Este trabalho apresenta uma proposta de aplicação da técnica de ray-tracing bidirecional em ambientes esféricos, contendo fontes luminosas puntiformes. Trata-se de um trabalho que discorre no contexto da área de Síntese de Imagens Realísticas dentro da Computação Gráfica. O trabalho tem como principal contribuição a definição e o desenvolvimento de uma técnica para simular o fenômeno físico de refração da luz proveniente das fontes luminosas puntiformes da cena. A Síntese de Imagens Realísticas é uma das principais áreas de aplicação e pesquisa da Computação Gráfica. Uma imagem realística é uma imagem que incorpora os efeitos da luz que interage com objetos fisicamente reais. A dificuldade fundamental para a síntese de imagens realísticas se encontra na complexidade do mundo real, que apresenta uma infinidade de graduações de cores, texturas, reflexões, sombras, etc. Para a criação destas imagens realísticas, percorre-se um grande número de estágios, englobando métodos de modelagem, definição da posição de visualização, remoção de elementos ocultos, efeitos de reflexão e refração, e assim por diante. O trabalho está organizado da seguinte forma. Inicialmente, faz-se um estudo aprofundado da Óptica, área da Física que estuda o comportamento da luz no mundo real. A seguir, são apresentados algoritmos que simulam este comportamento da luz, enfatizando-se o algoritmo de rastreamento de raios (ray-tracing). Discute-se a seguir os principais problemas relacionados a simulação de objetos transparentes na Computação Gráfica. Então, uma proposta para a simulação em ambientes esféricos da refração da luz que provem diretamente das fontes luminosas puntiformes da cena a apresentada. Esta proposta baseia-se na utilização do algoritmo de rastreamento bidirecional de raios. O algoritmo apresentado é composto de duas fases. Na primeira etapa, são geradas as fontes secundarias de luz. Na segunda etapa, utiliza-se a informação obtida na primeira etapa para simular a refração da luz que provem diretamente das fontes luminosas da cena. As fontes secundarias de luz tem sua origem na utilização dos objetos esféricos transparentes como lentes esféricas convergentes. A fonte luminosa secundaria localiza-se no ponto imagem da lente, considerando-se como ponto objeto a fonte luminosa puntiforme original. A localização da fonte luminosa secundaria é obtida através da equação dos pontos conjugados. Também armazena-se uma informação relacionada com a área de atuação da fonte luminosa secundaria (angulo de espalhamento). 0 angulo de espalhamento é essencial para que, na segunda fase do algoritmo, seja possível identificar se o ponto atual é iluminado ou não pela fonte secundaria em questão. Finalizando, são geradas imagens tanto no protótipo implementado quanto em um algoritmo de ray-tracing convencional. Os resultados obtidos são comparados em nível de realismo e tempo de execução. / This work presents a proposal of using the bidirectional ray tracing method in spherical modeling environments containing punctual light sources. This project was developed within the field of Computer Graphics, more precisely in the area of synthesis of realistic images. The main contribution of this work is the definition and the development of a method that simulates the light refraction proceeding from localized light sources in the scene. The synthesis of realistic images is one of the main areas of application and research in Computer Graphics. A realistic image is an image that contains light effects interacting with physically real objects. The major difficulty for rendering realistic images is the complexity of the real world, with several color graduations, textures, reflections, shadows, etc. For this rendering, many steps like modeling methods, definition of visualization position, hidden-surface algorithms, reflection and refraction effects, and so forth, are developed. At first, this work presents a study about Optics, the area of Physics that studies the behaviour of light in the real world. In sequence, algorithms that simulate that behaviour are presented, with special attention to ray tracing method. After that, the principal problems of the simulation of transparency in Computer Graphics are discussed. So, a proposal for simulation of the light refraction proceeding from light source in spherical modeling environment, is presented. This proposal is based on use of the bidirectional ray tracing algorithm. This algorithm is divided in two main stages. In the first stage, the secondary light sources are generated. In the second stage, the information about the secondary light sources is utilized to simulate the light refraction directly proceeding from light sources of the scene. The secondary light sources are originated from transparent spherical objects like convergent spherical lenses. The position of the secondary light source is the image point of the lens, corresponding to punctual light source like object point. The position of the secondary light source is calculated by the equation of the conjugated points. Also the information about the scattering angle of the secondary light source is stored. The scattering angle is essential, in first stage of algorithm, to establish if the current point is illuminated by any secondary light source. Finally, images are generated both in the implemented prototype as in conventional ray tracing. The final results of this work are evaluated based on realism and runtime.

