Animating physical phenomena with embedded surface meshes

Accurate computational representations of highly deformable surfaces are indispensable in the fields of computer animation, medical simulation, computer vision, digital modeling, and computational physics. The focus of this dissertation is on the animation of physics-based phenomena with highly detailed deformable surfaces represented by triangle meshes. We first present results from an algorithm that generates continuum mechanics animations with intricate surface features. This method combines a finite element method with a tetrahedral mesh generator and a high resolution surface mesh, and it is orders of magnitude more efficient than previous approaches. Next, we present an efficient solution for the challenging problem of computing topological changes in detailed dynamic surface meshes. We then introduce a new physics-inspired surface tracking algorithm that is capable of preserving arbitrarily thin features and reproducing realistic fine-scale topological changes like Rayleigh-Plateau instabilities. This physics-inspired surface tracking technique also opens the door for a unique coupling between surficial finite element methods and volumetric finite difference methods, in order to simulate liquid surface tension phenomena more efficiently than any previous method. Due to its dramatic increase in computational resolution and efficiency, this method yielded the first computer simulations of a fully developed crown splash with droplet pinch off.Ph.D.Committee Chair: Turk, Greg; Committee Member: Essa, Irfan; Committee Member: Liu, Karen; Committee Member: Mucha, Peter J.; Committee Member: Rossignac, Jare

Collision Detection and Merging of Deformable B-Spline Surfaces in Virtual Reality Environment

This thesis presents a computational framework for representing, manipulating and merging rigid and deformable freeform objects in virtual reality (VR) environment. The core algorithms for collision detection, merging, and physics-based modeling used within this framework assume that all 3D deformable objects are B-spline surfaces. The interactive design tool can be represented as a B-spline surface, an implicit surface or a point, to allow the user a variety of rigid or deformable tools. The collision detection system utilizes the fact that the blending matrices used to discretize the B-spline surface are independent of the position of the control points and, therefore, can be pre-calculated. Complex B-spline surfaces can be generated by merging various B-spline surface patches using the B-spline surface patches merging algorithm presented in this thesis. Finally, the physics-based modeling system uses the mass-spring representation to determine the deformation and the reaction force values provided to the user. This helps to simulate realistic material behaviour of the model and assist the user in validating the design before performing extensive product detailing or finite element analysis using commercially available CAD software. The novelty of the proposed method stems from the pre-calculated blending matrices used to generate the points for graphical rendering, collision detection, merging of B-spline patches, and nodes for the mass spring system. This approach reduces computational time by avoiding the need to solve complex equations for blending functions of B-splines and perform the inversion of large matrices. This alternative approach to the mechanical concept design will also help to do away with the need to build prototypes for conceptualization and preliminary validation of the idea thereby reducing the time and cost of concept design phase and the wastage of resources

SOFA: A Multi-Model Framework for Interactive Physical Simulation

International audienceSOFA (Simulation Open Framework Architecture) is an open-source C++ library primarily targeted at interactive computational medical simulation. SOFA facilitates collaborations between specialists from various domains, by decomposing complex simulators into components designed independently and organized in a scenegraph data structure. Each component encapsulates one of the aspects of a simulation, such as the degrees of freedom, the forces and constraints, the differential equations, the main loop algorithms, the linear solvers, the collision detection algorithms or the interaction devices. The simulated objects can be represented using several models, each of them optimized for a different task such as the computation of internal forces, collision detection, haptics or visual display. These models are synchronized during the simulation using a mapping mechanism. CPU and GPU implementations can be transparently combined to exploit the computational power of modern hardware architectures. Thanks to this flexible yet efficient architecture, \sofa{} can be used as a test-bed to compare models and algorithms, or as a basis for the development of complex, high-performance simulators

Robust interactive simulation of deformable solids with detailed geometry using corotational FEM

