Transition Portal for daylighting calculations in early phase design

Accepted Manuscript

Transition Portal for Daylighting Calculations in Early Phase Design Joseph T. Kider, Bruce Walter, Sandy Fang, Ege Sekkin, Donald P. Greenberg PII: DOI: Reference:

S0378-7788(18)32842-1 https://doi.org/10.1016/j.enbuild.2019.03.034 ENB 9097

To appear in:

Energy & Buildings

Received date: Revised date: Accepted date:

10 September 2018 20 February 2019 22 March 2019

Please cite this article as: Joseph T. Kider, Bruce Walter, Sandy Fang, Ege Sekkin, Donald P. Greenberg, Transition Portal for Daylighting Calculations in Early Phase Design, Energy & Buildings (2019), doi: https://doi.org/10.1016/j.enbuild.2019.03.034

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Transition Portal for Daylighting Calculations in Early Phase Design Joseph T. Kider Jr.a,b,∗, Bruce Waltera , Sandy Fanga , Ege Sekkina , Donald P. Greenberga b School

a Program of Computer Graphics, Cornell University, Ithaca NY 14852 of Modeling, Simulation, and Training, University of Central Florida, Orlando, FL 32826

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Abstract

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Daylighting studies are becoming increasingly important for early stage design of buildings and their facades. As architects generate increasingly complex building models in early phase design, this necessity for daylighting simulations is growing. Unfortunately, simulation models used for daylighting analysis are often over-simplified to reduce computation time, and these models tend not to simulate sufficient results for accurate facade studies and room detail. We present an accurate, easy-to-use, interactive, physicallybased daylighting Transition Portal simulation method for design and analyses for daylighting in early phase design. The Transition Portal can enable comprehensive visual interfaces for building designers yielding global illumination solutions for their design by leveraging a radiosity based approach to calculate daylighting illumination studies. This novel method is significantly faster and more accurate than existing early design simulation techniques. These procedures can be used to determine the illumination at any specific point in time or space, or averaged on a monthly or yearly basis for any given weather model. After a priori computations, solutions at any time step can be obtained in a few milliseconds on modern computer workstations. Keywords: Daylighting, Radiosity, Transition Portal, Illuminance 1. Introduction

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Daylighting studies are becoming increasingly important for early stage design of buildings and their facades [1, 2]. Recent research has shown that environmental satisfaction is far superior when occupants have views of external scenes and the luxury of natural daylighting with its continuously changing illumination [3]. Knowles [4, 5] discussed daylight from an ecological perspective describing the importance of daylighting on the structure and layout of a building. Although necessary for all buildings, this is particularly true for office environments, medical facilities, old age homes, and rehabilitation centers [6, 7]. For this reason there is a desire to maximize the transparency of a facade, sometimes measured as the percentage of a building’s exterior which is transparent. Fortunately today building technology has radically changed, allowing high transparency without excessive heat gain or loss [8]. Thermally efficient multi-layer window constructions, glazing with automatic time-varying tinting or clever geometrically changing facades can now modulate the shade, shadow, and radiation effects for continuously-changing illumination. Today with the proliferation of wirelessly connected accurate sensors [9], the tendency has also been to increase the number of building zones [10] which can be more easily controlled locally depending on their purpose, occupancy, orientation, and exposure, all yielding individual comfort [11, 12] and better utilization of energy resources. All of these factors require faster simulations and consideration of daylighting earlier in the design process [13]. ∗ Corresponding

author Email address: [email protected] (Joseph T. Kider Jr.)

