Procedural, animated Landscape using Math only

[minxomat]

Hi there.
 
This script is an implicit function plotter, plotting a graph that simulates a landscape.
 
Basically, everything you see in this picture is based on implicit equations and functions. I modified the original equations a bit and added animation for the sea, a moving sun and two different kinds of lighting.

• Procedural Scene (only per-pixel-colors are calculated, no drawing function is used)
• Animated sea waves
• Animated sun
• Ambient light
• Directional light

The animation has 60 Frames and runs @30FPS. The animation must be pre-buffered due the massive calculations done for every pixel, this takes approximately 5 minutes (get a coffee ).
 
Here are the equations I used in the final version (don't change anythin in the script, except you want to redo all the math):
 
Tree trunks: 
 
Light leaves: 
 
Dark leaves: 
 
Ground: 
 
Water: 
 
The Sun: 
 
Movement of the Sun: 
 
Calculation of the RGB values: 
 
 
If you really can't wait 5 minutes for the animation to calculate, here is a GIF (rendered with GDI+):
 

Have fun 

LandScape.au3

Edited January 3, 2014 by minx

[coffeeturtle]

Thank you, minx for this excellent example!

Very well done!

This could also be a good teaching tool and inspire interest in higher mathematics!

[DatMCEyeBall]

I'm more interested in the script you used to render the .gif.

[minxomat]

A bit more math. (Well, not too complicated math). The color of the sun and the sky are now calculated, too. As well as the effect of the redness of the sun on the whole scene. I attached the script. (I can add the formulas if anyone is interested).

landscape.au3

[Lakes]

Heh, the gif animation reminded me of this.

[DatMCEyeBall]

I re-wrote the frame drawing code (the "heavy" math path) in C++ and compiled it to .dll -- attached below, source included.

It takes about 10 seconds to render all the frames.

It kinda tells you how slow the AutoIt interpreter is.

Could you post the code you used to render the .gif file?

Landscape .dll ver.7z

Edited January 23, 2014 by DatMCEyeBall

[DatMCEyeBall]

Updated the script above using static linking (you don't need the Visual C++ Redist) and with the "_xp" tools (can run on win XP(for all you old people))

Edited January 23, 2014 by DatMCEyeBall