This thesis focuses on the interactive simulation of highly detailed deformable solids modelled with the Corotational Finite Element Method. Starting from continuum mechanics we derive the discrete equations of motion and present a simulation scheme with support for user-in-the-loop interaction, geometric constraints and contact treatment. The interplay between accuracy and computational cost is discussed in depth, and practical approximations are analyzed with an emphasis on robustness and efficiency, as required by interactive simulation. The first part of the thesis focuses on deformable material discretization using the Finite Element Method with simplex elements and a corotational linear constitutive model, and presents our contributions to the solution of widely reported robustness problems in case of large stretch deformations and finite element degeneration. First,we introduce a stress differential approximation for quasi-implicit corotational linear FEM that improves its results for large deformations and closely matches the fullyimplicit solution with minor computational overhead. Next, we address the problem ofrobustness and realism in simulations involving element degeneration, and show that existing methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new continuous-time approach, degeneration-aware polar decomposition, that avoids such flaws and yields robust degeneration recovery. In the second part we focus on geometry representation and contact determination for deformable solids with highly detailed surfaces. Given a high resolution closed surface mesh we automatically build a coarse embedding tetrahedralization and a partitioned representation of the collision geometry in a preprocess. During simulation, our proposed contact determination algorithm finds all intersecting pairs of deformed triangles using a memory-efficient barycentric bounding volume hierarchy, connects them into potentially disjoint intersection curves and performs a topological flood process on the exact intersection surfaces to discover a minimal set of contact points. A novel contact normal definition is used to find contact point correspondences suitable for contact treatment.Aquesta tesi tracta sobre la simulació interactiva de sòlids deformables amb superfícies detallades, modelats amb el Mètode dels Elements Finits (FEM) Corotacionals. A partir de la mecànica del continuu derivem les equacions del moviment discretes i presentem un esquema de simulació amb suport per a interacció d'usuari, restriccions geomètriques i tractament de contactes. Aprofundim en la interrelació entre precisió i cost de computació, i analitzem aproximacions pràctiques fent èmfasi en la robustesa i l'eficiència necessàries per a la simulació interactiva. La primera part de la tesi es centra en la discretització del material deformable mitjançant el Mètode dels Elements Finits amb elements de tipus s'implex i un model constituent basat en elasticitat linial corotacional, i presenta les nostres contribucions a la solució de problemes de robustesa àmpliament coneguts que apareixen en cas de sobreelongament i degeneració dels elements finits. Primer introduïm una aproximació dels diferencials d'estress per a FEM linial corotacional amb integració quasi-implícita que en millora els resultats per a deformacions grans i s'apropa a la solució implícita amb un baix cost computacional. A continuació tractem el problema de la robustesa i el realisme en simulacions que inclouen degeneració d'elements finits, i mostrem que els mètodes existents presenten inconvenients que posen en perill la robustesa plausibilitat de la simulació en aplicacions interactives. Proposem un enfocament nou basat en temps continuu, la descomposició polar amb coneixement de degeneració, que evita els inconvenients esmentats i permet corregir la degeneració de forma robusta. A la segona part de la tesi ens centrem en la representació de geometria i la determinació de contactes per a sòlids deformables amb superfícies detallades. A partir d'una malla de superfície tancada construím una tetraedralització englobant de forma automàtica en un preprocés, i particionem la geometria de colisió. Proposem un algorisme de detecció de contactes que troba tots els parells de triangles deformats que intersecten mitjançant una jerarquia de volums englobants en coordenades baricèntriques, els connecta en corbes d'intersecció potencialment disjuntes i realitza un procés d'inundació topològica sobre les superfícies d'intersecció exactes per tal de descobrir un conjunt mínim de punts de contacte. Usem una definició nova de la normal de contacte per tal de calcular correspondències entre punts de contacte útils per al seu tractament.Postprint (published version

