Veach thesis  formula question
Re: Veach thesis  formula question
Thanks a lot for your answer,
So, I have redo the same but taking care of X(o)...X(n) and here is what I got : You see, in the last equation, there is a p_t(Xj) in the denominator and the nominator, they cancel ! Or they are not the same ?
Something else, in the equation (3.3) you use L_i(X_i), then even in your recursive MIS computation you need to keep track of each vertex position, normal etc... to compute each L_i(X_i)... so, you're still limited with the path length ?
Thx
So, I have redo the same but taking care of X(o)...X(n) and here is what I got : You see, in the last equation, there is a p_t(Xj) in the denominator and the nominator, they cancel ! Or they are not the same ?
Something else, in the equation (3.3) you use L_i(X_i), then even in your recursive MIS computation you need to keep track of each vertex position, normal etc... to compute each L_i(X_i)... so, you're still limited with the path length ?
Thx
Re: Veach thesis  formula question
I have just discover that Anthony Pajot also has this formulation in his thesis, page 47 http://www.irit.fr/~Anthony.Pajot/publi ... erIrit.pdf.
But so, why not directly computing thus formulation ?
But so, why not directly computing thus formulation ?
Re: Veach thesis  formula question
Yes, for the balance heuristic they do cancel. However in the power heuristic they do not cancel out. Also, sometimes it is acceptable (and convenient) to use approximations of the probabilities for computing MIS weights, in which case they no longer cancel. For example, for practical Russian roulette schemes it is often somewhat cumbersome to compute the correct reverse Russian roulette probabilities. Instead you could use a simpler approximation for the Russian roulette probability (or ignore it altogether) for the MIS weights. Although using approximations can compromise the theoretical optimality of your MIS weights, this may be acceptable for the sake of convenience.
Re: Veach thesis  formula question
Thanks, I see... interestingDietger wrote:Yes, for the balance heuristic they do cancel. However in the power heuristic they do not cancel out. Also, sometimes it is acceptable (and convenient) to use approximations of the probabilities for computing MIS weights, in which case they no longer cancel. For example, for practical Russian roulette schemes it is often somewhat cumbersome to compute the correct reverse Russian roulette probabilities. Instead you could use a simpler approximation for the Russian roulette probability (or ignore it altogether) for the MIS weights. Although using approximations can compromise the theoretical optimality of your MIS weights, this may be acceptable for the sake of convenience.
And about the following question http://igad2.nhtv.nl/ompf2/viewtopic.ph ... =526#p1531, do you have an advice ?
Thx
Re: Veach thesis  formula question
Hi,
Just another question, what to do in a BDPT when a lightray or cameraray hit a light ?
Should I :
1) If the previous vertex is not specular, I stop the ray
2) If the previous vertex is specular, I accumulate the light radiance
Should I do this for both camera and light path ?
Just another question, what to do in a BDPT when a lightray or cameraray hit a light ?
Should I :
1) If the previous vertex is not specular, I stop the ray
2) If the previous vertex is specular, I accumulate the light radiance
Should I do this for both camera and light path ?
Re: Veach thesis  formula question
These are just yet other sampling strategies, so you should just mix them with the all the others bidirectional strategies using MIS. If an eye path hits a light source, you should accumulate the MIS corrected radiance, weather the last vertex was specular or not (this is already accounted for by MIS). The same is true for light paths hitting the camera, although most people just ignore this strategy for simplicity, as its contribution is usually low. The probability of randomly hitting the image plane is infinitely small for pinhole camera's and close to zero for finite aperture lenses except for regions with massive DOF.

 Posts: 12
 Joined: Mon May 07, 2012 3:28 am
Re: Veach thesis  formula question
Quick question:
I was writing out and simplifying the path integral formula and noticed an extra cos term appearing near the sensor parts. Am I simplifying something incorrectly? I've always seen eye path throughputs start at 1.
For example, for a EDL path with 1 light vertex, we have (all pdfs are in solid angle, geometrylike terms in [...])
We * W(a>b) * [cos(a_wi) * cos(b_wo) / ab^2] * f(a>b>c) * [cos(b_wi) * cos(c_wo) / bc^2] * Le
divided by
P(We) * P(Wa>b) * [cos(b_wo) / ab^2] * P(C)
becomes
We/P(We) * W(a>b)/P(Wa>b) * cos(a_wi) * f(a>b>c) * [cos(b_wi) * cos(c_wo) / bc^2] * Le/P(C)
And for a pinhole camera, We*W(a>b)/(P(We)*P(Wa>b)) = 1 (is this incorrect?) so we get
cos(a_wi) * f(a>b>c) * [cos(b_wi) * cos(c_wo) / bc^2] * Le/P(C)
Why is there an extra cos(a_wi) in there?
We*W(a>b)/(P(We)*P(Wa>b)) = 1 comes from https://sites.google.com/site/qmcrender ... edirects=0
I was writing out and simplifying the path integral formula and noticed an extra cos term appearing near the sensor parts. Am I simplifying something incorrectly? I've always seen eye path throughputs start at 1.
For example, for a EDL path with 1 light vertex, we have (all pdfs are in solid angle, geometrylike terms in [...])
We * W(a>b) * [cos(a_wi) * cos(b_wo) / ab^2] * f(a>b>c) * [cos(b_wi) * cos(c_wo) / bc^2] * Le
divided by
P(We) * P(Wa>b) * [cos(b_wo) / ab^2] * P(C)
becomes
We/P(We) * W(a>b)/P(Wa>b) * cos(a_wi) * f(a>b>c) * [cos(b_wi) * cos(c_wo) / bc^2] * Le/P(C)
And for a pinhole camera, We*W(a>b)/(P(We)*P(Wa>b)) = 1 (is this incorrect?) so we get
cos(a_wi) * f(a>b>c) * [cos(b_wi) * cos(c_wo) / bc^2] * Le/P(C)
Why is there an extra cos(a_wi) in there?
We*W(a>b)/(P(We)*P(Wa>b)) = 1 comes from https://sites.google.com/site/qmcrender ... edirects=0