'''. The letters "MIP" in the name are an acronym of the [[Latin]] phrase ''multum in parvo'', meaning "much in little".<ref name="staff">http://staff.cs.psu.ac.th/iew/cs344-481/p1-williams.pdf</ref> Since mipmaps cannot be calculated in real time, additional storage space is required to take advantage of them. They also form the basis of [[wavelet compression]].


==Basic Use==
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Mipmaps are used for:<br>
-Speeding up rendering times. (Smaller textures equate to less memory usage.)<br>
-Improving the quality. Rendering large textures where only small subsets of points are used can easily produce [[moiré pattern]]s.<br>
-Reducing stress on [[GPU]].<br>
 
==Origin==
Mipmapping was invented by [[Lance Williams]] in 1983 and is described in his paper ''Pyramidal parametrics''.<ref name="staff" /> From the abstract: "This paper advances a 'pyramidal parametric' prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images." The "pyramid" can be imagined as the set of mipmaps stacked on top of each other.
 
==How it works==
[[Image:MipMap Example STS101.jpg|frame|An example of mipmap image storage: the principal image on the left is accompanied by filtered copies of reduced size.]]
 
Each bitmap image of the mipmap set is a downsized duplicate of the main [[Texture (computer graphics)|texture]], but at a certain reduced level of detail. Although the main texture would still be used when the view is sufficient to render it in full detail, the renderer will switch to a suitable mipmap image (or in fact, [[Interpolation (computer graphics)|interpolate]] between the two nearest, if [[trilinear filtering]] is activated) when the texture is viewed from a distance or at a small size. Rendering speed increases since the number of texture pixels ("[[Texel (graphics)|texels]]") being processed can be much lower with the simple textures. Artifacts are reduced since the mipmap images are effectively already [[Spatial anti-aliasing|anti-aliased]], taking some of the burden off the real-time renderer.
Scaling down and up is made more efficient with mipmaps as well.
 
If the texture has a basic size of 256 by 256 pixels, then the associated mipmap set may contain a series of 8 images, each one-fourth the total area of the previous one: 128&times;128 pixels, 64&times;64, 32&times;32, 16&times;16, 8&times;8, 4&times;4, 2&times;2, 1&times;1 (a single pixel). If, for example, a scene is rendering this texture in a space of 40&times;40 pixels, then either a scaled up version of the 32&times;32 (without [[trilinear interpolation]]) or an interpolation of the 64&times;64 and the 32&times;32 mipmaps (with trilinear interpolation)  would be used. The simplest way to generate these textures is by successive averaging; however, more sophisticated algorithms (perhaps based on [[signal processing]] and [[Fourier transforms]]) can also be used.
 
[[File:Mipmap illustration1.png|left|frame|The original RGB image]][[File:Mipmap illustration2.png|text-top|frame|In the case of an RGB image with three channels stored as separate planes, the total mipmap can be visualized as fitting neatly into a square area twice as large as the dimensions of the original image on each side. It also shows visually how using mipmaps requires 33% more memory.]] The increase in storage space required for all of these mipmaps is a third of the original texture, because the sum of the areas [[1/4 + 1/16 + 1/64 + 1/256 + · · ·]] converges to 1/3.  In the case of an RGB image with three channels stored as separate planes, the total mipmap can be visualized as fitting neatly into a square area twice as large as the dimensions of the original image on each side (twice as large on each side is four times the original area - one plane of the original size for each of red, green and blue makes three times the original area, and then since the smaller textures take 1/3 of the original, 1/3 of three is one, so they will take the same total space as just one of the original red, green, or blue planes). This is the inspiration for the tag "''multum in parvo''".
 
== Anisotropic filtering ==
{{main|Anisotropic filtering}}
When a texture is seen at a steep angle, the filtering should not be uniform in each direction (it should be [[anisotropic]] rather than [[isotropic]]), and a compromise resolution is used. If a higher resolution is used, the [[cache coherence]] goes down, and the aliasing is increased in one direction, but the image tends to be clearer. If a lower resolution is used, the cache coherence is improved, but the image is overly blurry.
 
Nonuniform mipmaps (also known as rip-maps) can solve this problem, although they have no direct support on modern graphics hardware. With an 8×8 base texture map, the rip-map resolutions are 8×8, 8×4, 8×2, 8×1; 4×8, 4×4, 4×2, 4×1; 2×8, 2×4, 2×2, 2×1; 1×8, 1×4, 1×2 and 1×1. In general, for a <math>2^n</math>×<math>2^n</math> base texture map, the rip-map resolutions are <math>2^i</math>×<math>2^j</math> for i and j from 0 to n.
 
== Summed-area tables ==
[[summed area table|Summed-area tables]] can conserve memory and provide more resolutions. However, they again hurt cache coherence, and need wider types to store the partial sums than the base texture's word size.  Thus, modern graphics hardware does not support them either.
 
==References==
 
{{reflist}}
 
==See also==
* [[Spatial anti-aliasing]]
* [[Anisotropic filtering]]
* [[Hierarchical modulation]] – similar technique in broadcasting
* [[Scale space]]
 
[[Category:Computer graphics data structures]]
[[Category:Texture filtering]]

Latest revision as of 01:23, 11 November 2014


Looking at playing a new digital video game, read the take advantage of book. Most on-line games have a book people can purchase separately. You may want to consider doing this and as well reading it before you play, or even even when you are playing. This way, you can easily get the most out of your game run.

Go on the internet for help. Just about any game has its legion of devoted devotees, lots of which blow countless hours crafting in depth maps and guides. Additionally there are newsgroups where you are that will speak one on an with other players. Benefit from this found diamond and it is easy to eventually get past that level of cla you have been into on forever.

If you want games which have been created till now, clash of clans is preferred by many individuals. The game which requires players to build villages and characters to get forward can quite hard at times. Enthusiastic gamers have to carry out side different tasks including raids and missions. Shopping lists or pads be very tough and often those players often get ensnared in one place. When this happens, it would be quite frustrating. On the contrary this can be influenced now because there is often a way out of this fact.

The main acceptable abatement for don't have any best stretches of stamina is essential. Without one prices would bound grow into prohibitive and cipher may purchase them.

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Now that you have read this composition, you need to a great easier time locating furthermore loving video games in your lifetime. Notwithstanding your favored platform, from your cellphone for the own computer, playing and enjoying video gaming can allow you to take the advantage of the worries of the actual busy week get specifics.

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