Topological modifications of animated surfaces

National audienceTo better understand the purposes of this work, I will first introduce the mathematical notions I used during this internship, as well as the applications that this work could have in the future. This work is mainly based on the Morse Theory and on the algorithms presented in [3] and [5], that is why I will give some details about my implementation and its integration in the original program. It is the starting point for the research step because it highlights the main problems of the previous solutions: thus, I will expose the ideas which have been proposed, implemented and tested. Finally, I will analyze the results provided by this new method, but also its limitations

Robust iso-surface tracking for interactive character skinning

International audienceWe present a novel approach to interactive character skinning, which is robust to extreme character movements, handles skin contacts and produces the effect of skin elasticity (sliding). Our approach builds on the idea of implicit skinning in which the character is approximated by a 3D scalar field and mesh-vertices are appropriately re-projected. Instead of being bound by an initial skinning solution used to initialize the shape at each time step, we use the skin mesh to directly track iso-surfaces of the field over time. Technical problems are two-fold: firstly, all contact surfaces generated between skin parts should be captured as iso-surfaces of the implicit field; secondly, the tracking method should capture elastic skin effects when the joints bend, and as the character returns to its rest shape, so the skin must follow. Our solutions include: new composition operators enabling blending effects and local self-contact between implicit surfaces, as well as a tangential relaxation scheme derived from the as-rigid-as possible energy to solve the tracking problem

Constitutive modelling of shape memory alloys and upscaling of deformable porous media

Shape Memory Alloys (SMAs) are metal alloys which are capable of changing their crystallographic structure as a result of externally applied mechanical or thermal loading. This work is a systematic effort to develop a robust, thermodynamics based, 3-D constitutive model for SMAs with special features, dictated by new experimental observations. The new rate independent model accounts in a unified manner for the stress/thermally induced austenite to oriented martensite phase transformation, the thermally induced austenite to self-accommodated martensite phase transformation as well as the reorientation of self-accommodated martensite under applied stress. The model is implemented numerically in 3-D with the help of return-mapping algorithms. Numerical examples, demonstrating the capabilities of the model are also presented. Further, the stationary Fluid-Structure Interaction (FSI) problem is formulated in terms of incompressible Newtonian fluid and a deformable solid. A numerical method is presented for its solution and a numerical implementation is developed. It is used to verify an existing asymptotic solution to the FSI problem in a simple channel geometry. The SMA model is also used in conjunction with the fluid-structure solver to simulate the behavior of SMA based filtering and flow regulating devices. The work also includes a numerical study of wave propagation in SMA rods. An SMA body subjected to external dynamic loading will experience large inelastic deformations that will propagate through the body as phase transformation and/or detwinning shock waves. The wave propagation problem in a cylindrical SMA is studied numerically by an adaptive Finite Element Method. The energy dissipation capabilities of SMA rods are estimated based on the numerical simulations. Comparisons with experimental data are also performed

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

A system for modelling deformable procedural shapes.

This thesis presents a new procedural paradigm for modelling. The method combines the benefit of compact object descriptions found in procedural modelling along with the advantage of the ability to interact in real-time as is found with interactive modelling techniques. The three main components to this paradigm are geometry generators (the creation of basic object shapes), selectors (the specification of a selection volume), and modifiers (the object transformation functions). The user interacts in real-time with the object, and has complete control over the object formation process. Interaction is stored within appropriate nodes in a creation-history list which can be replayed or partially replayed at any time during the creation process. The parameters associated with each interaction are stored within the node, and are available for editing at any time during the creation process. The concepts presented here remove the problems that most modelling software have, in that the arbitrary editing of object parameters is destructive, in the sense that changing the parameter of one node may cause the object to behave unpredictably. This takes place in real-time, rather than off-line. In some cases real-time interaction is made possible by trading visual quality vs. speed of rendering. This results in the object being rendered at a lower quality, and therefore decisions on whether the object parameters need adjustment may be predicated upon a poor representation of the object. The work presented herein attempts to bridge the divide between the two approaches by providing the user with a powerful and descriptive procedural modelling language that is entirely generated through real-time interaction with the geometric object via an intuitive user interface. The main contributions of this work are that it allows: Procedural objects are specified interactively. Modelling takes place independently of representation (meaning the user does not base their modelling on the (mesh) representation, but rather on the shape they see). Changes to the object are coherent and non-destructive

Animating jellyfish through numerical simulation and symmetry exploitation

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. 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. 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

Contemporary Robotics

This book book is a collection of 18 chapters written by internationally recognized experts and well-known professionals of the field. Chapters contribute to diverse facets of contemporary robotics and autonomous systems. The volume is organized in four thematic parts according to the main subjects, regarding the recent advances in the contemporary robotics. The first thematic topics of the book are devoted to the theoretical issues. This includes development of algorithms for automatic trajectory generation using redudancy resolution scheme, intelligent algorithms for robotic grasping, modelling approach for reactive mode handling of flexible manufacturing and design of an advanced controller for robot manipulators. The second part of the book deals with different aspects of robot calibration and sensing. This includes a geometric and treshold calibration of a multiple robotic line-vision system, robot-based inline 2D/3D quality monitoring using picture-giving and laser triangulation, and a study on prospective polymer composite materials for flexible tactile sensors. The third part addresses issues of mobile robots and multi-agent systems, including SLAM of mobile robots based on fusion of odometry and visual data, configuration of a localization system by a team of mobile robots, development of generic real-time motion controller for differential mobile robots, control of fuel cells of mobile robots, modelling of omni-directional wheeled-based robots, building of hunter- hybrid tracking environment, as well as design of a cooperative control in distributed population-based multi-agent approach. The fourth part presents recent approaches and results in humanoid and bioinspirative robotics. It deals with design of adaptive control of anthropomorphic biped gait, building of dynamic-based simulation for humanoid robot walking, building controller for perceptual motor control dynamics of humans and biomimetic approach to control mechatronic structure using smart materials

Nanoparticle-membrane interactions

Biological membranes are fluid thin films composed of lipids, proteins and sugars. Nanoparticles are one specific nano-scale cargo that can be engineered with controlled structure, composition, and physicochemical surface properties. However, the mechanical mechanisms for nanoparticle-membrane interactions are still debated. For the interaction of nanoparticles with non-spherical vesicles, the roles of particle size, vesicle size, vesicle shape, and membrane spontaneous curvature on both nanoparticle wrapping and vesicle shape are studied. For non-spherical vesicle shapes, such as stomatocytes, oblates, and prolates, not only the local curvature at the point where the particle attaches but also the deformation energy of the free membrane is important. For fixed vesicle volume and membrane area, complex wrapping behavior is found, where particle wrapping transitions and vesicle shape transitions can be coupled. Furthermore, partial-wrapped membrane-bound particles impose boundary conditions for the free membrane that stabilize oblates and stomatocytes for particle entry, and prolates and stomatocytes for particle exit. If the vesicle volume can vary upon nanoparticle wrapping, the presence of solute inside the vesicle gives rise to a compression energy contribution to the vesicle deformation energy. The deformation-induced osmotic pressure difference stabilizes partial-wrapped states for both nanoparticles entering and exiting vesicles. For high solute concentrations, the transition between the partial-wrapped and the complete-wrapped state becomes discontinuous. Finally, wrapping of nanoparticles at membrane tubes is investigated. Here, both wrapping transitions and membrane-mediated particle-particle interactions are studied. Contrary to the literature, both mutual attraction and repulsion between nanoparticles are observed. The results presented in the thesis contribute to systematical understanding of membrane wrapping of nanoparticles