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Die Seite wurde neu angelegt: „This is an example of an easy water-simulation. The algorithm is fast and stable and looks like water - not perfect, but it fits my needs. Just move the mouse over the applet: {Applet code='WaveApplet' archive='WaveApplet.jar'} It is just a 2D Version, but it is easy to extend it to 3D as you can see in Jopulous. ==== SourceCode==== * Java-SourceCode ==== Descriptio…“

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This is an example of an easy water-simulation. The algorithm is fast and stable and looks like water - not perfect, but it fits my needs.

Just move the mouse over the applet:

[[Applet Code Wave Applet Archive Wave Applet Jar|{Applet code='WaveApplet' archive='WaveApplet.jar'}]]

It is just a 2D Version, but it is easy to extend it to 3D as you can see in [[Jopulous]].

==== SourceCode====

* [[Water Applet Source Code|Java-SourceCode]]

==== Description====

A physical and mathematical description will follow, but the main idea is to use a height-field of seperated water columns and to calculate the pressure and the amount of water flowing between direct neighbour columns. The runtime is O(n) where n is the number of columns.

The base idea is to use Newton's second law of motion

[[Math Fontsize18 Ffracdpdt Fracddtmv Mfracdvdtma|{Math fontsize='18'

F=\frac{dp}{dt}= \frac{d}{dt}(mv) =m\frac{dv}{dt}=ma
}]]

in a combination with Bernoulli's principle

[[Math Fontsize18 Fracv22gyfrac Prhoconstant|{Math fontsize='18'

\frac{v^2}{2}+gy+\frac{P}{\rho}=constant
}]]

where

{| class="wikitable"
|-
| ''v''
| fluid velocity along the streamline
|-
| ''g''
| gravitational constant
|-
| ''y''
| elevation in the direction of gravity
|-
| ''P''
| pressure along the streamline
|-
| [[Math Latexbr Rho Fontsize8|{Math latex='<br />rho' fontsize='8'}]]
| fluid density
|}
The algorithm is far from beeing a realistic simulation, if you look at the following.

[[Datei:water-glass.jpg]]

But with modern algorithms it is possible to get close to the original (sadly not in real time ; -) :

* [http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/GDC03.pdf Real Time Fluid Dynamics For Games]
* [http://graphics.stanford.edu/papers/water-sg02/ Animation and Rendering of Complex Water Surfaces]
* [http://www.vis.uni-stuttgart.de/vmv01/dl/papers/17.pdf Towards Real-Time Visual Simulation of Water Surfaces]
* [http://www.cis.upenn.edu/~fostern/pdfs/cgi97.pdf Controlling Fluid Animation]
* [http://portal.acm.org/citation.cfm?id=97884 Rapid, Stable Fluid Dynamics for Computer Graphics]
* [http://www.sciencemeetsart.com/wade/Projects/WaterFX2/index.html deep water simulation with DirectX9]

And here an other naive algorithms like the one I use:

* [http://freespace.virgin.net/hugo.elias/graphics/x_water.htm Rapid 2d Water]

==== TODO ====

* Make it better by suppressing the unnatural high frequent waves. This could be done by adding some not-accelerated amount of the water differnece to the left and right direct neighbour columns.

Simple Water Simulation - Versionsgeschichte