Preprint submitted to Energy & Buidlings

In the architecture profession, typically lighting studies are conducted after much of the building has already been designed, despite their importance for energy considerations and LEED ratings. A major reason is that they take too long to compute and thus cannot easily be performed at early design stages. One factor is the increasing geometric complexity of the building facades [14, 15, 16], which are more expensive to simulate (Figure 1). Another is that daylighting often must be computed for time sequences spanning many hours and days to capture its daily and seasonal variations. Depending on the sampling frequency, a daylighting study can require solving at hundreds, or even thousands, of different times to accurately estimate the daylighting over a year. At present, most standard approaches today are based on ray tracing technologies [17] derived from computer graphics for daylighting studies [18, 19]. Unfortunately many of the algorithmic rays to the sun/sky illumination sources are blocked by the building exterior resulting in wasted computation. They also solve each time instant independently, failing to take advantage of the considerable temporal coherence. Although techniques derived for importance sampling [20] and irradiance caching [21] have greatly improved timings, this is still an inefficient computational process. Thus in order to reduce the computation time numerous simplifications are frequently made. Building models are approximated. Shorter time periods are used and the size of time increments is increased. The number of rays utilized for sampling are reduced, or the number of bounces for each ray is sometimes restricted, truncating the interreflections between interior zonal surfaces. The end result is a considerable loss of accuracy in the illumination solution. In this paper, we present a new methodology for daylighting April 3, 2019

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Figure 1: Figure 1: Illustration of various static shading devices. The figure shows four currently used facade designs: (A) New York Times Building, featuring ceramic rods (Renzo Piano Building Workshop, FXFOWLE Architects); (B) Carpenter Center for the Visual Arts, featuring a rectangular grid of concrete walls (Le Corbusier); (C) Brian C. Nevin Welcome Center, Cornell, featuring horizontal wooden slats (Baird Sampson Neuert); (D) The Broad Museum, featuring a honeycomb facade (Diller Scofidio + Renfro).

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Figure 2: Illumination forcing functions. (a) The path of the sun on a daily basis; (b) A single patch of the sky dome (blue). Note that the luminance from each patch changes with the position of the sun and the atmospheric conditions and is recomputed per timestep.

rior domain is simulated using a pre-computed form factor matrix and a very fast solution procedure to solve the full global illumination. The lengthy form factor calculations need only to be computed once for the static diffuse interior environment. This method has a significant advantage. For the fixed geometry interior spaces, many of the redundant computations required at each time step using standard ray-tracing procedures can be eliminated resulting in much faster simulations. As will be shown in this paper, once the a priori calculations have been computed, accurate lighting simulations can be obtained in tens of milliseconds for each time step. This significant computational speed-up allows for easy to use facade studies at the early stage design phase. This type of approach has been limited in the past by machine memory constraints, but today’s modern workstation (desktop) machines have sufficient memory capacity and bandwidth to allow radiosity computation with tens of thousands of polygons or patches. This is sufficient to adequately mesh many complex interior environments for daylighting simulations. Early design models are also often less geometrically complex, which makes our radiosity approach more advantageous. Another limitation is that radiosity is mainly limited to diffuse (Lambertian) materials. While non-diffuse radiosity methods have been proposed, they are more expensive and are not considered here. Interior surfaces are often predominately diffuse both for aesthetic reasons and to reduce glare issues. Additionally in early design, the material details may not yet be fully determined, and diffuse relfection behavior is often the most appropriate proxy at this stage. Thus we believe the diffuse restriction is reasonable for early design daylighting analysis, however our technique is not suitable for glare analysis, which generally requires more detailed material models. In the following sections we describe in detail how each of these modules works in detail. Section 2 describes the methodology of the Transition Portal. We review how the entire process can be made computationally efficient for various types of shading techniques including three dimensional building elements as well as two-dimensional window treatments (Figure 3). Section 3 details the simulation method by describing the algorithm used to simulate the global illumination using the radiosity approach, and discusses the calculation of the form factors for the building interior geometry, computation of the solar and sky irradance, and final matrix computation for the daylighting illuminance values. After showing several examples and case studies on real building examples in Section 4, we add our concluding remarks and discuss the advantages and disadvantages of our approach. The key to allowing the separation between the external and internal environments is our introduction of a unique Transition Portal method. This Transition Portal, which acts like a conduit of light, contains all of the elements considered by daylighting studies for the facade design of buildings. These include the bris-soleil (fins and awnings) of any shape, other threedimensional shading devices, two-dimensional fixed or moveable such as screens, blinds etc., or window glass parameters, such as frits, transparency, tints, etc.

