### Confused about near-specular reflection that is not energy conserving.

Posted:

**Fri Dec 02, 2016 2:10 pm**Hello,

I've been puzzled by a lighting problem that is giving non-intuitive results. I'm sure the answer must be very simple because this is really basic stuff.

Consider a ground plane with a near-specular brdf. The brdf is going to return extremely high values close to the mirror direction that drop off to zero quickly away from that direction. In the limit, a specular mirror would have a delta distribution with a single infinite value along the mirror direction and zero everywhere else.

Consider also a point light above the ground with an intenty Li. The reflected radiance Lr on a point x, on the ground, is:

Lr(wo) = brdf(wi,wo)*Li/r^2, where r is the distance from x to the point light and wi points towards the light.

Now, if the incoming direction wi is nearly aligned with the mirror direction, the brdf term will be huge and we have Lr > Li, which is not energy-conserving. How can this be?

The only thing I can think of is that point lights are not real physical lights, whereas a near-specular brdf is physically correct. The two solutions to the problem would then either be:

1- Give the point light a small radius and treat it as a spherical light.

2- If I insist on using the point light, I need to normalise the brdf to make sure it is always less than white.

I've been puzzled by a lighting problem that is giving non-intuitive results. I'm sure the answer must be very simple because this is really basic stuff.

Consider a ground plane with a near-specular brdf. The brdf is going to return extremely high values close to the mirror direction that drop off to zero quickly away from that direction. In the limit, a specular mirror would have a delta distribution with a single infinite value along the mirror direction and zero everywhere else.

Consider also a point light above the ground with an intenty Li. The reflected radiance Lr on a point x, on the ground, is:

Lr(wo) = brdf(wi,wo)*Li/r^2, where r is the distance from x to the point light and wi points towards the light.

Now, if the incoming direction wi is nearly aligned with the mirror direction, the brdf term will be huge and we have Lr > Li, which is not energy-conserving. How can this be?

The only thing I can think of is that point lights are not real physical lights, whereas a near-specular brdf is physically correct. The two solutions to the problem would then either be:

1- Give the point light a small radius and treat it as a spherical light.

2- If I insist on using the point light, I need to normalise the brdf to make sure it is always less than white.