Frictional Contact in Interactive Deformable Environments

L\u2019uso di simulazioni garantisce notevoli vantaggi in termini di economia, realismo e di flessibilit\ue0 in molte aree di ricerca e in ambito dello sviluppo tecnologico. Per questo motivo le simulazioni vengono usate spesso in ambiti quali la prototipazione di parti meccaniche, nella pianificazione e nell\u2019addestramento di procedure di assemblaggio e disassemblaggio inoltre, di recente, le simulazioni si sono dimostrate validi strumenti anche nell\u2019assistenza e nell\u2019addestramento ai chirurghi, in particolare nel caso della chirurgia laparoscopica. La chirurgia laparoscopica, infatti, \ue8 considerata lo standard per molte procedure chirurgiche. La principale differenza rispetto alla chirurgia tradizionale risiede nella notevole limitazione che ha il chirurgo nell\u2019interagire e nel percepire l\u2019ambiente in lavora, sia nella vista che nel tatto. Questo rappresenta una forte limitazione per il chirurgo a cui \ue8 richiesta una lunga fase di addestramento prima di poter ottenere la necessaria destrezza per intervenire in laparoscopia con profitto. Queste limitazioni, d\u2019altra parte, rendono la laparoscopia il candidato ideale per l\u2019introduzione della simulazione nell\u2019addestramento. Attualmente sono disponibili in commercio dei software per l\u2019addestramento alla laparoscopia, tuttavia essi sono in genere basati su modelli rigidi, o modelli che comunque mancano del necessario realismo fisico. L\u2019introduzione di modelli deformabili migliorerebbe notevolmente l\u2019accuratezza e il realismo delle simulazioni. Nel caso dell\u2019addestramento il maggior realismo permetterebbe all\u2019utente di acquisire non solo le conoscenze motorie basilari ma anche capacit\ue0 e conoscenze di pi\uf9 alto livello. I corpi rigidi, infatti, rappresentano una buona approssimazione della realt\ue0 solo in situazioni particolari ed entro intervalli di sollecitazioni molto ristretti. Quando si considerano materiali non ingegneristici, come accade nelle simulazioni chirurgiche, le deformazioni non possono essere trascurate senza compromettere irrimediabilmente il realismo dei risultati. L\u2019uso di modelli deformabili tuttavia introduce notevole complessit\ue0 computazionale per il calcolo della fisica che regola le deformazioni e limita fortemente l\u2019uso di dati precalcolati, spesso utilizzati per velocizzare la fase di identificazione delle collisioni tra i corpi. I ritardi dovuti all\u2019uso di modelli deformabili rappresentano un grosso limite soprattutto nelle applicazioni interattive che, per consentire all\u2019utente di interagire con l\u2019ambiente, richiedono il calcolo della simulazione entro intervalli di tempo molto ridotti. In questa tesi viene affrontato il tema della simulazione di ambienti interattivi composti da corpi deformabili che interagiscono con attrito. Vengono analizzati e sviluppati differenti tecniche e metodi per le diverse componenti della simulazione: dalla simulazione di modelli deformabili, agli algoritmi di identificazione e soluzione delle collisioni e alla modellazione e integrazione dell\u2019attrito nella simulazione. In particolare vengono valutati i principali metodi che rappresentano lo stato dell\u2019arte nella modellazione di materiali deformabili. L\u2019analisi considera i fondamenti fisici su cui i modelli si basano e quindi sul grado di realismo che possono garantire in termini di deformazioni modellabili e la semplicit\ue0 d\u2019uso degli stessi (ovvero la facilit\ue0 di comprensione del metodo, la calibrazione del modello e la possibilit\ue0 di adattare il modello a situazioni differenti) ma viene considerata anche la complessit\ue0 computazionale di ciascun metodo in quanto essa rappresenta un fattore estremamente importante nella scelta e nell\u2019uso dei modelli deformabili nelle simulazioni. Il confronto dei differenti modelli e le caratteristiche identificate hanno motivato lo sviluppo di un metodo innovativo per fornire un\u2019interfaccia comune ai vari metodi di simulazione dei tessuti deformabili. Tale interfaccia ha il vantaggio di fornire dei metodi omogenei per la manipolazione dei diversi modelli deformabili. Ci\uf2 garantisce la possibilit\ue0 di scambiare il modello usato per la simulazione delle deformazioni mantenendo inalterati le altre strutture dati e i metodi della simulazione. L\u2019introduzione di tale interfaccia unificata si dimostra particolarmente vantaggiosa in quanto permette l\u2019uso di un solo metodo per l\u2019identificazione delle collisioni per tutti i differenti modelli deformabili. Ci\uf2 semplifica molto l\u2019analisi e la definizione dei requisiti di tale modulo software. L\u2019identificazione delle collisioni tra modelli rigidi generalmente precalcola delle partizioni dello spazio in cui i corpi sono definiti oppure sfrutta la suddivisione del corpo analizzato in parti convesse per velocizzare la simulazione. Nel caso di modelli deformabili non \ue8 possibile applicare tali tecniche a causa dei continui cambiamenti nella configurazione dei corpi. Dopo che le collisioni tra i corpi sono state riconosciute e che i punti di contatto sono stati identificati e necessario risolvere le collisioni tenendo conto della fisica sottostante i contatti. Per garantire il realismo \ue8 necessario assicurare che i corpi non si compenetrino mai e che nella simulazione delle collisioni tutti i fenomeni fisici di interesse coinvolti nel contatto tra i corpi vengano considerati: questi includono le forze elastiche che si esercitano tra i corpi e le forze di attrito che si generano lungo le superfici di contatto. L\u2019innovativo metodo proposto per la soluzione delle collisioni garantisce il realismo della simulazione e l\u2019integrazione con l\u2019interfaccia proposta per la gestione unificata dei modelli. Una caratteristica importante dei tessuti biologici \ue8 il comportamento anisotropico, dovuto, in genere, alla loro struttura fibrosa. In questa tesi viene proposto un nuovo metodo per aggiungere l\u2019anisotropia al comportamento dei modelli massa molla. Il metodo ha il vantaggio di mantenere la velocit\ue0 computazionale e la semplicit\ue0 di implementazione dei modelli massa molla classici e riesce a differenziare efficacemente la risposta del modello alle sollecitazioni lungo le differenti direzioni. Le tecniche descritte sono state integrate in due applicazioni che forniscono la simulazione della fisica di ambienti con corpi deformabili. La prima delle due implementa tutti i metodi descritti per la simulazione dei modelli deformabili, identifica le collisioni con precisione e le risolve fornendo la possibilit\ue0 di scegliere il modello di attrito pi\uf9 adatto, dimostrando cos\uec la fattibilit\ue0 dell\u2019approccio proposto. La limitazione principale di tale simulatore risiede nell\u2019alto tempo di calcolo richiesto per la simulazione dei singoli passi di simulazione. Tale limitazione \ue8 stata superata in una seconda implementazione che sfrutta il parallelismo intrinseco delle simulazioni fisiche per ottimizzare gli algoritmi e che, quindi, riesce a sfruttare al meglio la potenza computazionale delle architetture hardware parallele. Al fine di ottenere le prestazioni richieste per la simulazione di ambienti interattivi con ritorno di forza, la simulazione \ue8 basata su un algoritmo di identificazione delle collisioni semplificato, ma implementa gli altri metodi descritti in questa tesi. L\u2019implementazione parallela sfrutta le capacit\ue0 di calcolo delle moderne schede video munite di processori altamente paralleli e ci\uf2 permette di aggiornare la scena ogni