So welcome for our computer graphics lecture.

We are right now speaking about integration techniques

for the rendering equation.

And we are still looking at the more simplified case

that we have the following set up.

We are looking with our camera or with our virtual eye

at a particular point in the scene.

And now we want to compute how much light at this point

is received from other objects and reflected towards the eye.

And we described that using an integral that I showed you.

And there's one particular case that is quite interesting.

And that's the relation with distribution ray tracing.

So the idea of distribution ray tracing, in that case,

if we assume that there's a pretty glossy surface,

we cast a number of rays that are slightly

scattered around the main reflection direction

and just average the incident light.

And in fact, we built the bridge to bring this together

with our rendering equations so that we have here

a simple formula that describes if this surface here is

a fong surface, a surface with fong material properties,

how do we have to distribute these rays so that

for distribution ray tracing, we get the precise result.

So this can all be derived.

It's a wonderful formalism.

And with some knowledge in computing with probabilities

and so on, that comes all together.

So now just to give you an idea what

are interesting topics that people are looking into now.

So let's look at the following case.

It's essentially the same case that we had before.

We have this point we are interested in.

We have a light source.

And I showed you that we have two different possibilities

to compute the illumination in that case now.

The first one is that we integrate over the hemisphere

to get the illumination at that point.

We can integrate over the hemisphere,

gather the incident light, and then compute the reflection.

And if we only have that light source,

that means essentially we cast rays over the hemisphere.

And we count how many of these hit the light source.

And this tells us how bright the illumination down here is.

And we have to wait with a BRDF.

But we have an integral here over the hemisphere.

Now I also showed you that we can change this integration

and that we can instead integrate over the area light

source.

This means our integral over the hemisphere

now becomes an integral over this light source.