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simulations for complex building design by separating the numerical computations of the simulation into three parts: the solar/sky model, the Transition Portal (i.e. the glazing and facade elements that determine how light enters the building), and the building interior. Our radiosity-based method also efficiently reuses information across time instants to greatly accelerate the computation of time sequences. The first part is the computation of the forcing function, the solar and sky dome radiation (Figure 2). This includes direct solar radiation plus any acceptable model of the radiation from the sky dome [22, 23, 24, 25] and potentially could include measured weather data [26, 27, 28, 29, 30]. Sky models can be physically accurate, including complex scattering with wavelength dependence and based on local weather information or simplified to the luminance from any direction [26]. The output from this first part is the illumination emanating from the sun and the sky dome. The solar and sky radiation and sun position are dynamically modeled and recomputed for each time step [31]. Chatzipoulka et al. [32] looked at sky view factors to analyze daylight on building facades. The second part of the Transition Portal computes how much of this exterior light penetrates through the Transition Portal, that is the transparent surfaces of the facade, to reach the building interior. The Solar/Skydome Illuminance vector represents the illumination each interior patch or polygon directly receives from external sources. This includes direct solar illumination plus the illumination from any visible sky dome patches, and includes any shadowing or attenuation due to shading devices or glazing. This calculation of the Solar/Skydome Illuminance vector must also be repeated for every time step but is extremely fast since it is direct illumination only. The third part is a novel approach to rapidly solve for the light distribution within the spatial confines of a building’s interior geometry (rooms or zone). This includes light which may have reflected multiple times in the interior and is known as the global illumination solution [33]. Our approach is based on the important observation that for daylighting studies the geometry of the interior of the building is usually assumed to remain constant. Thus the relationships between all internal surfaces (walls, ceilings, furniture, etc.) remains invariant. This assumption enables us to use an efficient radiosity method at each time step. After computing the direct illumination from both the sun and sky dome, the distribution of the light throughout the inte-

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opening

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fritting

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Figure 3: Components of a Transition Portal: (A) Visualizes different types of shading devices that affect the daylighting illuminance in a building space. (B) We show an ‘exploded’ view of the ‘in-plane’ fenestration components that effect lighting through the Transition Portal. Each of these types of components can be dynamically changed per timestep.

2. Methodology

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be subdivided increasing the polygon count. Polygon clipping is, at best, an O(n2 ) algorithm with respect to the number of vertices that participate as the shading surface and thus these methods are no longer used due to their inefficiency. Compagnon [39] looked at daylight availability for different building layouts.

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The Transition Portal approach decomposes the building geometry into interior, glazing, and shading components and then uses a radiosity method to efficiently calculate the total illumination (i.e. global illumination) for each time step in daylighting simulation (e.g., over a typical year). This process can be broken up into the following steps: • Precompute and store the form factors between the interior surface patches and from the sky regions • Calculate the skydome and solar luminance values for the current time • Determine the forcing function which is the direct solar and sky illuminances for each patch • Calculate the global illumination including interreflections using radiosity We define the Transition Portal as all the elements of the building’s exterior that allow light (energy) to enter the interior space of a building from any direction. As shown in Figure 4(A), this includes windows and three dimensional shading devices that can cast shadows on the transmissive surfaces reducing the light illumination from source directions. While direct solar light is often the most important, the light from segments of the sky dome is also included and handled in the same manner. A variety of methods have been proposed to predict the amount of direct solar radiation which enters simple geometric portals. Awning and fin approaches [34, 35] calculate simple horizontal and vertical building shading devices through a series of trigonometric relationships. These algorithms utilized only a few pre-defined geometric parameters and could not capture the types of complex shading device geometry used today. A second approach used projection routines and successive polygon clipping [36, 37, 38]. These approaches were more general than awning and fin approaches and could produce exact results. Unfortunately, polygon clipping approaches are still limited to certain shading geometries and sensitive to numerical stability. For more complex and curved shading devices, such as those used today, the geometry must

