Length Constrained Multiresolution Deformation for Surface Wrinkling

International audienceWe present a method for deforming piescewise linear 3D curves on surfaces with constant length constraint. We show how this constraint can be integrated into a multiresolution editing tool allowing an intuitive control of the deformation's extent and aspect. The constraint is enforced following two steps. A first step consists in approximating the initial length by modifying the multiresolution decomposition at some specified scale. In a second step the constraint is axactly enforced by constrained minimization of a smoothness criterion. This process then provides the core of an integrated wrinkling tool for soft tissues modelling. A curve on the mesh is deformed, providing a deformation profile which is propagated in a user-defined neighbourhood

Fast Simulation of Skin Sliding

Skin sliding is the phenomenon of the skin moving over underlying layers of fat, muscle and bone. Due to the complex interconnections between these separate layers and their differing elasticity properties, it is difficult to model and expensive to compute. We present a novel method to simulate this phenomenon at real--time by remeshing the surface based on a parameter space resampling. In order to evaluate the surface parametrization, we borrow a technique from structural engineering known as the force density method which solves for an energy minimizing form with a sparse linear system. Our method creates a realistic approximation of skin sliding in real--time, reducing texture distortions in the region of the deformation. In addition it is flexible, simple to use, and can be incorporated into any animation pipeline

Iterative Solvers for Physics-based Simulations and Displays

La génération d’images et de simulations réalistes requiert des modèles complexes pour capturer tous les détails d’un phénomène physique. Les équations mathématiques qui composent ces modèles sont compliquées et ne peuvent pas être résolues analytiquement. Des procédures numériques doivent donc être employées pour obtenir des solutions approximatives à ces modèles. Ces procédures sont souvent des algorithmes itératifs, qui calculent une suite convergente vers la solution désirée à partir d’un essai initial. Ces méthodes sont une façon pratique et efficace de calculer des solutions à des systèmes complexes, et sont au coeur de la plupart des méthodes de simulation modernes. Dans cette thèse par article, nous présentons trois projets où les algorithmes itératifs jouent un rôle majeur dans une méthode de simulation ou de rendu. Premièrement, nous présentons une méthode pour améliorer la qualité visuelle de simulations fluides. En créant une surface de haute résolution autour d’une simulation existante, stabilisée par une méthode itérative, nous ajoutons des détails additionels à la simulation. Deuxièmement, nous décrivons une méthode de simulation fluide basée sur la réduction de modèle. En construisant une nouvelle base de champ de vecteurs pour représenter la vélocité d’un fluide, nous obtenons une méthode spécifiquement adaptée pour améliorer les composantes itératives de la simulation. Finalement, nous présentons un algorithme pour générer des images de haute qualité sur des écrans multicouches dans un contexte de réalité virtuelle. Présenter des images sur plusieurs couches demande des calculs additionels à coût élevé, mais nous formulons le problème de décomposition des images afin de le résoudre efficacement avec une méthode itérative simple.Realistic computer-generated images and simulations require complex models to properly capture the many subtle behaviors of each physical phenomenon. The mathematical equations underlying these models are complicated, and cannot be solved analytically. Numerical procedures must thus be used to obtain approximate solutions. These procedures are often iterative algorithms, where an initial guess is progressively improved to converge to a desired solution. Iterative methods are a convenient and efficient way to compute solutions to complex systems, and are at the core of most modern simulation methods. In this thesis by publication, we present three papers where iterative algorithms play a major role in a simulation or rendering method. First, we propose a method to improve the visual quality of fluid simulations. By creating a high-resolution surface representation around an input fluid simulation, stabilized with iterative methods, we introduce additional details atop of the simulation. Second, we describe a method to compute fluid simulations using model reduction. We design a novel vector field basis to represent fluid velocity, creating a method specifically tailored to improve all iterative components of the simulation. Finally, we present an algorithm to compute high-quality images for multifocal displays in a virtual reality context. Displaying images on multiple display layers incurs significant additional costs, but we formulate the image decomposition problem so as to allow an efficient solution using a simple iterative algorithm

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Animation, Simulation, and Control of Soft Characters using Layered Representations and Simplified Physics-based Methods

Realistic behavior of computer generated characters is key to bringing virtual environments, computer games, and other interactive applications to life. The plausibility of a virtual scene is strongly influenced by the way objects move around and interact with each other. Traditionally, actions are limited to motion capture driven or pre-scripted motion of the characters. Physics enhance the sense of realism: physical simulation is required to make objects act as expected in real life. To make gaming and virtual environments truly immersive,it is crucial to simulate the response of characters to collisions and to produce secondary effects such as skin wrinkling and muscle bulging. Unfortunately, existing techniques cannot generally achieve these effects in real time, do not address the coupled response of a character's skeleton and skin to collisions nor do they support artistic control. In this dissertation, I present interactive algorithms that enable physical simulation of deformable characters with high surface detail and support for intuitive deformation control. I propose a novel unified framework for real-time modeling of soft objects with skeletal deformations and surface deformation due to contact, and their interplay for object surfaces with up to tens of thousands of degrees of freedom.I make use of layered models to reduce computational complexity. I introduce dynamic deformation textures, which map three dimensional deformations in the deformable skin layer to a two dimensional domain for extremely efficient parallel computation of the dynamic elasticity equations and optimized hierarchical collision detection. I also enhance layered models with responsive contact handling, to support the interplay between skeletal motion and surface contact and the resulting two-way coupling effects. Finally, I present dynamic morph targets, which enable intuitive control of dynamic skin deformations at run-time by simply sculpting pose-specific surface shapes. The resulting framework enables real-time and directable simulation of soft articulated characters with frictional contact response, capturing the interplay between skeletal dynamics and complex,non-linear skin deformations

