Efficient representations of large radiosity matrices

The radiosity equation can be expressed as a linear system, where light interactions between patches of the scene are considered. Its resolution has been one of the main subjects in computer graphics, which has lead to the development of methods focused on different goals. For instance, in inverse lighting problems, it is convenient to solve the radiosity equation thousands of times for static geometries. Also, this calculation needs to consider many (or infinite) light bounces to achieve accurate global illumination results. Several methods have been developed to solve the linear system by finding approximations or other representations of the radiosity matrix, because the full storage of this matrix is memory demanding. Some examples are hierarchical radiosity, progressive refinement approaches, or wavelet radiosity. Even though these methods are memory efficient, they may become slow for many light bounces, due to their iterative nature. Recently, efficient methods have been developed for the direct resolution of the radiosity equation. In this case, the challenge is to reduce the memory requirements of the radiosity matrix, and its inverse. The main objective of this thesis is exploiting the properties of specific problems to reduce the memory requirements of the radiosity problem. Hereby, two types of problems are analyzed. The first problem is to solve radiosity for scenes with a high spatial coherence, such as it happens to some architectural models. The second involves scenes with a high occlusion factor between patches. For the high spatial coherence case, a novel and efficient error-bounded factorization method is presented. It is based on the use of multiple singular value decompositions along with a space filling curve, which allows to exploit spatial coherence. This technique accelerates the factorization of in-core matrices, and allows to work with out-of-core matrices passing only one time over them. In the experimental analysis, the presented method is applied to scenes up to 163K patches. After a precomputation stage, it is used to solve the radiosity equation for fixed geometries and infinite bounces, at interactive times. For the high occlusion problem, city models are used. In this case, the sparsity of the radiosity matrix is exploited. An approach for radiative exchange computation is proposed, where the inverse of the radiosity matrix is approximated. In this calculation, near-zero elements are removed, leading to a highly sparse result. This technique is applied to simulate daylight in urban environments composed by up to 140k patches.La ecuación de radiosidad tiene por objetivo el cálculo de la interacción de la luz con los elementos de la escena. Esta se puede expresar como un sistema lineal, cuya resolución ha derivado en el desarrollo de diversos métodos gráficos para satisfacer propósitos específicos. Por ejemplo, en problemas inversos de iluminación para geometrías estáticas, se debe resolver la ecuación de radiosidad miles de veces. Además, este cálculo debe considerar muchos (infinitos) rebotes de luz, si se quieren obtener resultados precisos de iluminación global. Entre los métodos desarrollados, se destacan aquellos que generan aproximaciones u otras representaciones de la matriz de radiosidad, debido a que su almacenamiento requiere grandes cantidades de memoria. Algunos ejemplos de estas técnicas son la radiosidad jerárquica, el refinamiento progresivo y la radiosidad basada en wavelets. Si bien estos métodos son eficientes en cuanto a memoria, pueden ser lentos cuando se requiere el cálculo de muchos rebotes de luz, debido a su naturaleza iterativa. Recientemente se han desarrollado métodos eficientes para la resolución directa de la ecuación de radiosidad, basados en el pre-cómputo de la inversa de la matriz de radiosidad. En estos casos, el desafío consiste en reducir los requerimientos de memoria y tiempo de ejecución para el cálculo de la matriz y de su inversa. El principal objetivo de la tesis consiste en explotar propiedades específicas de ciertos problemas de iluminación para reducir los requerimientos de memoria de la ecuación de radiosidad. En este contexto, se analizan dos casos diferentes. El primero consiste en hallar la radiosidad para escenas con alta coherencia espacial, tal como ocurre en algunos modelos arquitectónicos. El segundo involucra escenas con un elevado factor de oclusión entre parches. Para el caso de alta coherencia espacial, se presenta un nuevo método de factorización de matrices que es computacionalmente eficiente y que genera aproximaciones cuyo error es configurable. Está basado en el uso de múltiples descomposiciones en valores singulares (SVD) junto a una curva de recubrimiento espacial, lo que permite explotar la coherencia espacial. Esta técnica acelera la factorización de matrices que entran en memoria, y permite trabajar con matrices que no entran en memoria, recorriéndolas una única vez. En el análisis experimental, el método presentado es aplicado a escenas de hasta 163 mil parches. Luego de una etapa de precómputo, se logra resolver la ecuación de radiosidad en tiempos interactivos, para geométricas estáticas e infinitos rebotes. Para el problema de alta oclusión, se utilizan modelos de ciudades. En este caso, se aprovecha la baja densidad de la matriz de radiosidad, y se propone una técnica para el cálculo aproximado de su inversa. En este cálculo, los elementos cercanos a cero son eliminados. La técnica es aplicada a la simulación de la luz natural en ambientes urbanos compuestos por hasta 140 mil parches