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Ray-Tracing Methods. Today ray-tracing [40, 18, 19] is the most commonly used approach for lighting simulations and many of the commercial software offerings are based on Radiance by Greg Ward [18]. These widely used approaches are particularly popular for rendering purposes for the pictorial depiction of design environments, manufactured products, the entertainment industry, and virtual reality. The pictorial accuracy is superb and produces beautiful imagery. However, there are multiple reasons why ray tracing may not be the preferred solution for daylighting simulation. Building codes are concerned with many time steps, not just single images. Additionally, the number of light paths ray-tracing generates is extremely large. The accuracy of the ray-tracing approaches also depends on the number of bounces (segments of the path). For practical purposes, ray generation is reduced and paths are usually limited to two-four bounces as the impact of each segment diminishes based on the reflectivities of the surfaces. Radiosity Methods. Radiosity approaches provide an accurate physically-based global illumination solution for diffuse environments [41, 42, 43]. Radiosity methods use finite element techniques to solve for the lighting in an environment. Computing the lighting requires considering all possible paths from the sources of illumination to each receiving surface. These paths include both light that arrives from the sources directly (i.e. without interacting with other surfaces) and indirectly (e.g., after reflecting from one or more other surfaces). This is also known as the global illumination problem because the lighting on a surface potentially depends on the lighting at all other surfaces. Our Transition Portal approach eliminates much of the redundancy in standard ray tracing methods for static environments by precomputing the visibility between patches as

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form factors and reusing them across all time steps. Furthermore since all light dispersion (bounces) is incorporated in a full radiosity solution, it computes the full global illumination. The accuracy of this approach is dependent on the physical size of the elements or patches. This weakness can be ameliorated by reducing the element size, thus increasing the number of elements to more accurately represent the geometry of the interior space but this choice increases computation times. Radiosity methods has been validated by Lischinski et al. [44] and Pattanaik and Bouatouch [45]. They computed the posteriori bounds and estimates for local and total errors in the radiosity solutions to demonstrate how accurate the approach is in practice. These bounds account for the propagation of errors due to interreflections [44]. The Transition Portal accelerates the calculation of complex building shading and glazing by accounting for (1) complex shading (e.g. fritting or venetian blinds) and (2) glazing transparency (i.e. transmission) separately in the radiosity forcing function calculation (Section 3.2). This greatly reduces the number of elements needed for complex shading devices. This approach then leverages radiosity to computer the interior global illumination.

2.2. Transition Portal

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Figure 4 shows an overview of the Transition Portal system we propose in this paper. The transition portal accounts both for light that is blocked by opaque geometry, such as shading devices, as well as light attenuation through any partially transmissive elements such as window tinting, fritting, or blinds. Attenuation, at least in simple spatially homogeneous cases, can be accounted for by applying fractional multipliers to the incoming illumination. The shadows, or occlusion, from three dimensional shading elements can be complex and highly directionally dependent and thus needs to be recomputed for each time step’s solar position. For each time step, we first use the transition portal to compute how much of the external solar and sky light reaches each interior surface. Then we use a radiosity system to account for the reflected illumination from these interior surfaces. Separating the transition portal from the static interior geometry, allows us to precompute and reuse the expensive parts of the interior solution process, namely the form factors and radiosity matrix. This way the daylighting for a time step can be computed rapidly and efficiently. The transition portal supports dynamic elements such as automated shading devices or parametric studies, since it is recomputed each time step.

2.1. Complex Building Shading

Today there are numerous innovative schemes which have been utilized to provide shading and thus reduce the impact of solar and sky dome radiation in heating and cooling, as well as daylighting. Several examples of these were shown in Figure 1. Our elements have been divided into two categories; (1) external shading devices, static or dynamic which are usually considered to be part of the building facade (Figure 3(A)) and (2) in-plane shading devices which can be treated as part of the two-dimensional portal opening and provide effects which can be composited (Figure 3(B)). We provide a simulation method which allows as much generality and flexibility as possible, e.g., incorporate multiple static and dynamic shading devices.

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3. Simulation Method: Global Illumination Solution

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Predicting the illumination on and interreflections between all surfaces is important in daylighting studies [46]. To predict the illumination in our environment, the Transition Portal simulation method accounts for complex building shading and transmission in the forcing function calculation and leverages a radiosity based approach. The amount of light arriving on a surface per unit area is known as its illuminance, which we denote as E [47, 27, 48]. The corresponding term for light leaving a surface is luminous exitance. A surface’s reflectivity, denoted as ρ, is the fraction of the incident light that it reflects. Luminous exitance is then equal to illuminance times reflectivity. To solve for the illuminance E using finite elements [49], we discretize the model’s surfaces into a set of patches and approximate the illuminance as being constant over a patch. The illuminance Ei on a patch i is then a sum of the light arriving directly from the sun, sky, or other light sources, denoted as D, plus the light that reaches it indirectly after being reflected by other surfaces. This can be expressed mathematically as: X E i = Di + Fi j ρ j E j (1) j

