Horizontal displacement

Recently I've been working on the code that computes fractal data - a bit of reorganization to be able to have more independent fractal channels that are used everywhere in the engine, as I was running short of them already. Previously we had one channel where the terrain elevation fractal was computed, another channel with low-pass filtered terrain slope and 2 independent fractal channels. After the redesign we have 4 independent fractal channels, but additionally the filtered slope is computed independently for u,v terrain directions.

The two-dimensional slope values allow for better horizontal displacement effect on the generated terrain, because now it's possible to make the rock bulge from the hill slope in the right direction. In the previous version only the absolute slope value was known, and the fractals extruded the mesh independently in two orthogonal directions, and of course that did not always look good.

The equation for the displacement was in addition parametrized, to be able to get more effects out of it. Currently it's possible to vary the dominant wavelength, bias and amplitude of the used fractal.

Here is a quick comparison of what the parameters do.

Bias +0.5 (bulging outwards from the slope), wavelength 19m


Wavelength 38m


Wavelength 76m



In the last screenshot the fractal used for the displacement is already only slightly visible and the bulbous shape of purely slope-dependent displacement shows up.
Here's how the displacement looks like when the bias is even larger, i.e. when the sloped parts are pushed even more outwards (bias +1.5):


It's also possible to use a negative bias values, that make the sloped parts carved into the hill (bias -1.0):



On the other hand, amplitude boost can emphasize the effect of the fractal, creating more visible overhangs here and there:


For comparison, here's how the same terrain looks like without any horizontal fractal effect at all:


... and without the vertical fractal, only a bicubic subdivision of original 76m terrain grid:



Next thing to try could be using a texture containing rough shape of specific type of erosion one would like to achieve. Current technique still cannot generate proper cliff and canyon walls, but combining it with the shape map lookup should theoretically do the job.

There's also an interactive comparison

Horizontal displacement

As always I do not keep strictly to the plan, and decided to try one of things I wanted to do someday - horizontal displacement of terrain.

The fractal map computed for quadtree node already contains 3 independent fractal noise channels. The first one computes elevation and is seeded from heightmap data. Other two are used for detail material mixing and other things. There is also a fourth channel containing global slope.
I modified the shader that computes vertex positions to displace also in horizontal directions, using one of the two independent fractal channels. Amount of displacement also varies with global slope - areas in flat regions are shifted minimally, but sloped parts that are also treated as rock are displaced a lot. This makes rocky parts much more interesting. For the record, the actual equation used for displacing point on a sphere in tangent space is this:



Next thing that had to be done was to compute the normals of such deformed surface. Article in GPU Gems about deformers provides nice info about Jacobian matrix that can be used for the job. After some pounding to my math circuits I managed to produce the following Jacobian of the above equation (in tangent space):



Normal is then computed as cross product between the second and third column, since the tangent and binormal are {0,1,0} and {0,0,1} respectively.

Finally, here is the result - left side original with only the vertical displacement, on the right side vertical&horizontal displacement:



There are still some issues but the overall effect is quite nice. Of course, collisions with sloped parts are no longer accurate and I'll have to do something with it later.

Outerra planetary engine