3d Hill generating algorithm?

Supposing you have a 3d box of cubes, with each cube having 3 indices: (x,y,z), and 1 additional attribute to specify if it represents land or air.

Let's say that we have a 3d array to represent this box of cubes, with each cube being an element in the 3d array.

The following array, for example, would represent a bowl shaped piece of land:

y=0:        
0 0 0 0 0     
0 0 0 0 0
1 1 1 1 1
1 1 1 1 1

y=1:
0 0 0 0 0
0 0 0 0 0
1 0 0 0 1
1 1 1 1 1

y=2:
0 0 0 0 0
0 0 0 0 0
1 0 0 0 1
1 1 1 1 1

y=3:
0 0 0 0 0  
0 0 0 0 0
1 1 1 1 1
1 1 1 1 1

What is an algorithm such that given a selection box it would generate hills with f frequency and with average h开发者_StackOverfloweight of h, with v average variation in height?

We can assume that the lowest level of the bonding box is the "baseline", or "sea-level".

function makeTrees(double frequency, int height, double variation)
{
    //return 3d array.
}

I'm writing a minecraft MCEdit filter plugin :P

Simplest way is to decompose the problem into three parts:

1. Write a routine to generate the cubes for a single hill of height h. Start off by making this a simple cone (play with apex angles till you find something that looks pleasing)

2. Generate a set of n heights between h-v and h+v, using the random number generator of your choice

3. Place n mountains randomly on your cube. It doesn't matter if they intersect - indeed, it will lead to a better-looking range.

However, I'd also suggest abandoning this approach, and simply generate a fractal terrain within your bounding cube, then discretize it. You can play with the paramaters to your fractal generator to bound the height and variance.

Assuming you would like sinusoidal hills of frequency f (or rather, wavenumber f, since "frequency" is usually used for temporal quantities) as a function of radius r = sqrt(x^2+y^2) from the center:

Define a threshold function like this:

Any element (x,y,z) with z < z_m will be land, and the rest will be air.