Re: [Algorithms] Tangential Curvature of terrain

[Klaus H. <k_h...@os...>]

Thanks, Joe :)

At some point I'll try everything I can get my hands on. I'll collect all
those mails, and will try other algorithms as soon as this terrain sample is
finished (do some improvements afterwards).
At the moment I have a solution that looks pretty cool. And guess what...
it's the solution that I thought would never work. I was wrong and the
results can look just beautiful, and it nicely breaks up the transition
between two ecosystem.

What I did is this:
For each data point Pm,n in the height field compute the
elevation-difference between Pm,n and its eight direct neighbors. Sum these
differences up and average them, by dividing the sum by 8. The result is a
single value R (for each data point).

I then modify the elevation line as follows:
elevLine' = elevLine + R * ecosystem.relEffect;

where elevLine' is the new elevation line, elevLine is the elevation line of
the ecosystem after elevation skewing (or before - shouldn't matter), and
relEffect is a scale factor which you can use to increase/decrease the
effect.

You would honestly be surprised by the results of this simple solution.
There are places in my terrain that look almost real, and I could further
enhance this by casting shadows.

...And I thought it wouldn't work.

Niki

----- Original Message -----
From: Joe Ante <jo...@ti...>
To: <gda...@li...>
Sent: Monday, August 21, 2000 3:19 PM
Subject: Re: [Algorithms] Tangential Curvature of terrain


> > Basically, the curvature of a function is its second derivative.
> I think geometrically viewn this is not the correct answer. Take as an
> simplyfied
> example: f(x) = x^2 f''(x) = 2
>
> Which meant that for every point the concavity/convexity is the same over
> the entire graph.
>
> What this concavity/convexity value actually specifies is how high a
heixel
> is in respect to the heixels in some distance around it. Maybe even in
> respect to all heightsamples in the heightmap.
>
> Consider for example an huge crater landscape and in the middle of this
> crater there is a small hill.
>
> The question now is, is the heixel on top of this small hill inside the
huge
> crater, more convex or concave?
>
>
> So what you want is that heixels that are near have more influence than
> heixels that are far away from the heixel, whose concavity/convexity you
> want to find out.
>
>
> So what you need to define is a function with a maximum distance, which
> gives you out a value between 0...1 when you give it a value from
> 0...maximumdistance.
> y = f (x)
> x e [0...maximumDistance]
> y e [0...1]
>
> A gauss-like curve is propably best suited:
> y = 360^-((x/maximumDistance)^5)
> (This function has worked out for me just fine.)
>
>
> Pseudocode:
>
> float ConcaveConvex (long inX, long inZ, float inMaxDistance)
> {
>     float itsHeight = GetHeight (inX, inZ);
>     float c = 0;
>
>     for (z=0;z<HowmanyHeixels;z++)
>     {
>         for (z=0;z<HowmanyHeixels;z++)
>         {
>             float difference = itsHeight - GetHeight (x, z);
>             float d = sqrt ((x-inX)*(x-inX) + (z-inZ)*(z-inZ));
>             c += difference  * GaussFunction (d, inMaxDistance);
>         }
>     }
>
>     c /= HowmanyHeixels* HowmanyHeixels;
>     return c;
> }
>
> float GaussFunction (float inX, float inMax)
> {
>     return powf (360.0F, -powf (inX / (inMax), 5.0F)
> }
>
> float GetHeight () should give back a height scaled to [0...1] in this
> context.
>
>
>
> There is plenty room for optimization here (tables, tables, tables)
> But even then it will be very slow. But it doesnt matter that much because
> you dont want to calculate the ecomap in realtime or as a preprocessing
> phase step anyways.
>
>
> Note that I havent integrated this into my terrain engine yet, I have only
> spent some thought on it, so I cant really guarentee that it works.
>
> bye joe
>
>
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