Este trabalho apresenta uma proposta de aplicação da técnica de ray-tracing bidirecional em ambientes esféricos, contendo fontes luminosas puntiformes. Trata-se de um trabalho que discorre no contexto da área de Síntese de Imagens Realísticas dentro da Computação Gráfica. O trabalho tem como principal contribuição a definição e o desenvolvimento de uma técnica para simular o fenômeno físico de refração da luz proveniente das fontes luminosas puntiformes da cena. A Síntese de Imagens Realísticas é uma das principais áreas de aplicação e pesquisa da Computação Gráfica. Uma imagem realística é uma imagem que incorpora os efeitos da luz que interage com objetos fisicamente reais. A dificuldade fundamental para a síntese de imagens realísticas se encontra na complexidade do mundo real, que apresenta uma infinidade de graduações de cores, texturas, reflexões, sombras, etc. Para a criação destas imagens realísticas, percorre-se um grande número de estágios, englobando métodos de modelagem, definição da posição de visualização, remoção de elementos ocultos, efeitos de reflexão e refração, e assim por diante. O trabalho está organizado da seguinte forma. Inicialmente, faz-se um estudo aprofundado da Óptica, área da Física que estuda o comportamento da luz no mundo real. A seguir, são apresentados algoritmos que simulam este comportamento da luz, enfatizando-se o algoritmo de rastreamento de raios (ray-tracing). Discute-se a seguir os principais problemas relacionados a simulação de objetos transparentes na Computação Gráfica. Então, uma proposta para a simulação em ambientes esféricos da refração da luz que provem diretamente das fontes luminosas puntiformes da cena a apresentada. Esta proposta baseia-se na utilização do algoritmo de rastreamento bidirecional de raios. O algoritmo apresentado é composto de duas fases. Na primeira etapa, são geradas as fontes secundarias de luz. Na segunda etapa, utiliza-se a informação obtida na primeira etapa para simular a refração da luz que provem diretamente das fontes luminosas da cena. As fontes secundarias de luz tem sua origem na utilização dos objetos esféricos transparentes como lentes esféricas convergentes. A fonte luminosa secundaria localiza-se no ponto imagem da lente, considerando-se como ponto objeto a fonte luminosa puntiforme original. A localização da fonte luminosa secundaria é obtida através da equação dos pontos conjugados. Também armazena-se uma informação relacionada com a área de atuação da fonte luminosa secundaria (angulo de espalhamento). 0 angulo de espalhamento é essencial para que, na segunda fase do algoritmo, seja possível identificar se o ponto atual é iluminado ou não pela fonte secundaria em questão. Finalizando, são geradas imagens tanto no protótipo implementado quanto em um algoritmo de ray-tracing convencional. Os resultados obtidos são comparados em nível de realismo e tempo de execução. / This work presents a proposal of using the bidirectional ray tracing method in spherical modeling environments containing punctual light sources. This project was developed within the field of Computer Graphics, more precisely in the area of synthesis of realistic images. The main contribution of this work is the definition and the development of a method that simulates the light refraction proceeding from localized light sources in the scene. The synthesis of realistic images is one of the main areas of application and research in Computer Graphics. A realistic image is an image that contains light effects interacting with physically real objects. The major difficulty for rendering realistic images is the complexity of the real world, with several color graduations, textures, reflections, shadows, etc. For this rendering, many steps like modeling methods, definition of visualization position, hidden-surface algorithms, reflection and refraction effects, and so forth, are developed. At first, this work presents a study about Optics, the area of Physics that studies the behaviour of light in the real world. In sequence, algorithms that simulate that behaviour are presented, with special attention to ray tracing method. After that, the principal problems of the simulation of transparency in Computer Graphics are discussed. So, a proposal for simulation of the light refraction proceeding from light source in spherical modeling environment, is presented. This proposal is based on use of the bidirectional ray tracing algorithm. This algorithm is divided in two main stages. In the first stage, the secondary light sources are generated. In the second stage, the information about the secondary light sources is utilized to simulate the light refraction directly proceeding from light sources of the scene. The secondary light sources are originated from transparent spherical objects like convergent spherical lenses. The position of the secondary light source is the image point of the lens, corresponding to punctual light source like object point. The position of the secondary light source is calculated by the equation of the conjugated points. Also the information about the scattering angle of the secondary light source is stored. The scattering angle is essential, in first stage of algorithm, to establish if the current point is illuminated by any secondary light source. Finally, images are generated both in the implemented prototype as in conventional ray tracing. The final results of this work are evaluated based on realism and runtime.