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The form factor Fi j is a geometry-based term that describes how much of the light leaving patch j arrives at patch i such that Fi j ρ j E j is equal to the illuminance on patch i due to light being reflected from patch j. This equation can be expressed as a simple matrix equation in the form:

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Figure 4: Overview of Transition Portal method for computing the interior daylighting. (A) We first calculate the solar position and the the sun and sky dome patch luminances; (B) then we track the light through the Transition Portal to account for shading and glazing; (C) this provides the interior forcing function from the direct solar and sky dome illuminance; (D) we use this and the interior geometry form factors to solve for the full global illumination.

AE = D 5

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where I is the identity matrix, F is the matrix of form factors, P is a diagonal matrix containing the patch reflectivities, D is the forcing function (i.e. the vector of sun/sky illuminances from the transition portal), and E is the unknown vector of total illuminances that we want to determine. This matrix equation can be solved in a variety of ways. We could invert the matrix A but inverting large matrices is computationally expensive. Instead we use an LU factorization which converts the matrix into a product of a lower L and an upper U triangular matrices (such that A = LU) which we precompute and store. This is less expensive than inverting the matrix, can be performed in place to save memory, and allows the equation to be solved cheaply and exactly for any values of D using a combination of forward and backward substitution operations. Approximate iterative solutions are sometimes used to avoid the cost of an exact solution, but in our applications, the factored matrix can often be reused many times, making the exact solution cost effective. Although these matrix equations must solved at each timestep, the LU factorization can be precomputed and reused across all time steps. The example timings in Table 1 illustrate that LU factorization is much faster than matrix inversion and can be further accelerated by utilizing the graphics hardware (GPU) available on modern workstations.

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Matrix Decomposition Time vs Patch Count (CPU vs GPU) CPU GPU

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Figure 5: Matrix LU factorization time for varying patch (matrix) sizes computed using the CPU or GPU. This graph demonstrates the considerable speedup by factoring the matrix using modern graphics hardware (GPU) as compared to using the computer’s main processor (CPU).

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Table 1: Example timings for matrix inversion, LU factorization (CPU), and LU factorization using graphics hardware (GPU) which can be used to solve the radiosity equation 2. These timings used the Eigen matrix library for CPU computations and NVidia’s Cusolver library for the GPU.

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x j − xi kx j − xi k

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is the direction from xi to x j , nˆ () is the local surface normal, Ai is the surface area of patch i, V() is the visibility between two + points, and (x) = max(x, 0) (i.e. the positive part of a function). For an opaque environment, the visibility will either be zero (if there is an occluding surface between the points) or one (if there is no occlusion). From this definition we can easily show that P Fi j Ai = F ji A j and j Fi j ≤ 1 (and equals 1 in a closed system). While simple analytic solutions for form factors exist for various special cases, in general an exact solution is either unknown or too expensive to compute, especially when the visibility function is non-trivial. Instead we will estimate them using an unbiased Monte Carlo estimator.

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As shown in Figure 5, cost increases as the the number of interior patches, and thus matrix size, grows but the GPU-based factorization maintains a large performance advantage. Our GPU could only handle up to 36,000 patches on our GPU due to its more limited memory size (12GB in our case), and larger matrices had to processed on the CPU. However GPUs with much larger memories are becoming available, so this limit will be relaxed in the future. By using LU decomposition and modern GPUs, we are able to handle much larger matrices at reasonable cost than could previously be handled using inversion based methods.

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3.1. Form Factors The form factor1 depends only on the geometry of the scene and does not depend on material or emission properties. It is defined by a double integral over the areas of the two respective Figure 6: Calculation of the form factors via a monte-carlo sampling approach. 1 Other

common names for form factors are view factors, configuration factors, or shape factors.

