Open Problems in 3D Model and Data Management
Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications
International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP) <15, 2020, Valetta, Malta>
In interdisciplinary, cooperative projects that involve different representations of 3D models (such as CAD data and simulation data), a version problem can occur: different representations and parts have to be merged to form a holistic view of all relevant aspects. The individual partial models may be exported by and modified in different software environments. These modifications are a recurring activity and may be carried out again and again during the progress of the project. This position paper investigates the version problem; furthermore, this contribution is intended to stimulate discussion on how the problem can be solved.
Bestimmung adjungierter Sensitivitäten als Grundlage einer prototypischen Topologieoptimierung
Darmstadt, TU, Bachelor Thesis, 2019
Diese Arbeit behandelt die Bestimmung von Sensitivitäten zur Lösung eines Optimierungsproblems. Ziel ist es dabei, mithilfe von Topologieoptimierung, eine optimale Struktur zu finden, die unter mechanischer Belastung eine Zielfunktion minimiert. Die Strukturbildung verläuft über einen elementbasierten Ansatz der Dichte. Der Optimierung unterliegt eine Nebenbedingung an die maximale Masse, die eine optimale Lösung unterschreiten muss. Für die Bestimmung des mechanischen Verhaltens wird eine Finite-Elemente-Analyse durchgeführt. Die Sensitivitäten sind dabei die Ableitungen der Zielfunktion nach den Designparametern. Die Sensitivitäten werden über einen adjungierten Ansatz hergeleitet und über Automatisches Differenzieren bestimmt. Bei der Bestimmung mit automatischem Differenzieren wird eine Graphenfärbung verwendet, um die Durchläufe des Vorwärtsmodus zu reduzieren. Die Errechneten Sensitivitäten werden auf Plausibilität untersucht und für die Lösung verschiedener Topologieoptimierungen eingesetzt.
Continuous Property Gradation for Multi-material 3D-printed Objects
Solid Freeform Fabrication 2018: Proceedings of the 29th Annual International Solid Freeform Fabrication Symposium - An Additive Manufacturing Conference
Annual International Solid Freeform Fabrication Symposium - An Additive Manufacturing Conference <29, 2018, Austin, TX, USA>
Modern AM processes allow for printing multiple materials. The resulting objects can be stiff/dense in some areas and soft/porous in others, resulting in distinct physical properties. However, modeling material gradients is still tedious with current approaches, especially when smooth transitions are required. Current approaches can be distinguished into a) NURBS-BReps-based and b) voxel-based. In case of NURBS-BReps, discrete material distributions can be modeled by manually introducing separate shells inside the object; smooth gradation can only be approximated in discrete steps. For voxel representations, gradation is discrete by design and comes along with an approximation error. In addition, interacting on a per-voxel basis is tedious for the designer/engineer. We present a novel approach for representing material gradients in volumetric models using subdivision schemes, supporting continuity and providing elegant ways for interactive modeling of locally varying properties. Additionally, the continuous volumetric representation allows for on-demand sampling at any resolution required by the 3D printer.
Exponential Integrators for Deformable Objects using Finite Elements
Darmstadt, TU, Master Thesis, 2018
Simulating deformable objects is often done with implicit integrator since they can robustly simulate large time steps. However, these integrators introduce significant artificial damping into the simulation. Recently, exponential integrators have attracted attention as an alternative to implicit integrators. They have shown to the potential to achieve large time steps without introducing artificial damping. In this thesis we implement and compare five promising exponential integrator on deformable object simulation tasks. They are the non-linear exponential time integrator (NETI), co-rotational exponential time integrator (CETI), exponential Rosenbrock-Euler (ERE) and two exponential propagation iterative methods of Runge-Kutta type (EPIRK). Additionally, we also propose a new way to compute the exponential-like functions inside ERE and EPIRK integrators. Four of the exponential integrators we present have been used before for deformable object simulation but their performance has not been compared on the same task. In our experiment we compare how well the exponential integrators preserve the energy of the system, how accurate they are, their runtime requirements, how damping effects the integrator and how important internal variables scale with the task. We show that the exponential integrators preserve energy much better than the popular semi-implicit Euler integrator. Of the exponential integrators the ERE integrator is the most stable on our experiments and performs well in terms of accuracy. However, ERE is not as stable as the semi-implicit Euler integrator. Our new computation of the exponential functions in ERE and EPIRK slightly improves their stability but also slightly increases runtime requirements.
Integrating Interactive Design and Simulation for Mass Customized 3D-Printed Objects - A Cup Holder Example
Solid Freeform Fabrication 2017: Proceedings of the 28th Annual International Solid Freeform Fabrication Symposium - An Additive Manufacturing Conference
Annual International Solid Freeform Fabrication Symposium - An Additive Manufacturing Conference <28, 2017, Austin, USA>
We present an approach for integrating interactive design and simulation for customizing parameterized 3D models. Instead of manipulating the mesh directly, a simplified interface for casual users allows for adapting intuitive parameters, such as handle diameter or height of our example object - a cup holder. The transition between modeling and simulation is performed with a volumetric subdivision representation, allowing direct adaption of the simulation mesh without re-meshing. Our GPU-based FEM solver calculates deformation and stresses for the current parameter configuration within seconds with a pre-defined load case. If the physical constraints are met, our system allows the user to 3D print the object. Otherwise, it provides guidance which parameters to change to optimize stability while adding as little material as possible based on a finite differences optimization approach. The speed of our GPU-solver and the fluent transition between design and simulation renders the system interactive, requiring no pre-computation.
Energy-Preserving Integrators for Fluid Animation with Discrete Exterior Calculus on Two-Dimensional Meshes
Darmstadt, TU, Bachelor Thesis, 2012
In the last decades a lot of approaches have been developed for implementing computational fluid dynamics (CFD) in the computer graphics community. One of the new approaches in fluid simulations is the discrete exterior calculus (DEC). DEC uses well-centered meshes to describe its integration space. Mullen et al. [MCP+09] introduced 2009 a new integration scheme based on DEC and the Navier-Stokes equations that preserves mass by definition of DEC. His discrete formulation of the Navier-Stokes equations provides full control about viscosity and moreover an almost perfect preservation of kinetic energy. We translate Mullens discretization into two dimensions and extend it to regular girds. We will discuss how to manage non-trivial boundary conditions. Finally we will analyze the results of Mullens approach, and analyze alternative methods to further improve those results.