Este trabalho apresenta uma proposta de aplicação da técnica de ray-tracing bidirecional em ambientes esféricos, contendo fontes luminosas puntiformes. Trata-se de um trabalho que discorre no contexto da área de Síntese de Imagens Realísticas dentro da Computação Gráfica. O trabalho tem como principal contribuição a definição e o desenvolvimento de uma técnica para simular o fenômeno físico de refração da luz proveniente das fontes luminosas puntiformes da cena. A Síntese de Imagens Realísticas é uma das principais áreas de aplicação e pesquisa da Computação Gráfica. Uma imagem realística é uma imagem que incorpora os efeitos da luz que interage com objetos fisicamente reais. A dificuldade fundamental para a síntese de imagens realísticas se encontra na complexidade do mundo real, que apresenta uma infinidade de graduações de cores, texturas, reflexões, sombras, etc. Para a criação destas imagens realísticas, percorre-se um grande número de estágios, englobando métodos de modelagem, definição da posição de visualização, remoção de elementos ocultos, efeitos de reflexão e refração, e assim por diante. O trabalho está organizado da seguinte forma. Inicialmente, faz-se um estudo aprofundado da Óptica, área da Física que estuda o comportamento da luz no mundo real. A seguir, são apresentados algoritmos que simulam este comportamento da luz, enfatizando-se o algoritmo de rastreamento de raios (ray-tracing). Discute-se a seguir os principais problemas relacionados a simulação de objetos transparentes na Computação Gráfica. Então, uma proposta para a simulação em ambientes esféricos da refração da luz que provem diretamente das fontes luminosas puntiformes da cena a apresentada. Esta proposta baseia-se na utilização do algoritmo de rastreamento bidirecional de raios. O algoritmo apresentado é composto de duas fases. Na primeira etapa, são geradas as fontes secundarias de luz. Na segunda etapa, utiliza-se a informação obtida na primeira etapa para simular a refração da luz que provem diretamente das fontes luminosas da cena. As fontes secundarias de luz tem sua origem na utilização dos objetos esféricos transparentes como lentes esféricas convergentes. A fonte luminosa secundaria localiza-se no ponto imagem da lente, considerando-se como ponto objeto a fonte luminosa puntiforme original. A localização da fonte luminosa secundaria é obtida através da equação dos pontos conjugados. Também armazena-se uma informação relacionada com a área de atuação da fonte luminosa secundaria (angulo de espalhamento). 0 angulo de espalhamento é essencial para que, na segunda fase do algoritmo, seja possível identificar se o ponto atual é iluminado ou não pela fonte secundaria em questão. Finalizando, são geradas imagens tanto no protótipo implementado quanto em um algoritmo de ray-tracing convencional. Os resultados obtidos são comparados em nível de realismo e tempo de execução. / This work presents a proposal of using the bidirectional ray tracing method in spherical modeling environments containing punctual light sources. This project was developed within the field of Computer Graphics, more precisely in the area of synthesis of realistic images. The main contribution of this work is the definition and the development of a method that simulates the light refraction proceeding from localized light sources in the scene. The synthesis of realistic images is one of the main areas of application and research in Computer Graphics. A realistic image is an image that contains light effects interacting with physically real objects. The major difficulty for rendering realistic images is the complexity of the real world, with several color graduations, textures, reflections, shadows, etc. For this rendering, many steps like modeling methods, definition of visualization position, hidden-surface algorithms, reflection and refraction effects, and so forth, are developed. At first, this work presents a study about Optics, the area of Physics that studies the behaviour of light in the real world. In sequence, algorithms that simulate that behaviour are presented, with special attention to ray tracing method. After that, the principal problems of the simulation of transparency in Computer Graphics are discussed. So, a proposal for simulation of the light refraction proceeding from light source in spherical modeling environment, is presented. This proposal is based on use of the bidirectional ray tracing algorithm. This algorithm is divided in two main stages. In the first stage, the secondary light sources are generated. In the second stage, the information about the secondary light sources is utilized to simulate the light refraction directly proceeding from light sources of the scene. The secondary light sources are originated from transparent spherical objects like convergent spherical lenses. The position of the secondary light source is the image point of the lens, corresponding to punctual light source like object point. The position of the secondary light source is calculated by the equation of the conjugated points. Also the information about the scattering angle of the secondary light source is stored. The scattering angle is essential, in first stage of algorithm, to establish if the current point is illuminated by any secondary light source. Finally, images are generated both in the implemented prototype as in conventional ray tracing. The final results of this work are evaluated based on realism and runtime.

