Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic.

Techniques based on interval and previous termaffine arithmetic next term and their modifications are shown to provide previous term reliable next term function range evaluation for the purposes of previous termsurface interrogation.next term In this paper we present a technique for the previous termreliable interrogation of implicit surfacesnext term using a modification of previous termaffine arithmeticnext term called previous term revised affine arithmetic.next term We extend the range of functions presented in previous termrevised affine arithmeticnext term by introducing previous termaffinenext term operations for arbitrary functions such as set-theoretic operations with R-functions, blending and conditional operators. The obtained previous termaffinenext term forms of arbitrary functions provide previous termfasternext term and tighter function range evaluation. Several case studies for operations using previous termaffinenext term forms are presented. The proposed techniques for previous termsurface interrogationnext term are tested using ray-previous termsurfacenext term intersection for ray-tracing and spatial cell enumeration for polygonisation. These applications with our extensions provide previous termfast and reliablenext term rendering of a wide range of arbitrary previous termprocedurally defined implicit surfacesnext term (including polynomial previous termsurfaces,next term constructive solids, pseudo-random objects, previous termprocedurally definednext term microstructures, and others). We compare the function range evaluation technique based on previous termextended revised affine arithmeticnext term with other previous termreliablenext term techniques based on interval and previous termaffine arithmeticnext term to show that our technique provides the previous termfastestnext term and tightest function range evaluation for previous termfast and reliable interrogation of procedurally defined implicit surfaces.next term Research Highlights The main contributions of this paper are as follows. ► The widening of the scope of previous termreliablenext term ray-tracing and spatial enumeration algorithms for previous termsurfacesnext term ranging from algebraic previous termsurfaces (definednext term by polynomials) to general previous termimplicit surfaces (definednext term by function evaluation procedures involving both previous termaffinenext term and non-previous termaffinenext term operations based on previous termrevised affine arithmetic)next term. ► The introduction of a technique for representing procedural models using special previous termaffinenext term forms (illustrated by case studies of previous termaffinenext term forms for set-theoretic operations in the form of R-functions, blending operations and conditional operations). ► The detailed derivation of special previous termaffinenext term forms for arbitrary operators

Fast Reliable Ray-tracing of Procedurally Defined Implicit Surfaces Using Revised Affine Arithmetic

Fast and reliable rendering of implicit surfaces is an important area in the field of implicit modelling. Direct rendering, namely ray-tracing, is shown to be a suitable technique for obtaining good-quality visualisations of implicit surfaces. We present a technique for reliable ray-tracing of arbitrary procedurally defined implicit surfaces by using a modification of Affine Arithmetic called Revised Affine Arithmetic. A wide range of procedurally defined implicit objects can be rendered using this technique including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others. We compare our technique with other reliable techniques based on Interval and Affine Arithmetic to show that our technique provides the fastest, while still reliable, ray-surface intersections and ray-tracing. We also suggest possible modifications for the GPU implementation of this technique for real-time rendering of relatively simple implicit models and for near real-time for complex implicit models

Ray Tracing Simulations of Weak Lensing by Large-Scale Structure

We investigate weak lensing by large-scale structure using ray tracing through N-body simulations. Photon trajectories are followed through high resolution simulations of structure formation to make simulated maps of shear and convergence on the sky. Tests with varying numerical parameters are used to calibrate the accuracy of computed lensing statistics on angular scales from about 1 arcminute to a few degrees. Various aspects of the weak lensing approximation are also tested. For fields a few degrees on a side the shear power spectrum is almost entirely in the nonlinear regime and agrees well with nonlinear analytical predictions. Sampling fluctuations in power spectrum estimates are investigated by comparing several ray tracing realizations of a given model. For survey areas smaller than a degree on a side the main source of scatter is nonlinear coupling to modes larger than the survey. We develop a method which uses this effect to estimate the mass density parameter Omega from the scatter in power spectrum estimates for subregions of a larger survey. We show that the power spectrum can be measured accurately from realistically noisy data on scales corresponding to 1-10 Mpc/h. Non-Gaussian features in the one point distribution function of the weak lensing convergence (reconstructed from the shear) are also sensitive to Omega. We suggest several techniques for estimating Omega in the presence of noise and compare their statistical power, robustness and simplicity. With realistic noise Omega can be determined to within 0.1-0.2 from a deep survey of several square degrees.Comment: 59 pages, 22 figures included. Matches version accepted for Ap

Indoor wireless communications and applications

Chapter 3 addresses challenges in radio link and system design in indoor scenarios. Given the fact that most human activities take place in indoor environments, the need for supporting ubiquitous indoor data connectivity and location/tracking service becomes even more important than in the previous decades. Specific technical challenges addressed in this section are(i), modelling complex indoor radio channels for effective antenna deployment, (ii), potential of millimeter-wave (mm-wave) radios for supporting higher data rates, and (iii), feasible indoor localisation and tracking techniques, which are summarised in three dedicated sections of this chapter

