# The problem of 4-phase method

what parameters should be used when calculating the F matrix in the 4 phase method. My model is a blinds, I used the below parameters per Sarith Subramaniam’s tutorial :

`rfluxmtx -v -ff -ad 1000 -ab 4 -lw 0.001 -c 1000 -n 16 fports/F1.rad skyDomes/skyglow.rad -i octrees/roomFmtx.oct > matrices/dmtx/F1.dmx`

But the reviewer says the sampling rates used (according to the scripts in the appendix) for the F matrix are way too low to accurately capture the small geometry of the venetian blinds. And he also says this system should use three phase method, but I got similar accuracy with 3 phase and 4 phase method.

1. Should I ajust the -ad and -c until the results are convergency? Or is there any empirical parameters?
2. Should I change to three phase method?

It is difficult to say if your parameters are sufficient. Despite the fine details in the blinds system, it is a repetitive structure so many rays distributed over its area will tend to average correctly.

Especially for a publication or any critical application, it pays to do some convergence testing. You can gradually increase -ad and decrease -lw to see if this reduces run-to-run differences. Increasing the -c parameter may also be useful.

In the end, I tend to agree with the reviewer that the F-matrix method, which is generally used for studying alternate out-of-plane shading systems, is not needed for external venetian blinds. These are close enough to planar for the 3-phase method to work well, and having fewer matrix multiplications is generally preferred for simplicity and for accuracy.

Best,
-Greg

Hi @1112 , the numerical values of the parameters in all the scripts in the tutorial were deliberately kept low so that one could run (and understand the working of ) the simulations without expending too much computational effort.

In case you haven’t already referred these, @Taoning_Wang1 had done some work with the F-matrix related simulations a few years ago:

https://www.sciencedirect.com/science/article/am/pii/S0378778818302457

Regards,
Sarith

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Hi Greg,

After reviewing Taoning’s study, I found that the resolution of the F matrix can be increased by using the Tregenza subdivision, and the T matrix can be removed from the matrix multiplication. In other words, spatial accuracy can be improved by using the 4-phase method, which may enhance the accuracy of glare calculation. However, when using the 3-phase method, the Klem’s BSDF is limited to 145x145.

So, I would like to ask if it is possible to use the 4-phase method with a higher resolution F matrix instead of the 3-phase method.

For glare calculations that involve direct solar penetrating the window, especially when it might be in view of the occupant, you really must use either a full point-in-time ray-tracing solution (easiest) or the 5-phase method developed by @Andrew_McNeil .

If you are just trying to get better resolution on the sky patches, I believe you are talking about an F-matrix method that uses Christoph Reinhart’s extension to Tregenza sky patches, where you can reduce the size and increase the density of patches through further subdivision. If you apply rfluxmtx to compute the flux transfer matrix, which is just an alternative form of a BTDF, then you can use either Reinhart or Shirley-Chiu to adjust the matrix resolution to suit your needs. However, as noted above, this method will never be adequate for glare calculations involving direct sun in view.

Cheers,
-Greg

I also used the 6-phase method to calculate the glare metrics. Actually, I intend to compare the values calculated with the four-phase method to those calculated with the 6-phase method to see if the values derived from both methods are significantly different when considering the frequency data of different glare levels.

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Hi Yongqing,

getting back to this: " However, when using the 3-phase method, the Klem’s BSDF is limited to 145x145."

Also in the 3-PM you can use higher resolution if you want. The important thing is that your BSDF is a matrix that can be multiplied to the daylight and view matrices, but not a variable resolution tensor tree. For example you can calculate a high-resolution BSDF using rfluxmtx directly instead of the genBSDF tool. The dimensions need to match the DMX and VMX dimensions, and you can use rmtxop to multiply the matrices then.

Best,
David

Hi David,

Thank you!

I also read the code of `genBSDF.pl` and found that `genBSDF` is implemented by calling `rfluxmtx` and `wrapBSDF`. The `wrapBSDF` script divides the matrix generated by `rfluxmtx` by the solid angle of each patch and packages it into an XML file. Therefore, I wonder if I can interpret the F matrix as the BTDF multiplied by Ω, where Ω is the solid angle of each patch. The method used in Taoning’s study is essentially a three-phase method. Is the method using `rfluxmtx` to generate the high-resolution BSDF the same as calculating the F matrix, but with `h=scN` in the sender and receiver scene files?

Best,
Yongqing

Yes, I believe this is all correct. I have used similar methods in my test simulations and found it to improve accuracy when higher-resolution window matrices are taken straight from rfluxmtx. This is in fact why rfluxmtx was written, and genBSDF is an application of these matrix calculations to derive a BSDF.

Cheers,
-Greg

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