Modern oil and gas exploration depends on a variety of geophysical prospect tools. One of them is reflection seismology that allows to obtain interwell information of sufficient resolution economically. This exploration method collects reflection seismic data on the surface of an area of prospect interest and then uses them to build seismic images of the subsurface. All imaging approaches can be divided into two groups: wave equation-based methods and integral schemes. Kirchhoff migration, which belongs to the second group, is an indispensable tool in seismic imaging due to its flexibility and relatively low computational cost. Unfortunately, the classic formulation of this method images only a part of the surface data, if so-called multipathing is present in it. That phenomenon occurs in complex geologic settings, such as subsalt areas, when seismic waves travel between a subsurface point and a surface location through more than one path. The quality of imaging with Kirchhoff migration in complex geological areas can be improved if multiple paths of ray propagation are included in the integral. Multiple arrivals can be naturally incorporated into the imaging operator if it is expressed as an integral over subsurface take-off angles. In this form, the migration operator involves escape functions that connect subsurface locations with surface seismic data values through escape traveltime and escape positions. These escape quantities are functions of phase space coordinates that are simply related to the subsurface reflection system. The angle-domain integral operator produces output scattering- and dip-angle image gathers, which represent a convenient domain for subsurface analysis. Escape functions for angle-domain imaging can be simply computed with initial-value ray tracing, a Lagrangian computational technique. However, the computational cost of such a bottom-up approach can be prohibitive in practice. The goal of this work was to construct a computationally efficient phase space imaging framework. I designed several approaches to computing escape functions directly in phase space for mapping surface seismic reflection data to the subsurface angle domain. Escape equations have been introduced previously to describe distribution of escape functions in the phase space. Initially, I employed these equations as a basis for building an Eulerian numerical scheme using finite-difference method in the 2-D case. I show its accuracy constraints and suggest a modification of the algorithm to overcome them. Next, I formulate a semi-Lagrangian approach to computing escape functions in 3-D. The second method relies on the fundamental property of continuity of these functions in the phase space. I define locally constrained escape functions and show that a global escape solution can be reconstructed from local solutions iteratively. I validate the accuracy of the proposed methods by imaging synthetic seismic data in several complex 2-D and 3-D models. I draw conclusions about efficiency by comparing the compute time of the imaging tests with the compute time of a well-optimized conventional initial-value ray tracing. / text

<p>Over the past 20 years, the development in ComputationalElectromagnetics has produced a vast choice of methods based onthe large number of existing mathematical formulations of theMaxwell equations. None of them dominate over the others,instead they complement each other and the choice of methoddepends on the frequency range of the electromagnetic waves.This work is focused on the most popular method in the highfrequency scenario, namely the Geometrical Theory ofDiffraction (GTD). The main advantage of GTD is the ability topredict the electromagnetic field asymptotically in the limitof vanishing wavelength, when other methods, such as the Methodof Moments, become computationally too expensive.</p><p>The low cost of GTD is due to both the fact that there is noruntime penalty in increasing the frequency and that the raytracing, which GTD is based on, is a geometrical technique. Thecomplexity is then no longer dependent on electrical size ofthe problem but instead on geometrical sub problems which aremanageable. For industrial applications the geometricalstructures, with which the rays interact, are modelled bytrimmed Non-Uniform Rational B-Spline (NURBS) surfaces, themost recent standard used to represent complex free-formgeometries.</p><p>Due to the introduction of NURBS, the geometrical subproblems tend to be mathematically and numerically cumbersome,but they can be highly simplified by proper Object Orientedprogramming techniques. This allowed us to create a flexiblesoftware package, MIRA: Modular Implementation of Ray Tracingfor Antenna Applications, with an architecture that separatesmathematical algorithms from their implementation details andmodelling. In addition, its design supports hybridisationtechniques in combination with other methods such as Method ofMoment (MoM) and Physical Optics (PO).</p><p>In a first hybrid application, a triangle-based PO solveruses the shadowing information calculated with the ray tracerpart of MIRA. The occlusion is performed between triangles andtheir facing NURBS surfaces rather than between their facingtriangles, thus reducing the complexity. Then the shadowinginformation is used in an iterative MoM-PO process in order tocover higher frequencies, where the contribution of theshadowing effects, in the hybrid formulation, is believed to bemore significant.</p><p>Thesis presented at the Royal Institute of Technology ofStockholm in 2003, for the degree of Licentiate in ScientificComputing.</p>