Automatic normal orientation in point clouds of building interiors

Orienting surface normals correctly and consistently is a fundamental problem in geometry processing. Applications such as visualization, feature detection, and geometry reconstruction often rely on the availability of correctly oriented normals. Many existing approaches for automatic orientation of normals on meshes or point clouds make severe assumptions on the input data or the topology of the underlying object which are not applicable to real-world measurements of urban scenes. In contrast, our approach is specifically tailored to the challenging case of unstructured indoor point cloud scans of multi-story, multi-room buildings. We evaluate the correctness and speed of our approach on multiple real-world point cloud datasets

Seismic Ray Impedance Inversion

This thesis investigates a prestack seismic inversion scheme implemented in the ray parameter domain. Conventionally, most prestack seismic inversion methods are performed in the incidence angle domain. However, inversion using the concept of ray impedance, as it honours ray path variation following the elastic parameter variation according to Snell’s law, shows the capacity to discriminate different lithologies if compared to conventional elastic impedance inversion. The procedure starts with data transformation into the ray-parameter domain and then implements the ray impedance inversion along constant ray-parameter profiles. With different constant-ray-parameter profiles, mixed-phase wavelets are initially estimated based on the high-order statistics of the data and further refined after a proper well-to-seismic tie. With the estimated wavelets ready, a Cauchy inversion method is used to invert for seismic reflectivity sequences, aiming at recovering seismic reflectivity sequences for blocky impedance inversion. The impedance inversion from reflectivity sequences adopts a standard generalised linear inversion scheme, whose results are utilised to identify rock properties and facilitate quantitative interpretation. It has also been demonstrated that we can further invert elastic parameters from ray impedance values, without eliminating an extra density term or introducing a Gardner’s relation to absorb this term. Ray impedance inversion is extended to P-S converted waves by introducing the definition of converted-wave ray impedance. This quantity shows some advantages in connecting prestack converted wave data with well logs, if compared with the shearwave elastic impedance derived from the Aki and Richards approximation to the Zoeppritz equations. An analysis of P-P and P-S wave data under the framework of ray impedance is conducted through a real multicomponent dataset, which can reduce the uncertainty in lithology identification.Inversion is the key method in generating those examples throughout the entire thesis as we believe it can render robust solutions to geophysical problems. Apart from the reflectivity sequence, ray impedance and elastic parameter inversion mentioned above, inversion methods are also adopted in transforming the prestack data from the offset domain to the ray-parameter domain, mixed-phase wavelet estimation, as well as the registration of P-P and P-S waves for the joint analysis. The ray impedance inversion methods are successfully applied to different types of datasets. In each individual step to achieving the ray impedance inversion, advantages, disadvantages as well as limitations of the algorithms adopted are detailed. As a conclusion, the ray impedance related analyses demonstrated in this thesis are highly competent compared with the classical elastic impedance methods and the author would like to recommend it for a wider application

Development of a Computer Vision-Based Three-Dimensional Reconstruction Method for Volume-Change Measurement of Unsaturated Soils during Triaxial Testing

Problems associated with unsaturated soils are ubiquitous in the U.S., where expansive and collapsible soils are some of the most widely distributed and costly geologic hazards. Solving these widespread geohazards requires a fundamental understanding of the constitutive behavior of unsaturated soils. In the past six decades, the suction-controlled triaxial test has been established as a standard approach to characterizing constitutive behavior for unsaturated soils. However, this type of test requires costly test equipment and time-consuming testing processes. To overcome these limitations, a photogrammetry-based method has been developed recently to measure the global and localized volume-changes of unsaturated soils during triaxial test. However, this method relies on software to detect coded targets, which often requires tedious manual correction of incorrectly coded target detection information. To address the limitation of the photogrammetry-based method, this study developed a photogrammetric computer vision-based approach for automatic target recognition and 3D reconstruction for volume-changes measurement of unsaturated soils in triaxial tests. Deep learning method was used to improve the accuracy and efficiency of coded target recognition. A photogrammetric computer vision method and ray tracing technique were then developed and validated to reconstruct the three-dimensional models of soil specimen

Mapping ionospheric backscatter measured by the SuperDARN HF radars - Part 1: A new empirical virtual height model

Accurately mapping the location of ionospheric backscatter targets (density irregularities) identified by the Super Dual Auroral Radar Network (SuperDARN) HF radars can be a major problem, particularly at far ranges for which the radio propagation paths are longer and more uncertain. Assessing and increasing the accuracy of the mapping of scattering locations is crucial for the measurement of two-dimensional velocity structures on the small and meso-scale, for which overlapping velocity measurements from two radars need to be combined, and for studies in which SuperDARN data are used in conjunction with measurements from other instruments. The co-ordinates of scattering locations are presently estimated using a combination of the measured range and a model virtual height, assuming a straight line virtual propagation path. By studying elevation angle of arrival information of backscatterred signals from 5 years of data (1997-2001) from the Saskatoon SuperDARN radar we have determined the actual distribution of the backscatter target locations in range-virtual height space. This has allowed the derivation of a new empirical virtual height model that allows for a more accurate mapping of the locations of backscatter targets