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rather than area to get: Fi j =

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where Ωi j is the solid angle of patch j as seen from xi . Monte Carlo estimates an integral by generating random samples of the integrand. For each patch i, we generate a random point xi on patch i and a random directions ω. ˆ However rather than preselecting a patch j, instead we generate directions over the entire cosine-weighted hemisphere around the local surface normal nˆ (xi ). This point and direction defines a ray and we can use efficient ray-casting methods to find which patch j and point x j is visible along this ray. In this way we guarantee the visibility between the points is unity. This allows us to estimate Fi j for a fixed i and all j in a single step as Fik = 1 if k = j and zero otherwise. Although unbiased, the estimate from a single sample will contain too much noise to be usable. However by averaging the results from many samples, we can reduce the noise and produce an accurate estimate of the form factor. The number of samples required depends on the scene and source configuration but we have found using between 512 and 2048 samples per patch sufficient in our tests. The form-factor computation is extremely fast, even for a large number of patches (> 10, 000). Furthermore, since the interior of the building is assumed to be constant (static geometry), this calculation is performed only once and can be used for all successive time steps.

Figure 7: Visualization of pixel counting for calculating the solar irradance vector per patch. The sun casts a shadow onto a patch, then we cycle through each patch and calculate the illuminance value of direct solar radiation per patch.

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3.2.1. Pixel Counting One practical method to compute the complex shading devices shown in the previous figures is to use Pixel Counting. The Pixel Counting method was first introduced by by Yezioro and Shaviv [53]. Subsequently, Jones et al. [50, 54] used a novel approach to significantly speed up the illuminance (E) which calculates AAst cos(θ) as an approximation by projecting the patch in an orthographic view, coloring the patch, and counting the illuminated pixels. For pixel counting, we use the center of the sun and each sky region and treat the light as parallel. Jones et al. used graphics hardware to accelerate and accurately calculate E. Here they calculate the E with the following equation: 1 As cos(θ) ≈ NA p (6) E= At At

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3.2. Solar and Sky Illuminance

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Before we can solve for the total daylight illuminance E, we need to estimate the direct illuminance D due to the sun and sky. Due to their very different properties, the sun and sky are handled as separate sources as we illustrated in Figure 2. The unoccluded solar illuminance can be easily estimated using existing solar models. To get the actual solar illuminance we need to estimate what fraction of each patch is unoccluded (i.e. is not in shadow) as well as any attenuation due to any partially transparent surfaces such as glazing, tinting, or fritting. The sunlight may be blocked either by other interior geometry or by the elements of the transition portal, and is recomputed for each time step. This can be done either using pixel counting (as in Jones et. al. [50]) or by randomly generating points over the patch and tracing rays to the sun to check its visibility. To approximate skylight, we can use the model(s) proposed in Kider et al. [30] to estimate sky dome luminances. Accurately calculating the skylight is important since it often provides the only source of daylight for a space for many times of the day (Figure 4A). We first break the sky dome into a set of regions and calculate an average luminance for every region at every timestep. This sky region sampling can follow the CIE pattern [51] or any novel pattern the user wants [30]. For each interior patch we estimate what fraction of each sky region is visible using either pixel counting or ray casting [52] to compute its direct illuminance from the sky.

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N is obtained by drawing the receiving direct illuminance patch with a color (and the shading occluders with black) then counting the remaining pixels either through the GPU (‘software’) or by occlusion queries (‘hardware’). This approach significantly speeds up the E calculation and is independent of the geometric complexity. This approach is visualized in Figure 7.

Computation Times of Pixel Counting Methods vs Patch Count

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Figure 8: Timings for the computing the Solar/Skydome Irradance vector using two implementations of pixel counting (’software’ and ’hardware’) as well as a ray casting approach using 2048 rays per patch.

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4. Case Studies

A second approach is to use ray casting to compute the direct illuminance. For ray casting, we generate random rays from each patch to either the sun or the sky dome, similar to the way we compute form factors. For the sky, if the ray reaches the sky, we determine which region it hit in order to compute sky region to interior patch form factors. These are then stored as a matrix so that the sky illuminance can be distributed to the interior patches using a simple matrix vector multiply. The runtimes of these approaches is shown in Figure 8. We found ray casting to generally be faster than pixel counting in our tests. Our ray casting was performed on the CPU using the Embree ray tracing library [55], but could likely be further accelerated using a GPU-based ray library such as Optix [56].