Saab AB Training &amp; Simulation is specialized on military training, including laserbased training. To continue being the world leader in this area, a new generationof laser simulators needs to be developed. To simplify the development of thishighly complex system, this master thesis have resulted in a MATLAB/Simulinkmodel which simulates the electro-opto/mechanical system representing theirlaser based simulation platform. The focus of this master thesis has been to simulateand control the laser beam deflection. To be more precise, the motors usedto rotate the Risley-prisms deflecting the laser beam is modelled. With a goodmodel of the motors, a control system is applied steering the wedges to a referencerotation angle. The reference rotation angle is difficult to calculate though,since the deflection following several rotary wedges is severely nonlinear. Thereare many ways to calculate the rotation angles, but in this master thesis it will bedone by solving optimization problems in MATLAB. / Saab AB Training &amp; Simulation är specialiserade på militär träning, bland annatbaserad på laser och för att fortsätta vara världsledande inom detta områdekrävs utveckling av en ny generation lasersimulatorer. För att underlätta utvecklingsarbetetav detta högst komplexa system, har i detta examensarbete en simulerbarmodell skapats i MATLAB/Simulink för att kunna simulera det elektroopto/mekaniska system som beskriver deras laserbaserade simulatorplattform.Fokus för detta examensarbete har varit att modellera avlänkningen. Mer ingåendeså modelleras de motorer som används för att rotera Risley-prisman så atten laserstråle uppnår önskad avlänkning. Med en bra modell av motorerna applicerasett reglersystem som styr de roterbara kilarna till referensposition. Referenspositionenär dock komplicerad att beräkna eftersom avlänkningen frånflera roterande kilar beter sig högst olinjärt. För att göra detta finns flera tillvägagångssätt,men i detta examensarbete kommer det att göras genom att lösaoptimeringsproblem i MATLAB.

QC 351 A7 no. 37 / This paper derives four one-parameter families of two-surface optical systems having the property that, relative to a well-defined pair of conjugate points, one finite and the other infinite, third-order spherical aberration is zero. The two surfaces can be either refracting or reflecting. Aperture planes are defined for which third-order astigmatism is zero. An expression for coma is also derived. Assuming that the systems will be constructible, a means of defining domains for the free parameter is indicated. Possible applications of these results to optical design are included.

A síntese de imagens é uma ferramenta valiosa na compreensão de diversos fenômenos da natureza. Nos últimos anos várias abordagens têm sido propostas para sintetizar tais fenômenos. A grande maioria de tais abordagens têm se centralizado no desenvolvimento de modelos procedurais. Porém, cada uma destas técnicas simula exclusivamente um fenômeno natural. Um dos métodos de síntese de imagens fotorealísticas mais proeminente é denominado de Traçado de Raios (Ray Tracing). Contudo, apesar de produzir imagens de excelente qualidade, este método é computacionalmente muito oneroso. A síntese de fenômenos naturais utilizando-se o traçado de raios é um desafio. É importante que este problema seja abordado, apesar da sua complexidade, pois a simulaçao fotorealista da natureza é muito importante para os cientistas e pesquisadores desde o surgimento dos computadores. Um algoritmo versátil e rápido para a síntese de fenômenos da natureza através do traçado de raios utilizando campos de altitude é proposto. O algoritmo utiliza uma modificação do algoritmo do Analisador Diferencial Digital de Bresenham para atravesar uma matriz bidimensional de valores de altitude. A determinação das primitivas geométricas a serem interseccionadas por um raio é obtida num tempo ( N ) , sendo N o número de altitudes no campo de altitude. Este trabalho faz uma comparação em termos de velocidade e realismo deste método com outras abordagens convencionais; e discute as implicações que a implementação deste método traz. Finalmente, destaca-se a simplicidade e versatilidade que este método proporciona devido à pequena quantidade de parâmetros necessária para a síntese de fenômenos naturais utilizando o traçado de raios. Para a criação de animações basta a especificação de novos parâmetros num intervalo de tempo diferente. / Visualization is a powerful tool for better undestanding of several natural phenomena. In recent years, several techniques have been proposed. Considerable interest in natural scene synthesis has focused on procedural models. However, these techniques produce synthetic scenes of only one natural phenomenon. Ray tracing is one of the most photorealistic methods of image syntesis. While providing images of excellent quality, ray tracing is a computationally intensive task. Natural scene synthesis is a challenging problem within the realm of ray tracing. It is important to tackle this problem, despite of its complexity, because photorealistic simulation have been important to scientific community since the appearance of computers. A fast and versatile algorithm for ray tracing natural scenes through height fields is presented. The algorithm employs a modified Bresenham DDA to traverse a two dimensional array of values. The objects tested for intersection are located in ( N ) time where N is the number of values in the field. This work compares the speed-up and photorealism achieved in natural scene synthesis using this method with other algorithms and discusses the implications of implementing this approach. As a final point, the simplicity and versatility of synthesizing complex natural scenes from a few parameters and data is especially attractive. Animated sequences require only the additional specifications of time modified parameters or data.

