Simple Water Simulation
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
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.
But with modern algorithms it is possible to get close to the original (sadly not in real time ; -) :
- Real Time Fluid Dynamics For Games
- Animation and Rendering of Complex Water Surfaces
- Towards Real-Time Visual Simulation of Water Surfaces
- Controlling Fluid Animation
- Rapid, Stable Fluid Dynamics for Computer Graphics
- deep water simulation with DirectX9
And here an other naive algorithms like the one I use:
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.