POV-Ray : Newsgroups : povray.off-topic : Differential equations FTW! : Re: Differential equations FTW! Server Time
11 Oct 2024 01:22:05 EDT (-0400)
  Re: Differential equations FTW!  
From: Invisible
Date: 8 Jan 2008 10:06:55
Message: <4783918f$1@news.povray.org>
scott wrote:
>>>> Does anybody know how either of these simulations actually work?
>>>
>>> I suspect they solve the differential equations in question :-D
>>
>> No... really? :-P
> 
> Really.
> 
> The wave tank one is easy, for every "pixel" it simply solves the wave 
> equation.
> 
> http://en.wikipedia.org/wiki/Wave_equation
> 
> It may look scary if you don't recognise the symbols, but the maths is 
> actually quite trivial.  All the wave equation says is that the 2nd 
> derivative wrt to time (ie acceleration) of the value of each pixel is 
> proportional to the 2nd derivative of the value wrt to distance summed 
> over every axis.
> 
> It's easy to code, you can just take the difference between neighbouring 
> pixel values twice to work out the 2nd derivative in the x and y 
> direction and hence the acceleration.  Then the acceleration can be used 
> to work out the velocity and new value using Euler integration.

So... acceleration = surface curvature?

How does that change when you have things like walls? Do you have to do 
anything special at those edges?

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


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