Multi-Objective Optimisation Framework for Designing Office Windows::Quality of View, Daylight and Energy Efficiency

This paper presents a new, multi-objective method of analysing and optimising the energy processes associated with window system design in office buildings. The simultaneous consideration of multiple and conflicting design objectives can make the architectural design process more complicated. This study is based on the fundamental recognition that optimising parameters on the building energy loads via window system design can reduce the quality of the view to outside and the received daylight – both qualities highly valued by building occupants. This paper proposes an approach for quantifying Quality of View in office buildings in balance with energy performance and daylighting, thus enabling an optimisation framework for office window design. The study builds on previous research by developing a multi-objective method of assessment of a reference room which is parametrically modelled using actual climate data. A method of Pareto Frontier and a weighting sum is applied for multi-objective optimisation to determine best outcomes that balance design requirements. The Results reveal the maximum possible window to wall ratio for the reference room. The optimisation model indicates that the room geometry should be altered to achieve the lighting and view requirements set out in building performance standards. The research results emphasise the need for window system configuration to be considered in the early design stages. This exploratory approach to a methodology and framework considers both building parameters and the local climate condition. It has the potential to be adopted and further refined by other researchers and designers to support complex, multi-factorial design decision-making

A sustainable complex fenestration system using recycled plastics

Daylighting in built spaces has several benefits. It helps in reaching satisfactory levels of energy consumption by reducing the usage of artificial lighting. Furthermore, daylighting is also a major contributor in altering the visual comfort of occupants. Consequently, it boosts occupants’ concentration and productivity, which affects their performance in work tasks. However, an inadequately designed daylighting scheme leads to excessive solar heat gain, especially in hot and arid climates, increasing the temperature of interior spaces. In addition, due to the high solar altitudes in summer, the direct sunlight may fall right beneath the fenestration system and will not reach the depth of the space this phenomena is known as the “cave effect”. Many proposed designs of blinds, louvers, shades and low emitting glass panels, tackled the side effects of the summer sun; on the other hand, a few of the proposed solutions incorporated the use of recycled materials, for an added sustainable value. The aim of this thesis is to achieve a sustainable complex fenestration system (CFS) design that can diffuse and redirect the direct daylight component through an optimized pattern on its translucent layer. The CFS will comprise recycled plastic waste, which results from the conventional household waste. The recycled plastic waste will be used as a translucent material, with an optimized prismatic array design, to ensure adequate daylighting in hot climate desert areas. An optimization model for designing a prismatic panel is developed to meet the objective of minimizing sun light near the window and redistributing the sunlight to the depth of the space, while a ray tracing program is used to validate the developed model’s results. Furthermore, Radiance, a validated ray tracing simulation program, is used to produce accurate analysis with detailed hourly illuminance measurements throughout the year for the proposed CFS design using the five-phase method. Finally, a physical small scale model is developed to prove the viability of the CFS using three different recycled plastics, polystyrene (PS), polycarbonate (PC) polypropylene (PP). The proposed design succeeded to improve the daylight performance by redirecting an average of 50% of the direct light to an upward direction, thus levelling the daylight within the room depth. The physical prototype exhibits great performance in the redirection of daylight into deep areas of the room especially at high solar altitudes. Polycarbonate proved to be the best of the three tested recycled plastic followed by the polystyrene, while polypropylene needs further research to develop a more feasible product

Tropical daylighting : predicting sky types and interior illuminance in north-east Brazil.

