So if we integrate it in
ignoring both the visibility and the fresnel terms we should use
?Far Cry 3 seems to be using (n+2)/2Pi (slide 43) which is incorrect? And the same goes for this topic.
Or am I missing something?
Physically Based Blinn Phong questions
Author
According to RTR3 and this article (n+8)/8Pi is the energy conservation term for Blinn-Phong.
So if we integrate it in
ignoring both the visibility and the fresnel terms we should use ?
Far Cry 3 seems to be using (n+2)/2Pi (slide 43) which is incorrect? And the same goes for this topic.
Or am I missing something?
So if we integrate it in
ignoring both the visibility and the fresnel terms we should use
?Far Cry 3 seems to be using (n+2)/2Pi (slide 43) which is incorrect? And the same goes for this topic.
Or am I missing something?
You have to distiguish between normalizing a BRDF and normalizing a microfacet distribution. (And between Phong and Blinn-Phong). This is a relatively nice online resource on the topic:
http://www.thetenthplanet.de/archives/255
(n+2)/(2*pi) is for the modified Phong BRDF (i.e. the BRDF without the cosine in the denominator).
It is also correct for the Blinn-Phong MF-distribution.
(n+8)/(8*pi) is an approximation commonly used for the modified Blinn-Phong BRDF. As far as I remember, it is slightly too large, but in most cases where this BRDF is used it doesn't really matter.
Author
Thanks! That link explained it.
Related questions:
Should I remove the Pi in every light source? Or just in point lights?
And the Lambert normalization factor is cdiff/Pi, should the Pi also be removed?
Related questions:
Should I remove the Pi in every light source? Or just in point lights?
And the Lambert normalization factor is cdiff/Pi, should the Pi also be removed?
Thanks! That link explained it.
Related questions:
Should I remove the Pi in every light source? Or just in point lights?
And the Lambert normalization factor is cdiff/Pi, should the Pi also be removed?
The factor of 1/pi is independent of the light source. If you integrate the Lambertian cosine term over the hemisphere of incoming directions, you get:
[eqn]\displaystyle \int_\Omega | \omega \cdot \mathbf{n} | ~ \text{d} \omega = \int_0^{2 \pi} \int_0^{\frac{\pi}{2}} \sin{\theta} \cos{\theta} ~ \text{d} \theta ~ \text{d} \phi = \pi[/eqn]
So to make sure your BRDF is normalized, you need to divide by pi. In realtime rendering this division is often precomputed into the light intensity values themselves, as you achieve essentially the same result by doing that (it should be clear by looking at the rendering equation).
Author
From macnihilist link:
The RDFs and NDFs necessarily containSo Pi or no Pi?, as the result of an integration over parts of a sphere. In the shader code however,
Consider a point light source modeled as a small and very far away sphere, at distance. Let this sphere have radius
and a homogeneous emissive surface of radiance
. From the point of view of the receiving surface, the solid angle subtended by this sphere is a spherical cap, and so the irradiance integrates to
. So there you have
The way I see it, the derivation in the link is a special case for a small circular area light. Small means small enough (as seen from the surface) that you can assume the fr*cos term is constant over the projected area and take it out of the integral. For this case it's correct, but I'm pretty sure you cannot generalize this to arbitrary lights.
But, as Bacterius said, for _direct_ illumination from delta lights, you can always pull the pi into the light's intensity. Example:
Consider a point light 1 unit above a surface normal to the light. Let's say the light causes an irradiance of E=1 at the surface point closest to the light. For a diffuse BRDF we get for every direction
L_o(wo) = fr*E.
Case 1: With fr = 1 we get L_o = 1 for every direction. The radiant exitance (Lo*cos integrated over hemisphere) is M = pi. So we have M>E which means we reflect more than came in.
Case 2: With fr = 1/pi we get exactly M=E, which is correct.
Of course, in case 1 you can always say "My light source was really causing E=1*pi and my BRDF was really 1/pi". You'll get the exact same image (if only direct illumination from this point light is considered), but you safe a division by pi.
Bottom line:
In my opinion, the pi should always be there. But if you're only doing direct illumination from delta lights and every multiplication counts, you can pull the pi into the light sources. But that's only my personal opinion, so you should take it with a pinch of salt.
EDIT: Of course, if you decide to "pull pi into the light source", you have to multiply _every_ BRDF by pi. (And every BRDF component, e.g. if you only remove pi in the diffuse term, you'll obviously shift the balance between diffuse and glossy.)
But, as Bacterius said, for _direct_ illumination from delta lights, you can always pull the pi into the light's intensity. Example:
Consider a point light 1 unit above a surface normal to the light. Let's say the light causes an irradiance of E=1 at the surface point closest to the light. For a diffuse BRDF we get for every direction
L_o(wo) = fr*E.
Case 1: With fr = 1 we get L_o = 1 for every direction. The radiant exitance (Lo*cos integrated over hemisphere) is M = pi. So we have M>E which means we reflect more than came in.
Case 2: With fr = 1/pi we get exactly M=E, which is correct.
Of course, in case 1 you can always say "My light source was really causing E=1*pi and my BRDF was really 1/pi". You'll get the exact same image (if only direct illumination from this point light is considered), but you safe a division by pi.
Bottom line:
In my opinion, the pi should always be there. But if you're only doing direct illumination from delta lights and every multiplication counts, you can pull the pi into the light sources. But that's only my personal opinion, so you should take it with a pinch of salt.
EDIT: Of course, if you decide to "pull pi into the light source", you have to multiply _every_ BRDF by pi. (And every BRDF component, e.g. if you only remove pi in the diffuse term, you'll obviously shift the balance between diffuse and glossy.)
For diffuse alone the pi factor isn't really that important. Like others have mentioned you can consider it to be "baked" into the light intensity and so the difference is mostly arbitrary. What's it's actually important for is balancing your diffuse with your specular, which is what machnilist mentioned above. If you don't properly account for the 1/pi you can easily end up with diffuse that's too bright, and your materials won't look right.
Author
Thanks for all answers! So the most important thing is consistency, either both diffuse and specular BRDF have the pi factor or neither.
I did a little more research, and found the calculations that eliminate the Pi factor and an explanation in SIGGRAPH 2012 PBR Course notes (page 21).
Especially if you're doing tone-mapping, a constant intensity difference everywhere will probably make little to no difference to the final render.
Of course, in case 1 you can always say "My light source was really causing E=1*pi and my BRDF was really 1/pi". You'll get the exact same image (if only direct illumination from this point light is considered), but you safe a division by pi.
I haven't understood which part should be divided by pi if the light is not implicitly causing pi*1 light.
Should it be:
((diffuse / pi) + (f_microfacet)) * light_energy
or
(diffuse + f_microfacet) * (light_energy / pi)This topic is closed to new replies.
Advertisement
Popular Topics
Advertisement
