What about the specular or the mirror component?
Now of course in a real mirror, you all learned this in high school physics.
Right?
There's only a reflection at the perfect mirror angle.
Remember, angle in equals angle out?
I'm sure you learned that somewhere in your, in your physics class.
Well, so using our, our diagramming again, what this says is
that all the incident light is reflected only in a single direction.
Okay.
And I'm going to call that direction m for the mirror direction.
And here, we have v for the viewing direction.
Okay?
And so that light is only going to be visible when v equals m.
All right. So I have to be in the exact, so if I've got a point coming
from right here, I'm going to see it right there at that, that point.
And everywhere else, it's not reflecting.
Or I might see it at a different point, but
all the light is being reflected along the particular ray.
All right.
And so the BRDF is just a, what's called a double-delta function.
If I'm, if I'm thinking about this on my surface, right?
This angle down and the angle out has to be equal, but this is drawn difficult.
It's, it's in 2D.
Not only do they have to be sort of at the, the same tilt, but
they have to be in a plane.
Right? All over to this and this have to be in the same plane,
because if I were to rotate it this way, all right?
Then it would now be bouncing off in another direction and
so, that's why there's two angles.
This is the tilt angle and this is the rotation around angle that says,
basically one has to be pi opposite the other.
So we take this BRDF and we stick it into our radiance equation.
And what it says is that the radiance, essentially the brightness that
we're going to see out is the magnitude of the source intensity.
The row sub s is the specular reflection.
So for example, it might be a darkened glass that filters out some light, so
it still acts as a mirror.
But only reflects some percentage of it, that's what the row would do.
And then we have these two delta functions, okay?
And these delta functions say that basically the angle in terms of
the tilt has to be the same and also the rotation around have to be
exactly pie different that's what those two things say.
Now remember, the delta function is a function where if the argument is zero,
it's a one.
Otherwise, it's, it's zero and that's why it's written as a delta function.
So I want to abuse the notation just a little bit and I'm going to say,
well, I can also write this as saying that the radiance in this particular case,
same as before.
But now I'm using, I guess what I'm calling a vector delta function.
Right?
So what we said before is that I only see a reflection if
the viewing angle is exactly the mirror angle, right?
So essentially these two things would have to be the same, so
that I'm lined up in exactly the right spot.
Another way of writing that is that the half angle is the same as
the normal, right?
So another way of saying that is if the vector
that's exactly halfway between the sensor and
the light is the same as the normal, then you get a mirror reflection.
And that would be for a sort of a, you know, a single perfect point.
So that's the Mirror BRDF.