Isogeometric Analysis on V-reps: first results

Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parametrization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justify our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffusion and linear elasticity.Comment: 36 pages, 44 figures. Reviewed versio

Sketch-based character prototyping by deformation

Master'sMASTER OF SCIENC

Arnold diffusion for a complete family of perturbations with two independent harmonics

We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several scattering maps. A complete description of the different kinds of scattering maps taking place as well as the existence of piecewise smooth global scattering maps is also provided.Comment: 23 pages, 14 figure

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

State-space model identification and feedback control of unsteady aerodynamic forces

Unsteady aerodynamic models are necessary to accurately simulate forces and develop feedback controllers for wings in agile motion; however, these models are often high dimensional or incompatible with modern control techniques. Recently, reduced-order unsteady aerodynamic models have been developed for a pitching and plunging airfoil by linearizing the discretized Navier-Stokes equation with lift-force output. In this work, we extend these reduced-order models to include multiple inputs (pitch, plunge, and surge) and explicit parameterization by the pitch-axis location, inspired by Theodorsen's model. Next, we investigate the na\"{\i}ve application of system identification techniques to input--output data and the resulting pitfalls, such as unstable or inaccurate models. Finally, robust feedback controllers are constructed based on these low-dimensional state-space models for simulations of a rigid flat plate at Reynolds number 100. Various controllers are implemented for models linearized at base angles of attack $\alpha_0=0^\circ, \alpha_0=10^\circ$, and $\alpha_0=20^\circ$. The resulting control laws are able to track an aggressive reference lift trajectory while attenuating sensor noise and compensating for strong nonlinearities.Comment: 20 pages, 13 figure

Improving Interaction in Visual Analytics using Machine Learning

Interaction is one of the most fundamental components in visual analytical systems, which transforms people from mere viewers to active participants in the process of analyzing and understanding data. Therefore, fast and accurate interaction techniques are key to establishing a successful human-computer dialogue, enabling a smooth visual data exploration. Machine learning is a branch of artificial intelligence that provides systems the ability to automatically learn and improve from experience without being explicitly programmed. It has been utilized in a wide variety of fields, where it is not straightforward to develop a conventional algorithm for effectively performing a task. Inspired by this, we see the opportunity to improve the current interactions in visual analytics by using machine learning methods. In this thesis, we address the need for interaction techniques that are both fast, enabling a fluid interaction in visual data exploration and analysis, and also accurate, i.e., enabling the user to effectively select specific data subsets. First, we present a new, fast and accurate brushing technique for scatterplots, based on the Mahalanobis brush, which we have optimized using data from a user study. Further, we present a new solution for a near-perfect sketch-based brushing technique, where we exploit a convolutional neural network (CNN) for estimating the intended data selection from a fast and simple click-and-drag interaction and from the data distribution in the visualization. Next, we propose an innovative framework which offers the user opportunities to improve the brushing technique while using it. We tested this framework with CNN-based brushing and the result shows that the underlying model can be refined (better performance in terms of accuracy) and personalized by very little time of retraining. Besides, in order to investigate to which degree the human should be involved into the model design and how good the empirical model can be with a more careful design, we extended our Mahalanobis brush (the best current empirical model in terms of accuracy for brushing points in a scatterplot) by further incorporating the data distribution information, captured by kernel density estimation (KDE). Based on this work, we then provide a detailed comparison between empirical modeling and implicit modeling by machine learning (deep learning). Lastly, we introduce a new, machine learning based approach that enables the fast and accurate querying of time series data based on a swift sketching interaction. To achieve this, we build upon existing LSTM technology (long short-term memory) to encode both the sketch and the time series data in two networks with shared parameters. All the proposed interaction techniques in this thesis were demonstrated by application examples and evaluated via user studies. The integration of machine learning knowledge into visualization opens further possible research directions.Doktorgradsavhandlin