millisecondo. Questo elimina ogni discontinuit\ue0 nel ritorno di forza reso all\u2019utente e nell\u2019aggiornamento della grafica della scena, inoltre garantisce il realismo necessario alla simulazione fisica sottostante. Le applicazioni implementate provano la fattibilit\ue0 della simulazione della fisica di interazioni complesse tra corpi deformabili. Inoltre, l\u2019implementazione parallela della simulazione rappresenta un promettente punto di partenza per la realizzazione di simulazioni interattive che potr\ue0 essere utilizzato in ambiti di ricerca differenti, quali l\u2019addestramento di chirurghi o la prototipazione rapida.The use of simulations provides great advantages in term of economy, realism, and adaptability to user requirements in many research and technological fields. For this reason simulations are currently exploited, for example, in prototyping of machinery parts, in assembly-disassembly test or training and, recently, simulations have also allowed the development of many useful and promising tools for the assistance and learning of surgical procedures. This is particularly true for laparoscopic intervention. Laparoscopy, in fact, represents the gold standard for many surgical procedures. The principal difference from standard surgery is the reduction of the surgeon ability to perceive the surgical scenario, both from visual and tactile point of view. This represents a great limitation for surgeons who undergo long training before being able to perform laparoscopic intervention with proficiency. This, on the other hand, makes laparoscopy an excellent candidate for the use of simulations for training. Some commercial training softwares are already available on the market, but they are usually based on rigid body models that completely lack the physical realism. The introduction of deformable models may leads to a great increment in terms of realism and accuracy. And, in the case of laparoscopy trainer it may allow the user to learn not only basic motor skills, but also higher level capabilities and knowledge. Rigid bodies, in fact, represents a good approximation of reality only in some situations and in very restricted ranges of solicitations. In particular, when non engineering materials are involved, as happens in surgical simulations, deformations cannot be neglected without completely loosing the realism of the environment. The use of deformable models, however, is limited for the high computational costs involved in the computation of the physics undergoing the deformations and because of the reduction in pre computable data in particular for collision detection between bodies. This represents a very limiting factor in interactive environments where, to allow the user to interactively control the virtual bodies, the simulation should be performed in real time. In this thesis we address the simulation of interactive environment populated with deformable models that interact with frictional contacts. This includes the analysis and the development of different techniques which implement the various parts of the simulation: mainly the methods for the simulation of deformable models, the collision detection and collision solution techniques but also the modelling and the integration of suitable friction models in the simulation. In particular we evaluated the principal methods that represent the state of the art in soft tissue modeling. Our analysis is based on the physical background of each method and thus on its realism in terms of deformations that the method can mimic and on the ease of use (i.e. method understanding, calibration and ability to adapt to different scenarios) but we also compared the computational complexity of different models, as it represents an extremely important factor in the choice and in the use of models in simulations. The comparison of different features in analyzed methods motivated us to the development of an innovative method to wrap in a common representation framework different methodologies of soft tissue simulation. This framework has the advantage of providing a unified interface for all the deformable models and thus it provides the ability to switch between deformable model keeping unchanged all other data structures and methods of the simulation. The use of this unique interface allows us to use one single method to perform the collision detection phase for all the analyzed deformable models, this greatly helped during the identification of requirements and features of such software module. Collision detection phase, when applied to rigid bodies, usually takes advantage of pre computation to subdivide body shapes in convex elements or to construct partitions of the space in which the body is defined to speed up the computation. When handling deformable models this is not possible because of the continuous changes in bodies shape. The collision detection method used in this work takes into account this problem and regularly adapt the data structures to the body configuration. After collisions have been detected and contact points have been identified on colliding bodies, it is necessary to solve the collision in a physics based way. To this extent we have to ensure that objects never compenetrate during the simulation and that, when solving collisions, all the physical phenomena involved in the contact of real bodies are taken into account: this include the elastic response of bodies during the contact and the frictional force exerted between each pair of colliding bodies. The innovative method for solving collision that we describe in this thesis ensures the realism of the simulation and the seamless interaction with the common framework used to integrate deformable models. One important feature of biologic tissues is their anisotropic behavior that usually comes from the fibrous structure of these tissues. In this thesis we propose a new method to introduce anisotropy in mass spring model. The method has the advantages of preserving the speed and ease of implementation of the model and it effectively introduces differentiation of the model behavior along the chosen directions. The described techniques have been integrated in two applications that allows the physical simulation of environments populated with deformable models. The first application implements all the described methods to simulate deformable models, it performs precise collision detection and solution with the possibility to chose the most suitable friction model for the simulation. It demonstrates the effectiveness of the proposed framework. The main limitation of this simulator, i.e. its high computation time, is tackled and solved in a second application that exploits the intrinsic parallelism of physical simulations to optimize the implementation and to exploit parallel architecture computational power. To obtain the performances required for an interactive environment the simulation is based on a simplified collision detection algorithm, but it features all the other techniques described in this thesis. The parallel implementation exploits graphic cards processor, a highly parallel architecture that update the scene every milliseconds. This allows the rendering of smooth haptic feedback to the user and ensures the realism of the physics simulation. The implemented applications prove the feasibility of the simulation of complex interactions between deformable models with physics realism. In addition, the parallel implementation of the simulator represents a promising starting point for the development of interactive simulations that can be used in different fields of research, such as surgeon training or fast prototyping