Daylight is present in tropical regions in a considerable intensity throughout the year. The sky characteristics are changeable and sunlight cannot be disregarded. Daylighting techniques are still wanted to answer particular tropical features. The main aim of this thesis is to present a daylighting analysis tool for the tropics developed out of existing procedures. It is structured in three parts. The first part provides a broad view of climatic aspects related to daylighting studies in a typical tropical city - Maceiö, Brazil. A brief climatic description of the city and a study relating climate and building are followed by a literature review of climatic fundamentals. A study is made of meteorological station measurements in relation to the city and a field investigation is described. These lead to a simplified method for sky type selection. It shows that a reasonable assumption about daylight climate can be made from very simple data and that new structure of CIE standard general sky could be applied everywhere. The second part investigates methods that could be appropriated for calculating daylighting in humid climates and concludes with a methodology based on an adaptation of existing techniques. The Monte Carlo and ray tracing techniques are reviewed, as well as the daylight coefficients concept. These are incorporated in prototype software, TropLux, written in MATLAB code. The development of the method in this thesis can be seen as an extension of the daylight factor concept to the CIE Standard General Sky and reflected sunlight. The software validation is done and results show that the level of prediction is comparable with those produced by Radiance and overall the results appear to be robust. Analysis indicates that it is not essential to have climate-specific calculation technique. Universal lighting software is viable, providing the local climate and architectural characteristics are taken into account. The last part applies TropLux to ground-reflected light. It is found that the influence of reflected sunlight on interior illuminance can be very large. Among shading devices analysed, overhang has shown the best performance. There is a key zone of ground outside window that provides the majority of the reflected light. A direct design implication can be the reduction of window size

On the robustness of thermal comfort against uncertain future climate: A Bayesian bootstrap method

Climate change mitigation and adaptation warrants their synergetic consideration in the building design process, yet past decades have witnessed an unbalanced focus on the mitigation of energy and carbon. In redressing the imbalance, the major challenge lies in the accurate prediction of future building performance via building energy modelling, which is considerably hindered by uncertainties in future climate data. Robustness analysis is a promising technique to inform uncertainty-based decision-making, but its application to future thermal comfort has yet to be sufficiently explored in the built environment. From the perspective of domestic overheating, this paper represents an initial investigation into the implementation of the Bayesian bootstrap method, to quantitatively evaluate the robustness of thermal comfort against uncertain future climate. This is demonstrated using a case study of two typical post-retrofit dwellings in England, where the Bayesian bootstrap also enables the statistical comparison of their expected future overheating risk with climate uncertainty considered. The main findings reveal the magnitude of both overheating risk and its variability experienced during nocturnal occupancy in regulation-compliant dwellings, respectively comprising nearly 15 and 12 times greater than during daytime in extreme cases. Results also imply that adaptive ventilation is potentially the key measure to enhance the robustness of thermal comfort against climate uncertainty. Overall, the Bayesian bootstrap is shown to provide a systematically consistent approach to the robustness assessment of future thermal comfort, which can facilitate the comparability of design alternatives that is vital to the building design decision-making process integrating both mitigation and adaptation strategies

Qualitative and quantitative optimization of skylights : a comprehensive and inclusive analysis of skylight sizes for an office while providing enough daylight, avoiding glare and saving energy