Numerical Methods in Shape Spaces and Optimal Branching Patterns

The contribution of this thesis is twofold. The main part deals with numerical methods in the context of shape space analysis, where the shape space at hand is considered as a Riemannian manifold. In detail, we apply and extend the time-discrete geodesic calculus (established by Rumpf and Wirth [WBRS11, RW15]) to the space of discrete shells, i.e. triangular meshes with fixed connectivity. The essential building block is a variational time-discretization of geodesic curves, which is based on a local approximation of the squared Riemannian distance on the manifold. On physical shape spaces this approximation can be derived e.g. from a dissimilarity measure. The dissimilarity measure between two shell surfaces can naturally be defined as an elastic deformation energy capturing both membrane and bending distortions. Combined with a non-conforming discretization of a physically sound thin shell model the time-discrete geodesic calculus applied to the space of discrete shells is shown to be suitable to solve important problems in computer graphics and animation. To extend the existing calculus, we introduce a generalized spline functional based on the covariant derivative along a curve in shape space whose minimizers can be considered as Riemannian splines. We establish a corresponding time-discrete functional that fits perfectly into the framework of Rumpf and Wirth, and prove this discretization to be consistent. Several numerical simulations reveal that the optimization of the spline functional—subject to appropriate constraints—can be used to solve the multiple interpolation problem in shape space, e.g. to realize keyframe animation. Based on the spline functional, we further develop a simple regression model which generalizes linear regression to nonlinear shape spaces. Numerical examples based on real data from anatomy and botany show the capability of the model. Finally, we apply the statistical analysis of elastic shape spaces presented by Rumpf and Wirth [RW09, RW11] to the space of discrete shells. To this end, we compute a Fréchet mean within a class of shapes bearing highly nonlinear variations and perform a principal component analysis with respect to the metric induced by the Hessian of an elastic shell energy. The last part of this thesis deals with the optimization of microstructures arising e.g. at austenite-martensite interfaces in shape memory alloys. For a corresponding scalar problem, Kohn and Müller [KM92, KM94] proved existence of a minimizer and provided a lower and an upper bound for the optimal energy. To establish the upper bound, they studied a particular branching pattern generated by mixing two different martensite phases. We perform a finite element simulation based on subdivision surfaces that suggests a topologically different class of branching patterns to represent an optimal microstructure. Based on these observations we derive a novel, low dimensional family of patterns and show—numerically and analytically—that our new branching pattern results in a significantly better upper energy bound

Adaptive Physically Based Models in Computer Graphics

International audienceOne of the major challenges in physically-based modeling is making simulations efficient. Adaptive models provide an essential solution to these efficiency goals. These models are able to self-adapt in space and time, attempting to provide the best possible compromise between accuracy and speed. This survey reviews the adaptive solutions proposed so far in computer graphics. Models are classified according to the strategy they use for adaptation, from time-stepping and freezing techniques to geometric adaptivity in the form of structured grids, meshes, and particles. Applications range from fluids, through deformable bodies, to articulated solids

Modeling of Facial Wrinkles for Applications in Computer Vision

International audienceAnalysis and modeling of aging human faces have been extensively studied in the past decade for applications in computer vision such as age estimation, age progression and face recognition across aging. Most of this research work is based on facial appearance and facial features such as face shape, geometry, location of landmarks and patch-based texture features. Despite the recent availability of higher resolution, high quality facial images, we do not find much work on the image analysis of local facial features such as wrinkles specifically. For the most part, modeling of facial skin texture, fine lines and wrinkles has been a focus in computer graphics research for photo-realistic rendering applications. In computer vision, very few aging related applications focus on such facial features. Where several survey papers can be found on facial aging analysis in computer vision, this chapter focuses specifically on the analysis of facial wrinkles in the context of several applications. Facial wrinkles can be categorized as subtle discontinuities or cracks in surrounding inhomogeneous skin texture and pose challenges to being detected/localized in images. First, we review commonly used image features to capture the intensity gradients caused by facial wrinkles and then present research in modeling and analysis of facial wrinkles as aging texture or curvilinear objects for different applications. The reviewed applications include localization or detection of wrinkles in facial images , incorporation of wrinkles for more realistic age progression, analysis for age estimation and inpainting/removal of wrinkles for facial retouching