DOE-2 Engineers Manual Version 2.1A - DOE-2.com

1. A new coordinate system is defined, which is called the shadow calculation
coordinate system (prime system, for short). It is embedded in the
receiving polygon. The transformation from the building coordinate system
to the prime system can be written
X'
y'
Z'
x-x o
y-yo
Z-Z
. 0
( III.l6)
The elements of the rotation matrix Aij and the translation vector (xo Yo
zo) are calculated.
2. The coordinates of the recelvlng polygon vertices are transformed from the
building coordinate system to the prime system. The RP now lies in the
x'y' plane.
3. The receiving polygon is enclosed in a rectangle.
divided into bars running parallel to the y' axis.
called the working space.
The rectangl e is
This rectangle is
4. The solar direction cosines are transformed to the prime system. If the
receiv ing polygon is facing away from the sun, no shading can occur and
the rest of the calculation is skipped.
5. The coordinates of the shading polygon vertices are transformed to the
prime system.
6. Points on the SP that are below the plane of the receiving polygon (the
x 'y' plane) are c 1 i pped off.
7. The cl ipped shading polygon is projected along the direction of the sun's
incoming rays onto the plane of the receiving polygon.
8. The shape of the projected shading polygon is stored by saving the
crossing points of the projected shape with the midline position of each
of the bars. The crossing points divide each bar into bar segments. A
relative intensity of the light reaching each bar segment is stored.
9. The bar segments and relative light intensities are used
amount of sunlight falling on the entire receiving polygon.
to obtain a shadow ratio for the hour.
Details and Derivation
to obta in the
Th is is used
Step 1. Derivation for transformation from the building coordinate system to
the prime system.
At the start of the shadow calculations, all coordinates are in the
building coordinate system. During the shadow calculations, the receiving
polygon, the shading polygons, and the solar direction cosines are transformed
III .36