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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='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|WaterApplet.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 fontsize='18'
F=\frac{dp}{dt}= \frac{d}{dt}(mv) =m\frac{dv}{dt}=ma
}]
in a combination with Bernoulli's principle
[{Math fontsize='18'
\frac{v^2}{2}+gy+\frac{P}{\rho}=constant
}]
where
| ''v'' | fluid velocity along the streamline
| ''g'' | gravitational constant
| ''y'' | elevation in the direction of gravity
| ''P'' | pressure along the streamline
| [{Math latex='\\rho' fontsize='8'}] | fluid density
The algorithm is far from beeing a realistic simulation, if you look at the following.
[water-glass.jpg]
But with modern algorithms it is possible to get close to the original (sadly not in real time ;-):
* [Real Time Fluid Dynamics For Games|http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/GDC03.pdf]
* [Animation and Rendering of Complex Water Surfaces|http://graphics.stanford.edu/papers/water-sg02/]
* [Towards Real-Time Visual Simulation of Water Surfaces|http://www.vis.uni-stuttgart.de/vmv01/dl/papers/17.pdf]
* [Controlling Fluid Animation|http://www.cis.upenn.edu/~fostern/pdfs/cgi97.pdf]
* [Rapid, Stable Fluid Dynamics for Computer Graphics|http://portal.acm.org/citation.cfm?id=97884]
* [deep water simulation with DirectX9|http://www.sciencemeetsart.com/wade/Projects/WaterFX2/index.html]
And here an other naive algorithms like the one I use:
* [Rapid 2d Water|http://freespace.virgin.net/hugo.elias/graphics/x_water.htm]
! 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.
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|WaterApplet.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 fontsize='18'
F=\frac{dp}{dt}= \frac{d}{dt}(mv) =m\frac{dv}{dt}=ma
}]
in a combination with Bernoulli's principle
[{Math fontsize='18'
\frac{v^2}{2}+gy+\frac{P}{\rho}=constant
}]
where
| ''v'' | fluid velocity along the streamline
| ''g'' | gravitational constant
| ''y'' | elevation in the direction of gravity
| ''P'' | pressure along the streamline
| [{Math latex='\\rho' fontsize='8'}] | fluid density
The algorithm is far from beeing a realistic simulation, if you look at the following.
[water-glass.jpg]
But with modern algorithms it is possible to get close to the original (sadly not in real time ;-):
* [Real Time Fluid Dynamics For Games|http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/GDC03.pdf]
* [Animation and Rendering of Complex Water Surfaces|http://graphics.stanford.edu/papers/water-sg02/]
* [Towards Real-Time Visual Simulation of Water Surfaces|http://www.vis.uni-stuttgart.de/vmv01/dl/papers/17.pdf]
* [Controlling Fluid Animation|http://www.cis.upenn.edu/~fostern/pdfs/cgi97.pdf]
* [Rapid, Stable Fluid Dynamics for Computer Graphics|http://portal.acm.org/citation.cfm?id=97884]
* [deep water simulation with DirectX9|http://www.sciencemeetsart.com/wade/Projects/WaterFX2/index.html]
And here an other naive algorithms like the one I use:
* [Rapid 2d Water|http://freespace.virgin.net/hugo.elias/graphics/x_water.htm]
! 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.
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