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Clouding the Issue

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Taking a break from hills and valleys, I thought I would have a go at adding some clouds to the otherwise featureless sky around my planets. There are various methods employed by people to simulate, model and render clouds depending on their requirements, some are real-time and some are currently too slow and thus used in off-line rendering - take a look at the Links section for a couple of references to solutions I have found out on the net.

Although I would like to add support for volumetric clouds at some point (probably using lit cloud particle sprites of some sort) to get things underway I thought a single background layer of cloud would be a good starting point. Keeping to my ethos, I do of course want to generate this entirely procedurally if at all possible and as with so many other procedural effects a bit of noise is a good starting point.

In this case while I get the mapping and rendering of the cloud layer working I've opted to use a simple fBm function (Fractional Brownian Motion) that combines various octaves of noise at differing frequencies and amplitudes to produce quite a nice cloudy type effect. It's not convincing on it's own and will need some more work later but for now it will do.

Now the fBm function can be evaluated in 3D which is great but of course to render it on the geodesic sphere that makes up my atmosphere geometry I need to map it somehow into 2D texture space - I could use a full 3D texture here which would make it simple but would also consume a vast amount of texture memory most of which would be wasted on interior/exterior points so I've decided not to do that. I could also evaluate the fBm function directly in the shader but as I want to add more complex features to it I want to keep it offline.

The simplest way to map the surface of a sphere into 2D is to use polar co-ordinates where 'u' is essentially the angle 'around' the sphere and 'v' the elevation up or down. This is simple to calculate but produces a very uneven mapping of texture space as the texels are squeezed more and more towards the poles producing massive warping of the texture data.

The two images here show my basic fBm cloud texture and that same texture mapped onto the atmosphere using simple polar co-ordinates.

(ignore the errant line of pixels across the planet - this is caused by an error of some sort in the shader that I couldn't see on inspection and I didn't want to spend time on it if the technique was going to be replaced anyway)

The distortion caused by the polar mapping is very obvious when applied to the cloud texture with significant streaking and squashing evident eminating from the pole - obviously far from ideal.

One way to improve the situation is the apply the inverse distortion to the texture when you are generating it, in this case treating texture generation as a 3D problem rather than a 2D one by mapping each texel in the cloud texture onto where it would be on the sphere after polar mapping and evaluating the fBm function from that point. As can be seen in the images below this produces a cloud texture that gets progressively more warped towards the regions that will ultimately be mapped to the poles so it looks wrong when viewed in 2D as a bitmap, but should produce better results when mapped onto the sphere:

As you can see in the planetary image, the streaking and warping is much reduced using this technique and the cloud effect is almost usable but if you look closely you will see that there is still an artifact around the pole albeit a much smaller one - it would be significantly larger when viewed from the planet's surface however so is still not acceptable. One way to 'cheat' around this problem is to simply ensure that cloud cover at the pole is always 100% cloud or 100% clear sky to hide the artifact and some released space based games that don't require you to get very close to the planets do this very effectively, but in a world of infinite planets it's a big restriction that I don't want to have to live with.

Another downside of polar mapping is that the non-uniform nature of the texel distribution means that many of the texels on the cloud texture aren't really contributing anything to the image depending on how close to the pole they are which is a waste of valuable texture memory.

So if polar mapping is out what are we left with? Well next I thought it was time to drop it altogether and move on to cubic mapping, a technique usually employed for reflection/environment mapping or directional ambient illumination. With this technique we generate not one cloud texture but six each representing one side of a virtual cube centred around our planet. With this setup when shading a pixel the normal of the atmospheric sphere is intersected with the cube and the texel from that point used. The benefit of cube mapping is that there is no discontinuity around the poles so it should be possible to get a pretty even mapping of texels all around the planet, making better use of texture storage and providing a more uniform texel density on screen amongst other things.

So ubiquitous is cube mapping that graphics hardware even provides a texture sampler type especially for this so we don't even need to do any fancy calculations in the pixel shader, we simply sample the texture using the normal directly which is great for efficiency. The only downside is that now we are storing six textures instead of one the memory use does go up, so I've dropped the texture size from 1024x1024 to 512x512 but as each texture is only mapped onto 1/6th of the surface of the sphere the overally texel density actually increases and the more effective use of texels means the 50% increase in memory usage is worthwhile.

The two images below show how one face of the texture cube and the planet now looks with this texture cube applied:

Again it's different but the edges of the cube are pretty clear and ruin the whole effect, so as a final adjustment we again need to apply the inverse of the distortion effect implied by moving from a cube to a sphere and map the co-ordinates of the points on our texture cube onto the sphere prior to evaluating fBm:

Finally we have a nice smooth and continuous mapping of the cloud texture over our sphere. Result! To show how effective even a simple cloud effect like this can be in adding interest to a scene here is a view from the planet surface with and without the clouds:

There is obviously more to do but I reckon it's a decent start.

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That's pretty cool! :D Terrain engines are always neat to watch progress. I've wanted to get into graphical programming for a while, but textual/system/tool programming is just easier and more fun for me.

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