Hollowed out 3D fractal cave

[twinbee]

Here's a (new?) idea for a 'fractal'. Imagine creating a 3D dimensional equivalent to the Diamond-Square Algorithm used for random 2D terrain.

Then go inside. Unfortunately, it's solid inside, since each voxel (mini-cube) represents a colour rather than that voxel existing.

However, then one can hollow out the inside by removing every voxel whose value/colour is below or above a certain threshold.

I wonder what such '3D caves' would look like.

Also cool, would be to chip away at the inside a little bit after hollowing (i.e. similar to what I said in this thread). This way, each voxel would have a different shade, and it could create some extremely interesting and beautiful coloured caves.

[cKleinhuis]

ok, here is the 1d version:
http://en.wikipedia.org/wiki/Midpoint_displacement_algorithm

hmm, never thought about that, you want to create sort of bubbles inside ?

hmmm, i will go on a train trip now, and when watching out of the window i will think about it
greets
 

[twinbee]

Wow, I bet that'd look cool too. Though I was thinking more of random terrain as demonstrated here (I'm guessing the Blancmange curve is a special case of the Midpoint Displacement algorithm).

You've got me mouth-watering for both now though. 

[cKleinhuis]

i know that terrain generation lacks the feature of caves in the terrain, because it is just like the name sais, a heightmap,
hehe, i have not thought about ths yet, will come back later

cheers
 

[twinbee]

Hehe, I'm a little worried about the CPU usage for this one . I imagine rendering billions of cubes is not any processor's idea of a fun day out.

Not sure if the 3D random cave could be expressed more mathematically, rather than an algorithmic "divide, redivide" type routine. I'm guessing not.

[cKleinhuis]

<a href="http://www.prollcoder.com/flash/midpointdisplacementtest.swf" target="_blank">http://www.prollcoder.com/flash/midpointdisplacementtest.swf</a>

ok, i made a test for the 1d version, this generates a heightmap line, and additionally to the vertical displacement i simply add a horizontal displacement ...
and i came to the following method ....

first, the 1d version simply extends to 2d version, but i will talk only about the 1d version here

the midpoint displacement algorithm is good for generating heightmaps, it is not good for creating caves in those heightmaps, simply because a heightmap does
not feature this

my idea would be to set the displacement direction to the normal at that point
and i have just implemented this idea in another flash example, now true caves are generated, but some problems occur because of intersection of line segments ...
<a href="http://www.prollcoder.com/flash/midpointdisplacement_normal.swf" target="_blank">http://www.prollcoder.com/flash/midpointdisplacement_normal.swf</a>

the above algorithm could be extended to a 2d plane, producing a 3d object .... but it would be hard for game programmers to maintain a the players position within that thing ...

currently the algorithm works like this:

1.take a line segment
2.determine the mid point
3.determine the normal
4.determine the distance between the points
5.move the point in the normal direction by a random factor ( 0..1 ) multiplied by the halve distance between the original points
6. repeat with the new line segments until max iteration is reached

and when i am thinking about step 5, it could be improved that it does not use the halve distance between the original points, but that it uses the halve x distance of the points ...
wait, i will go and try this out, to avoid overlapping ...

just a moment ... oh, no, using only the halve x distance leads to quadratic results

ok, thats it for now with me ...

[twinbee]

Love your applet - it certainly produces some good cliffs and cave-like structures. I wonder if the 2D Worms game uses a similar technique to get the pattern. Why can't mountain rendering programs use something like this. Landscapes would look a LOT more interesting.

I still reckon it's possible to extend the "Diamond-Square Algorithm" to 3 dimensions, and get an enclosed 3D cave though.

Here's the 2D version, and what happens when I hollow this one out:

[cKleinhuis]

thx  i am working right now on a little overlap avoiding method

yes, this one is fine perlin noise/turbulence, you could use that as 3d value field and make an iso surface countour this is also a good way for generating 3d objects

[Sockratease]

I have peeked inside 3D Fractals made in Chaos Pro.

Found some Amazing Things in there, too!



Who knew such Beauty resided in there?

The animation seems to play a bit too fast now that I have a better computer.  It was different before I upgraded...

But the point is that 3D Models made in Chaos Pro are hollow and easily viewed "from the inside" just by zooming in to it.

It's not the landscapes you mentioned, but fun.  I'll see about making a view of just the interior, without the Special Bonus Surprise inside.  I just had that image on hand (made it a while ago).

[GFWorld]

Sockratease wrote >Found some Amazing Things in there, too!

:-)))
Margit

[twinbee]

Lol, who would have thought that the Special Bonus Surprise of Lisa's face would be hiding inside? 

Look forward to seeing the results of our inferior creation from the proposed 3D-erized diamond square alg.