Eurographics Workshop on Urban Data Modelling and Visualisation (2016) F. Biljecki and V. Tourre (Editors) Optimizing Window Shape for Daylighting: An Urban Context Approach E. Fernández 1† , J.P. Aguerre 1 , B. Beckers 2 and G. Besuievsky 3 1 Centro de Cálculo, Universidad de la República, Uruguay 2 Université de Pau et des Pays de l’Adour, France 3 ViRVIG, Universitat de Girona, Spain Abstract Configuring the optimal shape and position of a building opening, such as windows or skylights, is a crucial task for daylight availability. Computing daylighting requires the use of climate-based data, which involves large data sets and a time-consuming task performed by procedures that in general are not well suited for optimization. In addition, optimal opening shapes may be strongly affected by the urban context, which is rarely taken into account or roughly approximated. In this paper we present a new opening shape optimization technique that considers the urban environment. The exterior contribution is computed through a radiosity approximation. A pinhole-based model is used to model the influence of daylight component on the interior surfaces. Our results show the importance of the exterior influence in the final optimal shapes by computing the same room at different building locations. 1. Introduction Daylighting plays a very important role for energy saving in sus- tainable building, and setting the optimal shapes and positions of the openings is crucial for improving the daylight availability. Op- timizing the use of daylight concerns the use of climate-based data, and the hourly data-set for the whole year must be taken into ac- count at each iteration of the optimization process. Concerning the daylight computation, we must evaluate the percentage in hours of daylight accessibility in a place, using any of the available metrics, like Daylight Autonomy (DA) [RMR06] or Useful Daylight Illumi- nance (UDI) [NM05]. Although consolidated methods are success- fully used for interior studies, the exterior environment with the full action of its components is rarely addressed. Exterior obstructions and reflections, typically due to adjacent buildings and trees, may affect considerably the indoor daylight provided. Therefore, it is a very important parameter to consider in lighting simulation. The problem of finding the optimal geometric model that achieves the goal of maximizing the daylight hours cannot be solved by standard CAD tools that work using forward-based strategies. Such strategies are unsuitable for optimization problems, where thousands of possible configurations should be tested. The problem should be stated as an inverse problem [FB12] and formu- lated with an optimization approach [CSFN11]. An additional dif- ficulty is that we need to evaluate the whole hourly data-set of the † eduardof@fing.edu.uy year, at each iteration of the optimization process. Available day- light methodologies like the daylight coefficient approach [TW83] or the "three-phase simulation method" [WML * 11, ML13] are not completely well suited for windows shape optimization. Recently, a fast methodology based on a pinhole approach has provided results that can achieve efficient opening shape optimization [FBB16]. However, the method does not take into account the exterior en- vironment. In this paper, we propose an opening shape optimization method that considers the urban context. That is, any exterior geometric model that can potentially obstruct or reflect light is integrated in the optimization procedure. The new method is based on the pin- hole radiosity method [FB15, FBB16] and the sparsity of the form factor matrix in urban environments [AFBB16]. The proposal can deal with a whole-year data-set, providing fast daylighting compu- tation for full global illumination solutions. Our test results show the different optimal window shape solution depending on the exte- rior environment. The results enhance the importance of computing all exterior components correctly for daylighting assessment. 2. Related Work 2.1. Daylighting Computation One of the most used daylight metric is the UDI [NM05], which indicates the number of hours in the year when the illuminance values are above a desired minimum, typically 100lx, and below a desired maximum, typically 2000lx. Unlike other similar metrics, c  2016 The Author(s) Eurographics Proceedings c  2016 The Eurographics Association. DOI: 10.2312/udmv.20161418