en>Frietjes: Removed sitelinks migrated to Wikidata

2013-12-13T22:26:39Z

Removed sitelinks migrated to Wikidata

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	~~Alyson~~ is the title ~~individuals use~~ to ~~contact me~~ and ~~I think it sounds quite great~~ when ~~you say it~~. ~~To perform lacross is~~ the ~~factor I love most~~ of ~~all~~. ~~My wife~~ and ~~I reside~~ in ~~Mississippi but now I'm contemplating other options~~. ~~For years she's been operating~~ as ~~a journey agent~~.<br>~~<br>my website~~ :: [http://~~srncomm~~.com/blog/~~2014~~/08/25/~~relieve~~-~~that~~-~~stress~~-~~find~~-a-~~new~~-~~hobby~~/ ~~best psychics~~]		[[Image:Plasmafractal.gif\|200px\|right\|thumb\|Plasma fractal]]
			[[File:-PLASMA-ColorCycling.Gif\|200px\|thumb\|right\|Animated plasma fractal]]

			The '''diamond-square algorithm''' is a method for generating [[heightmap]]s for [[computer graphics]]. It is a slightly better algorithm than the three-dimensional implementation of the midpoint displacement algorithm which produces two-dimensional landscapes. It is also known as the '''random midpoint displacement fractal''', the '''cloud fractal''' or the '''plasma fractal''', because of the [[plasma effect]] produced when applied.

			The idea was first introduced by [[Alain Fournier\|Fournier]], [[Don Fussell\|Fussell]] and [[Loren Carpenter\|Carpenter]] at [[SIGGRAPH]] 1982.<ref name=fournier>{{cite journal\|last=Fournier\|first=Alain\|last2=Fussell\|first2=Don\|last3=Carpenter\|first3=Loren\|title=Computer rendering of stochastic models\|journal=Communications of the ACM\|date=June 1982\|volume=25\|issue=6\|pages=371–384\|accessdate=3 November 2011}}</ref> It was later analyzed by [[Gavin S. P. Miller]] in SIGGRAPH 1986<ref name=miller>{{cite journal\|last=Miller\|first=Gavin S. P.\|title=The definition and rendering of terrain maps\|journal=ACM SIGGRAPH Computer Graphics\|date=August 1986\|volume=20\|issue=4\|pages=39–48\|accessdate=3 November 2011}}</ref> who described it as flawed — the algorithm produces noticeable vertical and horizontal "creases" due to the most significant perturbation taking place in a rectangular grid.

			The algorithm starts with a 2D grid then [[terrain generation\|randomly generates terrain height]] from four seed values arranged in a grid of points so that the entire plane is covered in squares.

			==Midpoint displacement algorithm==
			[[Image:Plasmafrac2.gif\|200px\|right\|thumb\|Example on first iteration]]

			*Assign a height value to each corner of the rectangle (image).
			*Divide the rectangle into 4 subrectangles, and let their height values be the mean values of the corners of the parent rectangle.
			:For example, the upper left sub-rectangle in

			:<math>
			\begin{bmatrix}
			0 & 2 \\
			4 & 8\\
			\end{bmatrix}
			</math> will have the height values <math>
			\begin{bmatrix}
			0 & (0+2)/2 \\
			(0+4)/2 & (0+2+4+8)/4 \\
			\end{bmatrix}
			=
			\begin{bmatrix}
			0 & 1 \\
			2 & 3.5\\
			\end{bmatrix}
			</math>

			:But when computing the middle height, one should add a small error that depends on the size of the rectangle (the standard is to let the error be proportional to the size of the rectangle and some constant. The constant controls the "roughness" of the fractal; a bigger constant results in more valleys and mountains).
			*Iterate and subdivide each rectangle into smaller ones. Eventually, they will be too small to produce a noticeable difference. When this occurs, stop the iteration, and render the pixel with the mean of the height values.

			The difference from the above algorithm is an intermediate step that regards diamond-shaped squares as well.
			This reduces the squared-shaped artifacts in the landscape, since the diamonds are rotated 45 degrees relative to the squares.

			==Applications==

			This [[algorithm]] can be used to generate realistic-looking [[Fractal landscape\|landscapes]], and different implementations are used in computer graphics software such as [[Terragen]].

			==References==
			<references />

			==External links==
			* [http://github.com/mlepage/heightmap Simple open source heightmap module for Lua] using diamond-square algorithm
			* [http://www.gameprogrammer.com/fractal.html#diamond Generating Random Fractal Terrain: The Diamond-Square Algorithm] from [http://www.gameprogrammer.com/ GameProgrammer.com]
			* [http://www.smokycogs.com/blog/plasma-fractals/ Implementing a plasma fractal in C#]
			* [http://www.ic.sunysb.edu/Stu/jseyster/plasma/ Plasma Fractal] from Justin Seyster's web page
			* [http://www.hyper-metrix.com/processing-js/docs/index.php?page=Plasma%20Fractals Processing.js Plasma Fractal Demo] Justin Seyster's code converted for Processing.js
			* [http://www2.vo.lu/homepages/phahn/fractals/plasma.htm Plasma fractals] from Patrick Hahn's home page
			* [http://www.lighthouse3d.com/opengl/terrain/index.php?mpd2 Terrain Tutorial] from Lighthouse3d.com
			* [http://www.somethinghitme.com/2009/12/06/terrain-generation-with-canvas-and-javascript/ Random Midpoint Displacement with Canvas]
			* [http://www.cescg.org/CESCG97/marak/node3.html Random midpoint displacement method]

			[[Category:Fractals]]
			[[Category:Computer graphics algorithms]]
			[[Category:Procedural generation]]

128.171.62.168: /* Example 1: linear system of equations */ Grammar

2012-06-07T19:05:02Z

Example 1: linear system of equations: Grammar

New page

Alyson is the title individuals use to contact me and I think it sounds quite great when you say it. To perform lacross is the factor I love most of all. My wife and I reside in Mississippi but now I'm contemplating other options. For years she's been operating as a journey agent.<br><br>my website :: [http://srncomm.com/blog/2014/08/25/relieve-that-stress-find-a-new-hobby/ best psychics]

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en>Frietjes: Removed sitelinks migrated to Wikidata

128.171.62.168: /* Example 1: linear system of equations */ Grammar