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polardataE

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:

ParameterDescription
EhIs the resulting horizontal illuminance E_h.
EvAre 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.
LIs 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)

See also: ciesky

Result:

Ev = 5.0554e+04

Reference

Peter Roy Tregenza: Subdivision of the sky hemisphere for luminance measurements. In: Lighting Research and Technology, vol. 19, no. 1, pp. 13-14, 1987, (DOI: 10.1177/096032718701900103).

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