In this thesis, I apply techniques from the field of computer graphics to ray tracing in astrophysical simulations, and introduce the grace software library. This is combined with an extant radiative transfer solver to produce a new package, taranis. It allows for fully-parallel particle updates via per-particle accumulation of rates, followed by a forward Euler integration step, and is manifestly photon-conserving. To my knowledge, taranis is the first ray-traced radiative transfer code to run on graphics processing units and target cosmological-scale smooth particle hydrodynamics (SPH) datasets. A significant optimization effort is undertaken in developing grace. Contrary to typical results in computer graphics, it is found that the bounding volume hierarchies (BVHs) used to accelerate the ray tracing procedure need not be of high quality; as a result, extremely fast BVH construction times are possible (< 0.02 microseconds per particle in an SPH dataset). I show that this exceeds the performance researchers might expect from CPU codes by at least an order of magnitude, and compares favourably to a state-of-the-art ray tracing solution. Similar results are found for the ray-tracing itself, where again techniques from computer graphics are examined for effectiveness with SPH datasets, and new optimizations proposed. For high per-source ray counts (≳ 104), grace can reduce ray tracing run times by up to two orders of magnitude compared to extant CPU solutions developed within the astrophysics community, and by a factor of a few compared to a state-of-the-art solution. taranis is shown to produce expected results in a suite of de facto cosmological radiative transfer tests cases. For some cases, it currently out-performs a serial, CPU-based alternative by a factor of a few. Unfortunately, for the most realistic test its performance is extremely poor, making the current taranis code unsuitable for cosmological radiative transfer. The primary reason for this failing is found to be a small minority of particles which always dominate the timestep criteria. Several plausible routes to mitigate this problem, while retaining parallelism, are put forward.

This thesis deals with computer generated images. The thesis begins with an overview of a generalised computer graphics system, including a brief survey of typical methods for generating photorealistic images. One such technique, ray tracing, is used as the basis for the work which follows. The overview section concludes with a statement of the aim which is to: Investigate the effective use of available processing power and effective utilisation of available memory by implementing a ray tracing programme which uses space subdivision, multiple processors and a distributed world model database. The problem formulation section describes the ray tracing principle and then introduces the main areas of study. The INMOS Transputer (a building block for concurrent systems) is used to implement the multiple process ray tracer. Space subdivision is achieved by repeated and regular subdivision of a world cube (which contains the scene to be ray traced) into named cubes, called octrees. The subdivision algorithm continues to subdivide space until no octree contains more than a specified number of objects, or until the practical limit of space subdivision is reached. The objects in the world model database are distributed in a round robin manner to the ray trace processes. During execution of the ray trace programme, information about each object is passed between processes by a message mechanism. The concurrent code for the transputer processes, written in OCCAM 2, was developed using timing diagrams and signal flow diagrams derived by analogy from digital electronics. Structure diagrams, modified to be consistent with OCCAM 2 processes, were derived from the timing diagrams and signal flow diagrams. These were used as a basis for the coding. The results show that space subdivision is an effective use of processor power because the number of trial intersections of rays with objects is dramatically reduced. In addition, distribution of the world model database avoids duplication of the database in the memory of each process and hence better utilisation of available memory is achieved. The programmes are supported by a menu driven interface (running on a PC AT) which enables the user to control the ray trace processes running on the transputer board housed in the PC.