A sharp interface isogeometric strategy for moving boundary problems

The proposed methodology is first utilized to model stationary and propagating cracks. The crack face is enriched with the Heaviside function which captures the displacement discontinuity. Meanwhile, the crack tips are enriched with asymptotic displacement functions to reproduce the tip singularity. The enriching degrees of freedom associated with the crack tips are chosen as stress intensity factors (SIFs) such that these quantities can be directly extracted from the solution without a-posteriori integral calculation. As a second application, the Stefan problem is modeled with a hybrid function/derivative enriched interface. Since the interface geometry is explicitly defined, normals and curvatures can be analytically obtained at any point on the interface, allowing for complex boundary conditions dependent on curvature or normal to be naturally imposed. Thus, the enriched approximation naturally captures the interfacial discontinuity in temperature gradient and enables the imposition of Gibbs-Thomson condition during solidification simulation. The shape optimization through configuration of finite-sized heterogeneities is lastly studied. The optimization relies on the recently derived configurational derivative that describes the sensitivity of an arbitrary objective with respect to arbitrary design modifications of a heterogeneity inserted into a domain. The THB-splines, which serve as the underlying approximation, produce sufficiently smooth solution near the boundaries of the heterogeneity for accurate calculation of the configurational derivatives. (Abstract shortened by ProQuest.

Data-driven quasi-interpolant spline surfaces for point cloud approximation

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data

Robust Poisson Surface Reconstruction

Abstract. We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator func-tion of the surface’s interior. Compared to previous models, our recon-struction is robust to noise and outliers because it substitutes the least-squares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hi-erarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, in-stead isogeometric finite-element techniques, to efficiently solve the min-imization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.

Multi-resolution mapping and planning for UAV navigation in attitude constrained environments

In this thesis we aim to bridge the gap between high quality map reconstruction and Unmanned Aerial Vehicles (UAVs) SE(3) motion planning in challenging environments with narrow openings, such as disaster areas, which requires attitude to be considered. We propose an efficient system that leverages the concept of adaptive-resolution volumetric mapping, which naturally integrates with the hierarchical decomposition of space in an octree data structure. Instead of a Truncated Signed Distance Function (TSDF), we adopt mapping of occupancy probabilities in log-odds representation, which allows representation of both surfaces, as well as the entire free, i.e.\ observed space, as opposed to unobserved space. We introduce a method for choosing resolution -on the fly- in real-time by means of a multi-scale max-min pooling of the input depth image. The notion of explicit free space mapping paired with the spatial hierarchy in the data structure, as well as map resolution, allows for collision queries, as needed for robot motion planning, at unprecedented speed. Our mapping strategy supports pinhole cameras as well as spherical sensor models. Additionally, we introduce a first-of-a-kind global minimum cost path search method based on A* that considers attitude along the path. State-of-the-art methods incorporate attitude only in the refinement stage. To make the problem tractable, our method exploits an adaptive and coarse-to-fine approach using global and local A* runs, plus an efficient method to introduce the UAV attitude in the process. We integrate our method with an SE(3) trajectory optimisation method based on a safe-flight-corridor, yielding a complete path planning pipeline. We quantitatively evaluate our mapping strategy in terms of mapping accuracy, memory, runtime performance, and planning performance showing improvements over the state-of-the-art, particularly in cases requiring high resolution maps. Furthermore, extensive evaluation is undertaken using the AirSim flight simulator under closed loop control in a set of randomised maps, allowing us to quantitatively assess our path initialisation method. We show that it achieves significantly higher success rates than the baselines, at a reduced computational burden.Open Acces