Derivative Mapping

I've been somewhat unhappy with the lighting on my terrain for a while now especially the way much of the time it looks pretty flat and uninteresting.  It's using a simple directional light for the sun at the moment along with a secondary perpendicular fill light as a gross simulation of sky illumination plus a little bit of ambient to eliminate the pure blacks.  Normals are generated and stored on the terrain vertices but even where the landscape is pretty lumpy they vary too slowly to provide high frequency light and shade and with no shadowing solution currently implemented there's not much visual relief evident leading to the unsatisfying flatness of the shading.

While I plan to add shadowing eventually I don't want to open that can of worms quite yet so I had a look around for a simpler technique that would add visual interest.  I thought about adding normal mapping but the extra storage required for storing tangent and binormal information on the vertices put me off as my vertices are already fatter than I would like.  While looking in to this however I came across a blog post by Rory Driscoll from 2012 discussing Derivative Mapping, itself a follow up to Morten Mikkelsen's original work on GPU bump mappng.  This technique offers a similar effect to normal mapping but uses screen space derivatives as a basis for perturbing the surface normal using either the screen space derivatives calculated from a single channel height map texture or the pre-computed texture space derivatives of said height map stored as a two channel texture.

This was appealing to me not just because I hadn't used the technique before and was therefore interested just to try it out, but also from an implementation point of view I would not have to pre-compute or store anything on the vertices to define the tangent space required for normal mapping saving a considerable amount of memory given the density of my geometry.  It also solves the problem of defining said tangent space consistently across the surface of a sphere, a non-trivial task in itself.

Thanks to the quality of the posts mentioned above it was a relatively quick and easy task to drop this in to my terrain shader. I started with the heightfield based version as with the tools I had available creating a heightfield was easier than a derivative map but while it worked the blocky artifacts caused by the constant height derivatives where the heightmap texels were oversampled were very visible especially as the viewpoint moved closer to the ground.  I could have increased the frequency of mapping to reduce this but when working at planetary scales at some point they are always going to reappear.  To get round this I moved on to the second technique described where the height map derivatives are pre-calculated in texture space and given to the pixel shader as a two channel texture rather than a single channel heightmap.  The principle here is that interpolating the derivatives directly produces a higher quality result than interpolating heights then computing the derivative afterwards.  I had to write a little code to generate this derivative map as I didn't have a tool to hand that could do it but it's pretty straightforward.

Although this takes twice the storage and a little more work in the shader the results were far superior in my context with the blocky artifacts effectively removed and the effect under magnification far better.

A desert scene as it was before I started.  With the sun overhead there is very little relief visible on the surface

The same view with derivative mapping added.  The surface close to the viewpoint looks considerably more interesting and the higher frequency surface normal allows steeper slope textures to blend in

As you can see here the difference between the two versions is marked with the derivative mapped normals showing far more variation as you would expect.  The maps I am using look like this:

The tiling bump map I am using as my source heightfield

The derivative map produced from the heightfield.  The X derivatives are stored in the red channel and the Y in the green.

Here is another example this time in a lowlands region:

A lowlands scene before derivative mapping is applied

The same scene with derivative mapping.

Particularly evident here is the additional benefit of higher frequency normals where it is the derivative-mapped normal not the geometric one that is being used to decide between the level ground texture (grass, sand, snow etc.) and the steep slope texture (grey/brown rock) on a per-pixel basis.  This produces the more varied surface texturing visible in the derivative mapped version of the scene above.

Finally, here are a couple more examples, one a mountainous region the other a slightly more elevated perspective on a mixed terrain:

Mountain scene before derivative mapping

The same scene with the mapping applied, the mountain in the foreground shows a particularly visible effect 

A mixed terrain scene without mapping

The same scene with the derivative mapping applied.  The boundaries between the flat and steeply sloped surface textures in particular benefit here with the transitions being far smoother

To make it work around the planet a tri-planar mapping is used with the normal for each plane being computed then blended together exactly as for the diffuse texture.  For a relatively painless effect to implement I am very pleased with the result, the ease of use however is entirely down to the quality of the blog posts I referenced so definitely thanks go to Rory and Morten for that.