Real-time hybrid cutting with dynamic fluid visualization for virtual surgery

It is widely accepted that a reform in medical teaching must be made to meet today's high volume training requirements. Virtual simulation offers a potential method of providing such trainings and some current medical training simulations integrate haptic and visual feedback to enhance procedure learning. The purpose of this project is to explore the capability of Virtual Reality (VR) technology to develop a training simulator for surgical cutting and bleeding in a general surgery

View-dependent adaptive cloth simulation

This paper describes a method for view-dependent cloth simulation using dynamically adaptive mesh refinement and coarsening. Given a prescribed camera motion, the method adjusts the criteria controlling refinement to account for visibility and apparent size in the camera's view. Objectionable dynamic artifacts are avoided by anticipative refinement and smoothed coarsening. This approach preserves the appearance of detailed cloth throughout the animation while avoiding the wasted effort of simulating details that would not be discernible to the viewer. The computational savings realized by this method increase as scene complexity grows, producing a 2× speed-up for a single character and more than 4× for a small group

Challenges and Status on Design and Computation for Emerging Additive Manufacturing Technologies

The revolution of additive manufacturing (AM) has led to many opportunities in fabricating complex and novel products. The increase of printable materials and the emergence of novel fabrication processes continuously expand the possibility of engineering systems in which product components are no longer limited to be single material, single scale, or single function. In fact, a paradigm shift is taking place in industry from geometry-centered usage to supporting functional demands. Consequently, engineers are expected to resolve a wide range of complex and difficult problems related to functional design. Although a higher degree of design freedom beyond geometry has been enabled by AM, there are only very few computational design approaches in this new AM-enabled domain to design objects with tailored properties and functions. The objectives of this review paper are to provide an overview of recent additive manufacturing developments and current computer-aided design methodologies that can be applied to multimaterial, multiscale, multiform, and multifunctional AM technologies. The difficulties encountered in the computational design approaches are summarized and the future development needs are emphasized. In the paper, some present applications and future trends related to additive manufacturing technologies are also discussed