GPU Pro 6

282 III Lighting

f

0

f

1

f

2

z

x

y

Figure 5.14. Layered heightfields for the x axis.

These heightfields define the split between neighboring cells. They produce a

collection of cells that can be indexed using three integers (i, j, k), where 0 ≤ i ≤

n

x

,0≤ j ≤ n

y

,and0≤ k ≤ n

z

. The resulting arrangement of cells are like a

distortion of an n

x

× n

y

× n

z

array of voxels.

The region covered by the cell (i, j, k) occupies the set of points (f

i

(y, z),

g

j

(x, z),h

k

(x, y)) where x ∈ (i, i +1),y ∈ (j, j +1),andz ∈ (k, k +1).

Defining the distortion in this way does not allow arbitrary distortions to be

represented. For instance, a twist distortion (like the “twirl” distortion