# multiply pi to calculate illuminance?

Hello:

I notice the almost all the published literature use the following equation
to show the three phase daylight coefficient method.

i = VTDs
where:
i = result vector (luminances, *illuminance*s, image, etc.)
V = view matrix, relating outgoing directions on window to desired results
at interior
T = transmission matrix, relating incident window directions to exiting
directions (BSD
D = daylight matrix, relating sky patches to incident directions on window
s = sky vector, assigning* luminance* values to patches representing sky
directions.

I am curious that if "i" means "illuminance", is that i = Pi*VTDs?

Thank you,

Jia

Hello Jia,

Good question. The "i" does derive from "illuminance," but can be used for luminance values or pretty much anything derived from a lighting calculation, including something like "sensor voltage" for an lighting control system. The "V" matrix includes the factor of pi (if necessary) and all other factors in the calculation of "i". Thus, the equation need not change depending on the values you choose to compute.

I hope that's clear enough.

Best,
-Greg

···

From: Jia Hu <[email protected]>
Date: November 21, 2011 10:23:36 PM PST

Hello:

I notice the almost all the published literature use the following equation to show the three phase daylight coefficient method.

i = VTDs
where:
i = result vector (luminances, illuminances, image, etc.)
V = view matrix, relating outgoing directions on window to desired results at interior
T = transmission matrix, relating incident window directions to exiting directions (BSD
D = daylight matrix, relating sky patches to incident directions on window
s = sky vector, assigning luminance values to patches representing sky directions.

I am curious that if "i" means "illuminance", is that i = Pi*VTDs?

Thank you,

Jia

Thank you, Greg. Now I am clear.

···

On Tue, Nov 22, 2011 at 1:30 AM, Greg Ward <[email protected]> wrote:

Hello Jia,

Good question. The "i" does derive from "illuminance," but can be used
for luminance values or pretty much anything derived from a lighting
calculation, including something like "sensor voltage" for an lighting
control system. The "V" matrix includes the factor of pi (if necessary)
and all other factors in the calculation of "i". Thus, the equation need
not change depending on the values you choose to compute.

I hope that's clear enough.

Best,
-Greg

> From: Jia Hu <[email protected]>
> Date: November 21, 2011 10:23:36 PM PST
>
> Hello:
>
> I notice the almost all the published literature use the following
equation to show the three phase daylight coefficient method.
>
> i = VTDs
> where:
> i = result vector (luminances, illuminances, image, etc.)
> V = view matrix, relating outgoing directions on window to desired
results at interior
> T = transmission matrix, relating incident window directions to exiting
directions (BSD
> D = daylight matrix, relating sky patches to incident directions on
window
> s = sky vector, assigning luminance values to patches representing sky
directions.
>
> I am curious that if "i" means "illuminance", is that i = Pi*VTDs?
>
> Thank you,
>
> Jia

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