Question

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 height 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 😛

Answer 1

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.