While windows connect inside to outside, daylight entering through windows is a key element in architectural design. Although electrical lighting is able to replace daylight as an essential lighting requirement, daylight has qualitative and quantitative aspects that distinguish it from its competitor, electrical lighting. One of the most unique characteristics of daylight is its variability in time, including different qualities of daylighting from sunset to sunrise, and from equinox to solstice. In addition, by regulating a circadian rhythm and hormone secretion, daylight impacts the physiological and psychological well-being of human beings. Moreover, daylight through windows carries information that flows from outside to inside and makes occupants aware of the outside world. While availability of daylight has been praised in building design, uneven distribution of daylight, reflective surfaces and excessive daylight may cause glare issues and visual discomfort which need to be avoided in daylight design. Beyond all the qualitative aspects of daylight, daylight, as a free resource, is able to illuminate the space and replace electrical lighting and lower electricity utility bills. This quantitative aspect of daylight has been the center of attention among researchers, designers and builders, as lowering CO₂ emissions and environmental design have gained momentum in the building industry. Different stakeholders have various interests in qualitative and quantitative aspects of daylight, which eventually shape the design context. The interests of different stakeholders, including owners, environmentalists and occupants, may merge or conflict in different projects, which shows that daylight quality and quantity may have different weights, depending on the context of the project at hand. This dissertation aims to provide an algorithmic platform to consider a context for skylight design by including all the interests of different stakeholders while either scaling importance of the different interests or requiring minimum qualities and performance targets. This dissertation proposes different methodological approaches for its platform to include both qualitative and quantitative aspects in designing skylights for a one-storey office building in different climates. Three different approaches are proposed in this dissertation, encompassing unconstrained optimization, constrained optimization and monetary metrics. In the unconstrained optimization approach, the algorithmic platform has been developed to implement Parametric Analysis (PA) and Gradient Descent (GD) methods in order to optimize Skylight to Floor area Ratio (SFR) while saving energy consumption, as a quantitative aspect of daylight, and improving daylighting quality by providing sufficient daylight without causing glare discomfort. This platform was built as an Inclusive Integrative Algorithm (IIA) to weight different qualitative and quantitative aspects of daylight. The algorithm is able to perform single or multi-objective optimization by either applying GD or PA. In this approach, a single-objective optimization, considering only energy efficiency, showed that the optimal SFR was 6% in the examined climates of Austin, Chicago and San Francisco, for 300 lux lighting level and Lighting Power Density of 0.8 watt/sqft. The unconstrained optimization approach implemented a weighting system for an aggregated metric, including Mean Daylight (MD) and imperceptible Daylight Glare Probability (iDGP) and Ratio of Energy Saving (RES), which resulted in a SFR of 11% as the inclusive optimal solution for all the examined climates. In addition to the discussion of inclusive optimization considering both daylight and energy performance and scaling their importance, this dissertation initiated the use of GD for the unconstrained optimization in single and multi-objective optimization. The result showed that GD is considerably faster than the traditional method, PA, while predicting the optimal solution with higher resolution. For example, GD resulted in 6.22% SFR for the San Francisco climate as an energy efficient optimal solution by only 9 iterations. However, PA required 10,000 iterations to find the optimal solution with the same resolution. Thus, GD has shown a promising result for the future of multi-objective optimization in building design. In addition to the unconstrained optimization, this dissertation applied the second approach, constrained optimization, by imposing different thresholds for two sets of metrics, including daylight availability and glare. Where Useful Daylight Illuminance (UDI) and spatial Daylight Autonomy (sDA) of 100% were used, the inclusive optimal SFRs were 9-10%, 8-10% and 9% for the climates of San Francisco, Austin and Chicago, respectively. For the other set of daylight metrics, MD of 50% and Mean Daylight Glare Probability (mDGP) of 35% were used, which resulted in optimal solutions of 7-14%, 7-11% and 8-13% SFR for San Francisco, Austin and Chicago, respectively. Therefore, multi-objective optimization considering both daylight and energy performance resulted in different inclusive optimal solutions to energy optimization alone. The study also concludes that optimal solutions depend on applied metrics and daylight thresholds. For the third approach this research investigated the monetary gains from energy efficiency and increased productivity. Assuming that productivity does not occur in spaces with poor daylight performance, inclusive optimal solutions will be the scenarios that most probably boost productivity. The study indicated that the energy cost saving is always negligible compared to the monetary gains from minimum increased productivity (1%). This conclusion may influence an owner’s perspective toward the quality of daylight performance and its resultant productivity increase. Although the proposed algorithm (IIA) has been used to perform multi-objective optimization for skylight design, this platform can be used in the design process to optimize any fenestration, including widows, based on daylight availability, glare and energy factors. GD as one of the contributions of this dissertation is a faster and more accurate method which can facilitate the application of multi-objective optimization for daylight analysis in the early stage of design.Architectur