CMSC 425 : Lecture 12 Procedural Generation : 2 D Perlin Noise

Let’s investigate the finer points. First, let us begin by assuming that we have an n×n grid of unit squares (see Fig. 1(a)), for a relatively small number n (e.g., n might range from 2 to 10). For each vertex [i, j] of this grid, where 0 ≤ i, j ≤ n, let us generate a random scalar value z[i,j]. (Note that these values are actually not very important. In Perlin’s implementation of the noise function, these value are all set to 0, and it still produces a remarkably rich looking noise function.) As in the 1-dimensional case, it is convenient to have the values wrap around, which we can achieve by setting z[i,n] = z[i,0] and z[n,j] = z[0,j] for all i and j. Given any point (x, y), where 0 ≤ x, y < n, the corner points of the square containing this point are (x0, y0), (x1, y0), (x1, y1), (x0, y1) where: