This thesis describes a method for using physically based techniques to model an explosion and the resulting side effects. Explosions are some of the most visually exciting phenomena known to humankind and have become nearly ubiquitous in action films. A realistic computer simulation of this powerful event would be cheaper, quicker, and much less complicated than safely creating the real thing. The immense energy released by a detonation creates a discontinuous localized increase in pressure and temperature. Physicists and engineers have shown that the dissipation of this concentration of energy, which creates all the visible effects, adheres closely to the compressible Navier-Stokes equation. This program models the most noticeable of these results. In order to simulate the pressure and temperature changes in the environment, a three dimensional grid is placed throughout the area around the detonation and a discretized version of the Navier-Stokes equation is applied to the resulting voxels. Objects in the scene are represented as rigid bodies that are animated by the forces created by varying pressure on their hulls. Fireballs, perhaps the most awe-inspiring side effects of an explosion, are simulated using massless particles that flow out from the center of the blast and follow the currents created by the dissipating pressure. The results can then be brought into Maya for evaluation and tweaking.

O crescente número de sistemas de animação que utilizam a cinemática para gerar movimento de objetos vem levando os pesquisadores a buscar outras alternativas para produzir resultados mais realistas. Com base nesta premissa, vários autores começaram a estudar a geração de movimento de objetos sintéticos através da aplicação da dinâmica. Assim surgiram os modelos baseados em leis físicas. Num primeiro momento foram abordados apenas objetos rígidos, passando-se mais tarde a considerar objetos articulados e, por fim, aqueles com características elásticas, também denominados de objetos flexíveis ou deformáveis. O objetivo principal do trabalho é a definição de um modelo para simulação de objetos deformáveis no espaço euclidiano. São abordados tanto o modelo geométrico utilizado como o modelo físico, sendo ressaltadas as forças aplicadas sobre o objeto e as restrições que podem ser impostas pelo mundo virtual no qual o mesmo está inserido. Dentre as forças descritas, pode-se destacar: força gravitacional, elasticidade, força de curvatura e torção, colisão e atrito. A fundamentação do trabalho desenvolvido é apresentada na forma de uma introdução aos sistemas de animação, enfatizando os sistemas baseados em leis físicas e de uma revisão bibliográfica dos métodos de deformação existentes. No que diz respeito à colisão de objetos elásticos, são descritos tanto os métodos estudados para a solução das mesmas, como as técnicas para detecção do choque. A simulação do movimento é descrita sob dois aspectos: o algoritmo utilizado para a geração do movimento e a integração numérica das equações diferenciais no tempo. É abordado ainda, em detalhe, o protótipo desenvolvido com o propósito de validar o modelo proposto, sendo descrita a linguagem criada a fim de permitir a especificação da animação e parâmetros diversos do modelo. Por fim, são apresentados e avaliados os resultados obtidos através do desenvolvimento do modelo proposto por intermédio do protótipo FLEX3D. É dedicada ainda especial atenção às perspectivas futuras deste trabalho. / The growing number of animation systems that use kinematics to generate the motion of objects have led to other alternatives to produce more realistic results. Some authors began to study the animation of synthetic objects through the application of the dynamic concepts, creating the modern physically based models. At first, only rigid objects were treated; later on articulated objects were considered. At last, those with elastic characteristics (called flexible or deformable objects) were taken into consideration. The main goal of this work is to define a simulation model for deformable objects in the euclidean space. Both the geometric and the physical models are presented, considering the forces applied to the object and the constraints defined by the virtual world. Described forces include gravity, elasticity, dumping force, collision and attrition. This work presents an introduction to animation systems focusing the physically based systems. After this, a bibliographic review of the existent deformation methods is made. Methods for detecting and solving the collision between two elastic objects are described. Two aspects of the motion simulation are described: the algorithm used to generate the motion and the numeric integration of the differential equations in time. A prototype named FLEX3D is presented to validate the proposed model. The language used for specifying the animation is described and results obtained through the use of FLEX3D are also presented. Special attention is given to the possible future works.

