polardataE – frudawski

The polardataE function calculates the resulting horizontal and vertical illuminances for a given Tregenza luminance distribution with 145 patches. The Tregenza hemisphere is assumed to have 100% coverage as in figure 1 in contrast to the original Tregenza model.

Figure 1: Tregenza hemisphere with 100% coverage

Usage:

[Eh,Ev] = polardataE(L,vdir)

Where:

Parameter	Description
`Eh`	Is the resulting horizontal illuminance $E_h$ .
`Ev`	Are the resulting vertical illuminances $E_{v,i}$ in $i$ vertical directions, specified by the vdir parameter. Note: this method neglects the influence of the sourrounding reflectances e.g. the environment terrain.
`L`	Is the Tregenza luminance distribution in $\textrm{cd}\cdot\textrm{m}^2$ as 145 $\times$ 1 vector.
`vdir (optional)`	Specifies the vertical compass direction using the azimuth angle, starting in north and going clockwise, default [0:359]. For compass directions north, east, south, west use: [0 90 180 270]

Examples

Horizontal and vertical illuminance (N,E,S,W) for CIE sky 5 with $\alpha_S=180°$ and $\gamma_S = 40°$ :

L = ciesky(5,180,40,'Eh',10000);
[Eh,Ev] = polardataE(L,[0 90 180 270])

See also: ciesky

Result:

Eh = 10000.0
Ev =

   4896.3
   4904.7
   4900.4
   4896.6

Note: CIE sky 5 has a uniform luminance distribution. The differences in the resulting vertical illuminances are due to different patch center coordinates which are used for cosine correction of the individual patch.

Vertical illuminance for $\alpha = 160°$ for CIE sky 12 with $\alpha_S=160°$ and $\gamma_S = 40°$ :

L = ciesky(12,160,40,'Eh',50000);
[~,Ev] = polardataE(L,160)

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