## (Almost) realtime GI

After my initial implementation of surfel based illumination I've extended it to do hierarchical clustering of surfels based on a similar idea to the one presented in GPU Gems 2.

A few differences:

I'm using a k-means clustering to build the approximation hierarchy bottom up. A couple of iterations of Lloyd's algorithm provides pretty good results. Really you could get away with one iteration.

To seed the clustering I'm simply selecting every n'th surfel from the source input. At first I thought I should be choosing a random spatial distribution but it turns out clustering based on regular intervals in the mesh works well. This is because you will end up with more detail in highly tesselated places, which is what you want (assuming your input has been cleaned).

For example, a two tri wall will be clustered into one larger surfel where as a highly tesselated sphere will be broken into more clusters.

The error metric I used to do the clustering is this:

Error = (1.0f + (1.0f-Dot(surfel.normal, cluster.normal)) * Length(surfel.pos-cluster.pos)

So it's a combination of how aligned the surfel and cluster are and how far away they are from each other. You can experiment with weighting each of those metrics individually but just summing seems to give good results.

When summing up the surfels to form your representative cluster surfel you want to:

a) sum the area

b) average the position, normal, emission and albedo weighted by area

Weighting by area is quite important and necessary for the emissive value or you'll basically be adding energy into the simulation.

Then you get to the traversal, Bunnel recommended skipping a sub-tree of surfels if the distance to the query point is > 4*radius of the cluster surfel. That gives results practically identical to the brute force algorithm and I think you can be more agressive without losing much quality at all.

I get between a 4-6x speed up using the hierarchy over brute force. Not quite realtime yet but I haven't optimised the tree structure at all, I'm also not running it on the GPU :)

It seems like every post I make here has to reference Christer Ericson somehow but I really recommend his book for ideas about optimising bounding volumes. Loads of good stuff in there that I have yet to implement.

Links:

Real-time Soft Shadows in Dynamic Scenes using Spherical Harmonic Exponentiation

Lightcuts: a scalable approach to illumination