We have run different daylighting studies to demonstrate the performance of our approach. The computational costs depend mainly on the number of interior patches used. Figures 9 and 10 show timings for our precomputation and per time step computation respectively for scenes with varying numbers of interior patches. For models of these sizes, the precomputation takes a few seconds while each time step takes less than a second. Below we pictorially show the results of our novel algorithmic approach for three different categories of building spaces. Timings for each of the above three examples, including the apriori computation of the form factor matrix and its precomputed and stored solution, are shown for each example.

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3.2.2. Ray Casting

4.1. Office Space

Precomputation Times vs Patch Count Form Factor Calculation Matrix Decomposition

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In the first example, shown in Figure 11 and Table 2, we utilize an existing office space model. Part of the purpose of this illustration is to show that the analyzed office space is not just a simplification of the room, but can include such items as furniture or display devices and still be rapidly computed. We also show an illuminance plane (11D) and the complete radiosity solutions at two different mesh scales (11E-F). We choose a typical office space in the northeast United States and varied the patch size solution between 600 and 1200 . Figure 12 shows one of the main target use cases for our approach - a parametric design and evaluation of various facade types. We show that adding three different facade types Figure 12(B-D) has almost no impact on the computation times (Table 3). The sub-second calculation time per time step allows architects to conduct full yearly global illumination daylighting studies with little wait time for results. In practice, we would expect an architectural designer to test a larger number of facade variations, which with our system is feasible even in early-phase design studies due to the rapid feedback it provides. Enabling accurate daylighting studies in early-phase design is one of the primary goals of our method.

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Figure 9: Timings for the precomputation of the matrix decomposition and form factor calculation. These computations only need to performed once as a precomputation for a given interior geometry. The results can then be reused across all time steps.

Computation Times Per Timestep vs Patch Count (Daylighting) Sun Illuminance Sky Illuminance Matrix Solution

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In the second example, we have selected a residential kitchen that is bounded by two transparent glass facades that light enter across a wide region. Again, the example illustrates the types of geometric complexity that can be simulated rapidly. We demonstrate the results of the case study in Figure 13. This is a more complicated space with a high number of patches, yet the computation time is still efficient (Table 4).

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Our last example depicts an atrium space in a university building whose attributes would be quite similar to a multi-story environment typical of tall office buildings, apartment lobbies, or convention spaces. We visualize the results of our daylighting study in Figure 14.

Figure 10: Timings for solar illuminance, sky illuminance, and daylight radiosity solution computations. These computations are performed once per time step and are measured in milliseconds.

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Figure 11: Illustration of the radiosity solutions of an office space (Rhodes Hall, Cornell University): (A) photograph; (B) rendered image; (C) geometry used for the analysis including the furniture; (D) illuminance plane; (E) solution for 600 mesh; (F) solution for 1200 mesh. (Note that the images have been tone mapped for clarity of the complete solution.)

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Table 2: Timings for the case study in Figure 11E-F. This table shows the impact of geometry variation on daylighting studies. # Patches

# Samples (per patch) Form Factor Computation LU Factorization Total Precomputation Sun/Sky Illuminance Matrix Solution Total Time per timestep

Office 600 (E) 12423 2048

Office 1200 (F) 6200 2048

0.74(s) 0.52(s) 1.26(s)

0.34(s) 0.15(s) 0.49(s)

123(ms) 6(ms) 129(ms)

59(ms) 4(ms) 63(ms)

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Figure 12: The Transition Portal allows architects to run parametric studies to test different facade designs. This figure shows the results of parametric daylight simulation for different facade types.

Table 3: Timings for the parametric facade design of an office space in Figure 12. We show the one time precomputation costs (namely form factor computation and LU factorization), and the cost per time step (namely sun/sky illuminance and matrix solution) which is very fast and measured in milliseconds.

