The Five-Phase Method
The Daylight Coefficient Method and The Three-Phase Method employ Reinhart sky patches. As explained in Figure 8, Reinhart skies with 145 or even 2305 patches greatly overestimate the size of the sun. The approximation of the actual position of the sun to three or four patches also leads to a misrepresentation of the sun’s actual position in the sky. Additionally, as explained in Figure 10, the Three-Phase Method also does not accurately account for the geometry of the fenestration systems from which the Transmission Matrix is derived.
The Five-Phase Method extends the Three-Phase Method by introducing some additional steps in the workflow to improve the accuracy with which direct solar component of the sky is treated in the simulations. These steps are loosely analogous to the improvements for the Daylight Coefficient Method proposed by (Bourgeois and others 2007). Figure 11 provides a pictorial representation of the Five-Phase Method.
Figure 11. The Five-Phase Method. As shown in the images above, this method seeks to improve upon the results generated through the Three-Phase Method (VTDs) by considering a more accurate calculation for the direct-sun component of the sky. Following a Three-Phase simulation(VTDS), the direct-only component (VdTdDds) is computed with a zero-reflection simulation on the same model with non-reflecting surfaces. Then a simulation with a sun-only sky matrix is performed (Cdsssun). The results from the three simulations are then combined through matrix subtraction (with VdTdDds) and addition (Cdsssun) as indicated by the + and - signs in the bottom image. The glazing system, incorporated as the T Matrix in the Three Phase calculations, is factored into the direct solar calculation by modeling it in the scene using the BSDF primitive.
The Three-Phase Method, described in Equation [3], is extended in the Five-Phase Method as:
…………………………… [4]
where the term denotes a separate three-phase simulation utilizing the same scene as the original three-phase calculation denoted by . , which stands for the direct-sun aspect of a Three-Phase Simulation, differs from the on account of its emphasis on isolating the direct-sun component of the simulation. The direct-sun component is isolated by performing a flux-transfer calculation with no ambient bounces and considering a sky-matrix with only the direct solar component.
The term denotes a more accurate simulation with direct solar contribution. denotes a coefficient matrix for direct sun that was calculated by also taking into account, wherever possible, the geometry of the shading device that was used to create the BSDF used as the T matrix. Incorporating the physical geometry of the shading system in such way overcomes the issue of obscured shadows shown in Figure 10.
Figure 12 provides an example of the phase-wise results generated through the Five-Phase Method. The resultant image shows the sharp shadows cast by the shading device, which are obscured in the case of the Three-Phase simulation. The Five-Phase Method was introduced by Andy McNeil during the 12th International Radiance Workshop (McNeil 2013a). The step-by-step workflow for this method is detailed in it’s tutorial (McNeil 2013c). Section 6.4 of Chapter 6 provides an updated version of that workflow.
The next two chapters provide some background information about the Radiance programs and the Radiance model that will be used for performing the simulations described in this tutorial.
Figure 12. Images rendered through the Five-Phase Method for a space with a daylight redirecting system (in upper windows) and venetian blinds. The patterns on the floor in the images on the upper-right and lower-right indicate the use of proxy-geometry of the venetian blinds in the simulation. The image on the upper-left, generated through the Three-Phase Method alone, has fuzzy shadows. The image on the lower-right was generated after subtracting out the direct component from the Three-Phase calculation and then adding a direct-sun component generated through a sky matrix with sun luminance only. Credit: (McNeil 2013b).