O crescente número de sistemas de animação que utilizam a cinemática para gerar movimento de objetos vem levando os pesquisadores a buscar outras alternativas para produzir resultados mais realistas. Com base nesta premissa, vários autores começaram a estudar a geração de movimento de objetos sintéticos através da aplicação da dinâmica. Assim surgiram os modelos baseados em leis físicas. Num primeiro momento foram abordados apenas objetos rígidos, passando-se mais tarde a considerar objetos articulados e, por fim, aqueles com características elásticas, também denominados de objetos flexíveis ou deformáveis. O objetivo principal do trabalho é a definição de um modelo para simulação de objetos deformáveis no espaço euclidiano. São abordados tanto o modelo geométrico utilizado como o modelo físico, sendo ressaltadas as forças aplicadas sobre o objeto e as restrições que podem ser impostas pelo mundo virtual no qual o mesmo está inserido. Dentre as forças descritas, pode-se destacar: força gravitacional, elasticidade, força de curvatura e torção, colisão e atrito. A fundamentação do trabalho desenvolvido é apresentada na forma de uma introdução aos sistemas de animação, enfatizando os sistemas baseados em leis físicas e de uma revisão bibliográfica dos métodos de deformação existentes. No que diz respeito à colisão de objetos elásticos, são descritos tanto os métodos estudados para a solução das mesmas, como as técnicas para detecção do choque. A simulação do movimento é descrita sob dois aspectos: o algoritmo utilizado para a geração do movimento e a integração numérica das equações diferenciais no tempo. É abordado ainda, em detalhe, o protótipo desenvolvido com o propósito de validar o modelo proposto, sendo descrita a linguagem criada a fim de permitir a especificação da animação e parâmetros diversos do modelo. Por fim, são apresentados e avaliados os resultados obtidos através do desenvolvimento do modelo proposto por intermédio do protótipo FLEX3D. É dedicada ainda especial atenção às perspectivas futuras deste trabalho. / The growing number of animation systems that use kinematics to generate the motion of objects have led to other alternatives to produce more realistic results. Some authors began to study the animation of synthetic objects through the application of the dynamic concepts, creating the modern physically based models. At first, only rigid objects were treated; later on articulated objects were considered. At last, those with elastic characteristics (called flexible or deformable objects) were taken into consideration. The main goal of this work is to define a simulation model for deformable objects in the euclidean space. Both the geometric and the physical models are presented, considering the forces applied to the object and the constraints defined by the virtual world. Described forces include gravity, elasticity, dumping force, collision and attrition. This work presents an introduction to animation systems focusing the physically based systems. After this, a bibliographic review of the existent deformation methods is made. Methods for detecting and solving the collision between two elastic objects are described. Two aspects of the motion simulation are described: the algorithm used to generate the motion and the numeric integration of the differential equations in time. A prototype named FLEX3D is presented to validate the proposed model. The language used for specifying the animation is described and results obtained through the use of FLEX3D are also presented. Special attention is given to the possible future works.

O crescente número de sistemas de animação que utilizam a cinemática para gerar movimento de objetos vem levando os pesquisadores a buscar outras alternativas para produzir resultados mais realistas. Com base nesta premissa, vários autores começaram a estudar a geração de movimento de objetos sintéticos através da aplicação da dinâmica. Assim surgiram os modelos baseados em leis físicas. Num primeiro momento foram abordados apenas objetos rígidos, passando-se mais tarde a considerar objetos articulados e, por fim, aqueles com características elásticas, também denominados de objetos flexíveis ou deformáveis. O objetivo principal do trabalho é a definição de um modelo para simulação de objetos deformáveis no espaço euclidiano. São abordados tanto o modelo geométrico utilizado como o modelo físico, sendo ressaltadas as forças aplicadas sobre o objeto e as restrições que podem ser impostas pelo mundo virtual no qual o mesmo está inserido. Dentre as forças descritas, pode-se destacar: força gravitacional, elasticidade, força de curvatura e torção, colisão e atrito. A fundamentação do trabalho desenvolvido é apresentada na forma de uma introdução aos sistemas de animação, enfatizando os sistemas baseados em leis físicas e de uma revisão bibliográfica dos métodos de deformação existentes. No que diz respeito à colisão de objetos elásticos, são descritos tanto os métodos estudados para a solução das mesmas, como as técnicas para detecção do choque. A simulação do movimento é descrita sob dois aspectos: o algoritmo utilizado para a geração do movimento e a integração numérica das equações diferenciais no tempo. É abordado ainda, em detalhe, o protótipo desenvolvido com o propósito de validar o modelo proposto, sendo descrita a linguagem criada a fim de permitir a especificação da animação e parâmetros diversos do modelo. Por fim, são apresentados e avaliados os resultados obtidos através do desenvolvimento do modelo proposto por intermédio do protótipo FLEX3D. É dedicada ainda especial atenção às perspectivas futuras deste trabalho. / The growing number of animation systems that use kinematics to generate the motion of objects have led to other alternatives to produce more realistic results. Some authors began to study the animation of synthetic objects through the application of the dynamic concepts, creating the modern physically based models. At first, only rigid objects were treated; later on articulated objects were considered. At last, those with elastic characteristics (called flexible or deformable objects) were taken into consideration. The main goal of this work is to define a simulation model for deformable objects in the euclidean space. Both the geometric and the physical models are presented, considering the forces applied to the object and the constraints defined by the virtual world. Described forces include gravity, elasticity, dumping force, collision and attrition. This work presents an introduction to animation systems focusing the physically based systems. After this, a bibliographic review of the existent deformation methods is made. Methods for detecting and solving the collision between two elastic objects are described. Two aspects of the motion simulation are described: the algorithm used to generate the motion and the numeric integration of the differential equations in time. A prototype named FLEX3D is presented to validate the proposed model. The language used for specifying the animation is described and results obtained through the use of FLEX3D are also presented. Special attention is given to the possible future works.

Background. Several methods have been used to simulate soft body deformation, such as mass-spring systems and position-based dynamics. This has been done using tetrahedral mesh models for preservation of shape and volume. In real-time applications however, there is a limitation to how high resolution the model can be, creating the need for optimizations. Objectives. To achieve better performance for high resolution models, tetrahedral deformation is used, making it possible for the tetrahedral mesh and triangle mesh to use different resolutions. In combination with this, the GPU is used to execute the simulation in parallel, improving performance further. Methods. For evaluation of performance and accuracy, an implementation was created to simulate soft body deformation using extended position-based dynamics and the Vulkan graphics API, with the option to use tetrahedral deformation. By experimentation, comparisons are made between using different resolutions on the tetrahedral mesh to the full resolution in terms of performance and accuracy. Results. The results show that performance and accuracy are altered when using tetrahedral deformation on lower resolution tetrahedral mesh. The performance is improved based on the decrease in workload, such as with higher base resolution models or multiple soft bodies. The accuracy is however not correlated to the reduction of resolution, but instead dependant on the rest shape of the model used. Conclusions. The implementation created demonstrates a new optimization that can be used to simulate soft body deformation in parallel on the GPU, with a smaller change in accuracy. Improvements exist in areas of usability, features and other optimizations that can be further explored in future research.

<p>This thesis describes a system for dealing with free surface fluid simulations, and the components needed in order to construct such a system. It builds upon recent research, but in a computer graphics context the amount of available literature is limited and difficult to implement. Because of this, the text aims at providing a solid foundation of the mathematics needed, at explaining in greater detail the steps needed to solve the problem, and lastly at improving some aspects of the animation process as it has been described in earlier works. </p><p>The aim of the system itself is to provide visually plausible renditions of animated fluids in three dimensions in a manner that allows it to be usable in a visual effects production context. </p><p>The novel features described include a generalized interaction layer providing greater control to artists, a new way of dealing with moving objects that interact with the fluid and a method for adding source and drain capabilities.</p>

This thesis presents an automatic animation system for jellyfish that is based on a physical simulation of the organism and its surrounding fluid. Our goal is to explore the unusual style of locomotion, namely jet propulsion, which is utilized by jellyfish. The organism achieves this propulsion by contracting its body, expelling water, and propelling itself forward. The organism then expands again to refill itself with water for a subsequent stroke. We endeavor to model the thrust achieved by the jellyfish, and also the evolution of the organism's geometric configuration. <p> We restrict our discussion of locomotion to fully grown adult jellyfish, and we restrict our study of locomotion to the resonant gait, which is the organism's most active mode of locomotion, and is characterized by a regular contraction rate that is near one of the creature's resonant frequencies. We also consider only species that are axially symmetric, and thus are able to reduce the dimensionality of our model. We can approximate the full 3D geometry of a jellyfish by simulating a 2D slice of the organism. This model reduction yields plausible results at a lower computational cost. From the 2D simulation, we extrapolate to a full 3D model. To prevent our extrapolated model from being artificially smooth, we give the final shape more variation by adding noise to the 3D geometry. This noise is inspired by empirical data of real jellyfish, and also by work with continuous noise functions from the graphics community. <p> Our 2D simulations are done numerically with ideas from the field of computational fluid dynamics. Specifically, we simulate the elastic volume of the jellyfish with a spring-mass system, and we simulate the surrounding fluid using the semi-Lagrangian method. To couple the particle-based elastic representation with the grid-based fluid representation, we use the immersed boundary method. We find this combination of methods to be a very efficient means of simulating the 2D slice with a minimal compromise in physical accuracy.

This thesis presents an automatic animation system for jellyfish that is based on a physical simulation of the organism and its surrounding fluid. Our goal is to explore the unusual style of locomotion, namely jet propulsion, which is utilized by jellyfish. The organism achieves this propulsion by contracting its body, expelling water, and propelling itself forward. The organism then expands again to refill itself with water for a subsequent stroke. We endeavor to model the thrust achieved by the jellyfish, and also the evolution of the organism's geometric configuration. <p> We restrict our discussion of locomotion to fully grown adult jellyfish, and we restrict our study of locomotion to the resonant gait, which is the organism's most active mode of locomotion, and is characterized by a regular contraction rate that is near one of the creature's resonant frequencies. We also consider only species that are axially symmetric, and thus are able to reduce the dimensionality of our model. We can approximate the full 3D geometry of a jellyfish by simulating a 2D slice of the organism. This model reduction yields plausible results at a lower computational cost. From the 2D simulation, we extrapolate to a full 3D model. To prevent our extrapolated model from being artificially smooth, we give the final shape more variation by adding noise to the 3D geometry. This noise is inspired by empirical data of real jellyfish, and also by work with continuous noise functions from the graphics community. <p> Our 2D simulations are done numerically with ideas from the field of computational fluid dynamics. Specifically, we simulate the elastic volume of the jellyfish with a spring-mass system, and we simulate the surrounding fluid using the semi-Lagrangian method. To couple the particle-based elastic representation with the grid-based fluid representation, we use the immersed boundary method. We find this combination of methods to be a very efficient means of simulating the 2D slice with a minimal compromise in physical accuracy.

This thesis describes a system for dealing with free surface fluid simulations, and the components needed in order to construct such a system. It builds upon recent research, but in a computer graphics context the amount of available literature is limited and difficult to implement. Because of this, the text aims at providing a solid foundation of the mathematics needed, at explaining in greater detail the steps needed to solve the problem, and lastly at improving some aspects of the animation process as it has been described in earlier works. The aim of the system itself is to provide visually plausible renditions of animated fluids in three dimensions in a manner that allows it to be usable in a visual effects production context. The novel features described include a generalized interaction layer providing greater control to artists, a new way of dealing with moving objects that interact with the fluid and a method for adding source and drain capabilities.

Dans cette thèse, nous proposons de nouvelles representations pourles poses du mouvement humain, apprises sur des données réelles, envue d’une synthèse de nouveaux mouvements en temps-réel. Dans unepremière partie, nous exploitons une méthode statistique adaptée auxgroupes de Lie (Analyse en Géodésiques Principales, AGP) pour approximerla variété des poses d’un sujet en mouvement, à partir de donnéesde capture de mouvement. Nous proposons un algorithme de cinématiqueinverse exploitant cette paramétrisation réduite, permettantpar construction de synthétiser des poses proches des données initiales.Nous validons ce modèle cinématique par une application à la compressionde données de mouvements, dans laquelle seules quelques trajectoiresdes extrémités des membres du squelettes permettent de reconstruireune bonne approximation de l’ensemble des données initiales.Dans une deuxième partie, nous étendons cette approche à l’animationphysique de personnages virtuels. La paramétrisation réduitepar AGP fournit les coordonnées généralisées de la formulation Lagrangiennede la mécanique. Nous dérivons un intégrateur temporelexplicite basé sur les intégrateurs variationnels. Afin d’en améliorer lastabilité, nous proposons un modèle d’amortissement inspiré de l’algorithmede Levenberg-Marquardt. Nous présentons également une méthodegéométrique d’apprentissage des limites angulaires sur des donnéesde capture de mouvement, ainsi que leur application comme contraintescinématiques.Dans une troisième partie, nous abordons le problème du contrôledu mouvement. En formulant les étapes de la simulation physique d’unepart, et de la cinématique inverse d’autre part comme deux programmesquadratiques, nous proposons un algorithme de pseudo-contrôle parinterpolation des métriques, permettant un compromis intuitif entre simulationphysique non-contrôlée, et cinématique inverse. Cette approchefaisant intervenir des forces externes, nous proposons une formulationalternative, utilisant uniquement les forces associées à la paramétrisationréduite des poses. Cette formulation est obtenue par relaxationdu problème théorique de contrôle sous contraintes unilatérales, nonconvexe,en un programme quadratique convexe. Ces algorithmes sontévalués sur des contrôleurs d’équilibre et de suivi. / In this thesis, we propose novel, data-driven representations for humanposes, suitable for real-time synthesis of novel character motion. Inthe first part, we exploit Lie group statistical analysis techniques (PrincipalGeodesic Analysis, PGA) to approximate the pose manifold of amotion capture sequence by a reduced set of pose geodesics. We proposean inverse kinematics algorithm using this reduced parametrizationto automatically produce poses that are close to the learning set. Wedemonstrate the efficiency of the resulting pose model by an applicationto motion capture data compression, where only a few end-effector trajectoriesare used to recover a good approximation of the initial data.In the second part, we extend this approach to the physically-basedanimation of virtual characters. The PGA-reduced parametrization providesgeneralized coordinates in a Lagrangian formulation of mechanics.We derive an explicit time integrator by approximating existingvariational integrators, and propose a damping model based on theLevenberg-Marquardt algorithm. We also describe a geometric, datadriven,angular limit learning algorithm, and the associated kinematicconstraints.In the third part, we reach the problem of task-space motion control.By formulating both physical simulation and inverse kinematicstime stepping schemes as two quadratic programs, we propose a simplepseudo-control algorithm that interpolates between the two metrics.This allows for an intuitive trade-off between uncontrolled simulationand kinematic manipulation. Since this approach makes use of externalforces, we propose an alternate formulation using only the generalizedforces associated to the pose parametrization. A control algorithmis obtained by the relaxation of the exact, non-convex control problemunder unilateral constraints, into a convex quadratic program. Thesealgorithms are evaluated on simple balance and tracking controllers.