Form Factor Computation LU Factorization Total Precomputation

Matrix Solution

Total Time per timestep

Facade (C) 9537 2048

Facade (D) 9537 2048

0.55(s) 0.31(s) 0.86(s)

0.55(s) 0.31(s) 0.86(s)

0.56(s) 0.31(s) 0.87(s)

89(ms) 5(ms) 94(ms)

92(ms) 5(ms) 97(ms)

94(ms) 5(ms) 99(ms)

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5. Discussion

93(ms) 5(ms) 98(ms)

CE

Sun/Sky Illuminance

0.55(s) 0.29(s) 0.84(s)

Facade (B) 9537 2048

ED

# Samples (per patch)

Facade (A) 9537 2048

PT

# Patches

age and computation costs increase with patch count, placing limits on the achievable solution detail and model complexity. In early-phase design though, fast feedback is often more important, simpler geometry is used, and less accuracy is required. Additionally, the exact materials not yet known to the designers. Radiosity approaches assume a diffuse material environment, and do not handle directionally diffuse materials easily. However when light propagates through a large number of bounces, effectively making each patch a directionally diffuse light source, the ultimate result is often close to the similar solution of a purely diffuse environment. The radiosity approach described in this paper is not satisfactory for “glare” studies. Since these are primarily caused by specular reflections, and

Our approach has various advantages for helping architects and designers in early-stage design. A major reason lighting studies have been postponed is that it takes too long to compute and thus can’t easily be performed at early design stages. However, if we can do this fast, then parametric design studies can be accomplished during the preliminary design stage. A major advantage of our proposed approach, the Transition Portal method, is that multiple solutions can be rapidly tested by changing only the geometrical description of any portal for any time step. There are also disadvantages with this approach. The stor10

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Figure 13: Illustration of the radiosity solution using a residential space (kitchen, Ithaca, NY): (A) photograph; (B) rendered image placed within the photo; (C) geometry used for the analysis including the furniture; (D) solution for 12 mesh. Note that the last image has been tone mapped for clarity of the complete solution

Table 4: Case study of a residential kitchen space with a large number of 12in. patches and high degree of detail.

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# Patches # Samples (per patch) Form Factor Computation

ED

LU Factorization Total Precomputation Time

Matrix Solution

CE

Total Time per timestep

0.37(s) 0.16(s) 0.53(s) 55(ms) 4(ms) 59(ms)

PT

Sun/Sky Illuminance

7062 2048

usually require one or a few simulations with a small number of sun positions, ray tracing is a more appropriate solution in this case.

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putes a full global illumination solution for static but complex building interiors. This approach takes advantage of modern computer hardware with advanced graphics acceleration boards, large memory sizes, parallel architectures, and faster clock speeds, resulting in sub-second solutions at each time-step. Results are presented for a typical office space, a residential kitchen, and a building atrium using both cpus and gpus. The amazing speed of the solutions imply that our approach will be applicable for dynamically changing facades, more complex geometry, fastchanging weather models, and thus suitable for the next generation individual building controls. Most importantly, architects and engineers will be able to test many shading and lighting design strategies at early stage design because of the rapid feedback of the complex lighting simulations.

6. Conclusions

We have presented a novel simulation method for daylighting studies suitable for early phase design. We separate the external illumination sources and dynamic shading devices from the static geometry interior surfaces using a transition portal. Our simulations utilize a ray casting algorithm to determine the light entering the interior of a building. The procedure is very fast, can simulate changing facade geometries, and is computed at each time step. The resultant direct illuminance on the interior surfaces is used as the forcing function or source vector for the next stage. A modified radiosity algorithm is then com11

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Figure 14: Illustration of the radiosity solution using an atrium space; Weill Hall, Cornell University: (A) photograph; (B) rendered image; (C) solution for 12 inch mesh. Note that the images have been tone mapped for clarity of the complete solution. Table 5: Timings for case study of a atrium space. The times are significantly longer for this example than the prior ones because it has an order of magnitude more patches and used the CPU for the matrix computations since it was too large to fit in GPU memory. However the times are still fast enough for early design daylighting studies and will improve as GPUs with larger memories are becoming available. # Samples (per patch) Form Factor Computation Total Precomputation Time

References

CE

References

858(ms) 2227(ms) 3085(ms)

PT

Sun/Sky Illuminance Total Time per timestep

15(s) 2135(s) 2150(s)

ED

LU Factorization

Matrix Solution

79316 2048

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# Patches

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