Computational Combination of the Optical Properties of Fenestration Layers at High Directional Resolution

Complex fenestration systems typically comprise co-planar, clear and scattering layers. As there are many ways to combine layers in fenestration systems, a common approach in building simulation is to store optical properties separate for each layer. System properties are then computed employing a fast matrix formalism, often based on a directional basis devised by JHKlems comprising 145 incident and 145 outgoing directions. While this low directional resolution is found sufficient to predict illuminance and solar gains, it is too coarse to replicate the effects of directionality in the generation of imagery. For increased accuracy, a modification of the matrix formalism is proposed. The tensor-tree format of RADIANCE, employing an algorithm subdividing the hemisphere at variable resolutions, replaces the directional basis. The utilization of the tensor-tree with interfaces to simulation software allows sharing and re-use of data. The light scattering properties of two exemplary fenestration systems as computed employing the matrix formalism at variable resolution show good accordance with the results of ray-tracing. Computation times are reduced to 0.4% to 2.5% compared to ray-tracing through co-planar layers. Imagery computed employing the method illustrates the effect of directional resolution. The method is supposed to foster research in the field of daylighting, as well as applications in planning and design.