====== Peak roughening ======
One method of making heightfields is to 'deposit' onto a flat heightfield a large number of geometric shapes like cones, pyramids or hemispheres. Prime examples of terrain made by this technique are shown on [[http://www.robot-frog.com/3d/hills/index.html|www.robot-frog.com]] (Bob Nystrom), using hemispheric peaks, and [[http://www.lighthouse3d.com/opengl/terrain/index.php3?circles|www.lighthouse3d.com]] (António Ramires Fernandes), using sinusoidal peaks.
The task of making the approximate land-shape in L3DT is handled by the [[l3dt:algorithms:hf:design_inflate|design/inflate]] routine, but peak overlays are added to make rolling hills on a scale smaller than a design-map pixel (64×64 heightfield pixels). The shape of the peaks used approximates a [[wp>Gaussian_curve|Gaussian curve]] (as of L3DT 2.2), but with a finite skirt, and is shown in the figure below (green curve labelled 'f(cos(x))*exp(x)').
| {{l3dt:algorithms:hf:peakrough:peakplot.gif}} |
^ Profile of several peak overlay functions ^
The mathematical form of the curve is:
y = er-1 × (1 - cos(πr)) ⁄ 2
where the radius //r// = 0..1.
The red curve is the cosine-based peak shape used previously in L3DT, with the mathematical form:
y = (1 - cos(πr)) ⁄ 2
These peaks made the map look a bit too lumpy.
The extra calculation time for making such mathematically complex these peaks is negligible because L3DT only generates 6 or so peak overlays (with different radii) and applies them many many times with random vertical scaling. The peaks are applied early in the inflation/overlay algorithm when the heightfield is at 1/16th final map resolution (or 1/256th final map area). The upshot is that the routine is pretty quick.
All these peaks are radially symmetric. I have tinkered with asymmetric peaks, but I found the computation penalty in generating and rotating such overlays to be quite unreasonable.