The Three-Phase Method
The Three-Phase Method makes it possible to perform annual or point-in-time parametric daylighting simulations with Complex Fenestration Systems (CFS). As depicted in Figure 9, the Three-Phase Method builds on the Daylight Coefficient Method by virtually splitting the flux-transfer path represented into three independent phases, namely:
- View (V): Flux transfer from illuminance grid-points or a view specification to glazing or CFS.
- Transmission (T): Flux transfer through the glazing or CFS.
- Daylight (D): Flux transfer from the exterior of glazing or CFS to the sky.3
The matrix equation [2] can be adapted to the Three-Phase Method as
…………………………….[3]
The process for creating the sky vector remains the same as that in the case of the Daylight Coefficients method. The matrices for the View (V) and Daylight (D) phases are generated through Radiance-based workflows involving rfluxmtx or rcontrib. The Transmission (T) matrix, which is usually a BSDF definition stored in XML format, can be generated either through genBSDF or through the LBNL Window software. The BSDF data structure employs a hemispherical sampling basis to store information about the optical properties of the glazing or CFS. As indicated by the patches on the glazing in Figure 10, the use of hemispherical sampling is noticeable in images generated through the Three-Phase Method.
The workflows and concepts pertaining to the Three-Phase Method have been extensively documented in peer-reviewed journal articles and tutorials. The principle behind the Three-Phase Method and a review of core theoretical concepts invoked in it are presented in (Ward and others 2011). A discussion focusing on the parametric and data-reuse aspect of the Three-Phase Method can be found in (Saxena and others 2010). Jonsson and others (2009), and McNeil and others (2013), include information about BSDFs that is relevant to the Three-Phase Method. Finally, Andy McNeil’s tutorial on the Three-Phase Method (McNeil 2013c) provides a step-by-step guide for applying this simulation technique to different types of daylighting scenarios. Section 6.3 of Chapter 6 presents a slightly revised and simplified workflow for the Three-Phase Method by utilizing the new rfluxmtx program.
Figure 9. A schematic comparison between the Daylight Coefficient Method and the Three-Phase Method. The flux transfer calculations are depicted through the arrow and letters. Daylight Coefficient Method involves a single step calculation for the flux transfer between a space and the sky. The Three-Phase Method involves three separate steps (phases) of flux transfer.
Figure 10. Images generated through Three-Phase Method and other more conventional methods for the same space and daylighting conditions. The two images on top highlight the fact that the external view is obscured in the Three-Phase Method. Discrete sky patches are visible in the image generated through the Daylight Coefficient Method. The external view is obscured in the case of the Three-Phase Method due to the use of hemispherical sampling basis. The lack of distinct shadows in the bottom-right image indicates that the shadows created by shading systems are obscured in the Three-Phase Method. Although the above observations are made in the context of image-based simulations, they are relevant to illuminance-based simualtions as well. (Credit for images in the bottom: (Saxena and others 2010))
3. Although light physically travels from a luminous source to the observer (or calculation point), the order of matrices is intentionally listed in reverse order and also indicated as such by arrows in figures denoting these matrices. This is to highlight the fact that Radiance performs reverse-tracing. Further details about the ray-tracing algorithms in Radiance can be found in ( ↩