Discrete differential operators on polygonal meshes

Geometry processing of surface meshes relies heavily on the discretization of differential operators such as gradient, Laplacian, and covariant derivative. While a variety of discrete operators over triangulated meshes have been developed and used for decades, a similar construction over polygonal meshes remains far less explored despite the prevalence of non-simplicial surfaces in geometric design and engineering applications. This paper introduces a principled construction of discrete differential operators on surface meshes formed by (possibly non-flat and non-convex) polygonal faces. Our approach is based on a novel mimetic discretization of the gradient operator that is linear-precise on arbitrary polygons. Equipped with this discrete gradient, we draw upon ideas from the Virtual Element Method in order to derive a series of discrete operators commonly used in graphics that are now valid over polygonal surfaces. We demonstrate the accuracy and robustness of our resulting operators through various numerical examples, before incorporating them into existing geometry processing algorithms

Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young\u27s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

Fast GPU-Based Two-Way Continuous Collision Handling

Step-and-project is a popular way to simulate non-penetrated deformable bodies in physically-based animation. First integrating the system in time regardless of contacts and post resolving potential intersections practically strike a good balance between plausibility and efficiency. However, existing methods could be defective and unsafe when the time step is large, taking risks of failures or demands of repetitive collision testing and resolving that severely degrade performance. In this paper, we propose a novel two-way method for fast and reliable continuous collision handling. Our method launches the optimization at both ends of the intermediate time-integrated state and the previous intersection-free state, progressively generating a piecewise-linear path and finally reaching a feasible solution for the next time step. Technically, our method interleaves between a forward step and a backward step at a low cost, until the result is conditionally converged. Due to a set of unified volume-based contact constraints, our method can flexibly and reliably handle a variety of codimensional deformable bodies, including volumetric bodies, cloth, hair and sand. The experiments show that our method is safe, robust, physically faithful and numerically efficient, especially suitable for large deformations or large time steps

On the derivation of an X-ray temperature function without reference to mass and the prediction of weak-lensing number counts from the statistics of Gaussian random fields

We present a novel approach for the derivation of the X-ray temperature function for galaxy clusters, which is based on the statistics of Gaussian random fields applied to the cosmic gravitational potential. It invokes only locally defined quantities so that no reference to the cluster's mass is made. To relate linear and non-linear potential and to take into account only structures that have collapsed, we include either spherical- or ellipsoidal-collapse dynamics and compare both resulting models to temperature functions derived from a numerical simulation. Since deviations from the theoretical prediction are found in the simulation for high redshifts, we develop an analytic model to include the effects of mergers in our formalism. We jointly determine the cosmological parameters Omega_m0 and sigma_8 from two different cluster samples for different temperature definitions and find good agreement with constraints from WMAP5. Introducing theoretically a refined detection definition based on the upcrossing criterion, we reformulate our analytic approach for 2D and use it to predict the number density of spurious detections caused by large-scale structure and shot noise in filtered weak-lensing convergence maps. Agreement with a numerical simulation is found at the expected level

Statistics of Intrinsic alignments and Weak Lensing

The content of this work is two-fold. In the first part we present a study on the contamination of the intrinsic alignments to weak lensing measurements in the future survey Euclid. On the grounds of the tidal torque theory, we have adopted from the literature two related prescriptions for modeling the intrinsic alignment signal and computed for both the resulting biases in the cosmological parameters.We find a slight discrepancy among the two models, which both significantly (up to > 3sigma) contaminate the estimates for Omega_m and sigma_8. The other parameters h, ns and w appear less affected. In the second part we present results based on an innovative statistical approach, the extreme value statistics. We investigate up to which level the primordial non-Gaussianities parameters fNL and gNL inherited by the bi- and trispectra of the weak lensing convergence can be constrained by the most extreme values of the convergence field.We find constraints of the order of 102 for fNL and 105 for gNL if individual extreme values are considered, therefore sadly showing only a relatively weak constraining power

Different aspects of the interplay between light and the large-scale structure of the Universe

The main subject of this thesis is the influence of intrinsic alignments on weak lensing measurements. One possible source of intrinsic alignments are correlations in the angular momenta of neighbouring galaxies. Employing an improved ansatz for the angular momentum correlation function I show that the typical correlation length of Milky Way-sized haloes is about 1 Mpc/h which is slightly smaller than earlier work in this field suggested. Establishing the constitutive formalism to describe intrinsic alignments consistently in the framework of 3d cosmic shear I compute the resulting covariance matrices of different alignment types. For a Eucild-like survey it turns out that intrinsic alignments are more than one order of magnitude smaller than the lensing signal. In addition the parameter estimation bias in a two-dimensional non-tomographic weak lensing measurement is computed. The matter density Omega_m and the normalization of the linear matter power spectrum sigma_8 are most severely biased if intrinsic alignments are described by an angular momentum based alignment model. In the second part of my thesis I address secondary anisotropies of the cosmic microwave background: weak gravitational lensing and the nonlinear integrated Sachs-Wolfe (iSW) effect. The characteristic imprint of lensing can be used to reconstruct the lensing potential power spectrum. I show how this reconstruction is biased in the presence of primordial non-Gaussianities. For current values of f_NL, however, the bias is completely negligible on all but the largest angular scales. Finally, a novel analytical approach for the computation of the nonlinear iSW effect valid in the translinear regime is presented. It allows to identify two distinct contributions: the change of the gravitational self-energy density of the large-scale structure with (conformal) time and the Birkinshaw-Gull effect

Weight Discretization due to Optical Constraints and its Influence on the Generalization Abilities of a Simple Perceptron

The optical implementation of neural networks can be realized by storing the weights in holograms with a limited number of gray values. Motivated by this fact, we focused our investigation in this thesis on analyzing the dependence of the generalization and training errors of a simple perceptron with discrete weights, on the training set size, and on the number of allowed discrete values

Machine vision techniques for inspection of dry-fibre composite preforms in the aerospace industry

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis presents the results of a three year investigation into machine vision techniques for in-process automated inspection of dry-fibre composite preforms. Efficient texture analysis based techniques have been developed, tested, and implemented in a prototype robotic assembly cell. Industrial constraints have been considered in the development of all the algorithms described. A single channel texture analysis model is described which can successfully segment images containing only a few textures. The model is based on convolution of the image with small kernels optimised for the task, and is elegant in the sense that it is computationally simple and easily realisable in low cost hardware. A new convolution kernel optimisation algorithm is described. It is demonstrated that convolution kernels can also be optimised to perform as edge operators in simple textured images. A novel boundary refinement algorithm is described which reduces the inspection errors inherent in texture based boundary estimates. The algorithm takes the form of a local search, using the texture estimate as a guiding template, and selects edge points by maximising a merit function. Optimum parameters for the merit function are obtained using multiple training images in conjunction with simple function optimisation algorithms.This study is funded by the Engineering and Physical Sciences Research Council (EPSRC) and Dowty Aerospace Propellers Ltd

Advances in Vibration Analysis Research

Vibrations are extremely important in all areas of human activities, for all sciences, technologies and industrial applications. Sometimes these Vibrations are useful but other times they are undesirable. In any case, understanding and analysis of vibrations are crucial. This book reports on the state of the art research and development findings on this very broad matter through 22 original and innovative research studies exhibiting various investigation directions. The present book is a result of contributions of experts from international scientific community working in different aspects of vibration analysis. The text is addressed not only to researchers, but also to professional engineers, students and other experts in a variety of disciplines, both academic and industrial seeking to gain a better understanding of what has been done in the field recently, and what kind of open problems are in this area