Gerrit Sobottka’s research while affiliated with Stanford University and other places

We devise a physically based approach to the accurate simulation of stiff fibers like human hair, wool, or yarn. For that we describe fibers as three-dimensional coupled oscillator networks. The application of special analytical mapping expressions allows us to mimic the existence of Youngs and shear modulus in the oscillator network so that real material parameters can be used. For the efficient numerical treatment of the stiff equations of motion of the system a Damped Exponential Time Integrator (DETI) is introduced. This type of integrator is able to take large time steps during the solution process of the stiff system while sustaining stability. It also handles Rayleigh damping analytically by employing the closed-form solution of the fully damped harmonic oscillator. We validate the fiber model against the outcome obtained by solving the special Cosserat theory of rods. Moreover, we demonstrate the efficiency of our approach on some complex fiber assemblies like human hair and fiber meshes. Compared to established methods we reach a significant speed up and at the same time achieve highly accurate results.

We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.

We consider a subsystem of the special cosserat theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary function in t. Assuming analyticity of the arbitrary functions in a domain under consideration, we prove that the obtained solution is analytic and general. The Special Cosserat Theory of Rods describes the dynamic equilibrium of 1-dimensional continua, i.e. slender structures like fibers, by means of a system of partial differential equations.

We investigate the application of exponential integrators to stiff elastodynamic problems governed by second-order differential equations. Classical explicit numerical integration schemes have the shortcoming that the stepsizes are limited by the highest frequency that occurs within the solution spectrum of the governing equations, while implicit methods suffer from an inevitable and mostly uncontrollable artificial viscosity that often leads to a nonphysical behavior. In order to overcome these specific detriments, we devise an appropriate class of exponential integrators that solve the stiff part of the governing equations of motion by employing a closed-form solution. As a consequence, we are able to handle up to three orders of magnitude larger time-steps as with conventional implicit integrators and at the same time achieve a tremendous increase in the overall long-term stability due to a strict energy conservation. The advantageous behavior of our approach is demonstrated on a broad spectrum of complex deformable models like fibers, textiles, and solids, including collision response, friction, and damping.

We devise a new algorithm for the extraction of vine leaf veins. Our method performs a directional edge tracing on the responses of appropriate adaptive Gabor filters in order to extract the network of the main veins. The respective curvature vectors are used for the classification of different cultivars using support vector machines. We evaluate the advantageous behavior and the robustness of our approach on a test set consisting of 150 light transmitted images of different vine leaves.

We illustrate the development of an application for cultivar classification of leaf images based on the extraction of the network of its main veins that runs on mobile devices like smart phones or tablets. Such mobile devices can be docked to farming robots in order to support the farming process. Our application uses an efficient Gabor filter-based tracing algorithm which is able to perform a robust network extraction. The results are used as input data for the classification with a support vector machine. In order to demonstrate the advantageous behavior and the robustness of this method, we perform an evaluation on a test set consisting of 150 light transmitted images of different vine leaves.

In this note we present a symbolic-numeric method to the problem of tube modeling in CAD systems. Our approach is based on the Kirchhoff kinetic analogy which allows us to find analytic solutions to the static Kirchhoff equa- tions for rods under given boundary conditions. Keywords: Kirchhoff rod; boundary value problems; automatic differentiation

We present a framework to study electrical charge phenomena on human hair. We propose a fiber based hair model which bases on the special theory of Cosserat Rods to overcome the well known difficulties one has to deal with when simple particle systems are used. We show how such models can efficiently be employed in conjunction with the fast multipole method to account for Coulomb far-field interactions. Furthermore, we extend our model such that we can account for environmental conditions.

We present a novel approach to the problem of hairstyle construction from raw surface data such as the ones obtained from surface scans. Our approach is based on a shape matching algorithm that fits individual hair fibers into a given volume according to a set of boundary conditions and additional hair density information. Our method employs a mechanical rod model based on the special theory of Cosserat rods. Such models can efficiently be used to simulate the deformation of individual fibers in subsequent manipulation steps

We study the practicability and performance of different classes of bounding volume hierarchies for self collision detection in complex human hair styles with authentic geometrical properties. In particular, we focus on topology based hierarchies which allow for fast update schemes as well as conventional spatially adapted hierarchies. In this context, we introduce a parameterized k-DOP approach based on Grassmanian spaces which allows for a systematic generation of normal sets for arbitrary k. This enables us to empirically determine optimal values of k for collision detection based on DOP hierarchies.