Accurate Algorithms for Spatial Operations on the Spheroid in a Spatial Database Management System

Some of the most powerful spatial analysis software solutions (Oracle, Google Earth Engine, PostgreSQL + PostGIS, etc.) are currently performing geometric calculations directly on the ellipsoid (a quadratic surface that models the earth shape), with a double purpose: to attain a high degree of accuracy and to allow the full management of large areas of territory (countries or even continents). It is well known that both objectives are impossible to achieve by means of the traditional approach using local mathematical projections and Cartesian coordinates. This paper demonstrates in a quantitative methodological way that most of the spatial analysis software products make important deviations in calculations regarding to geodesics, being the users unaware of the magnitude of these inaccuracies, which can easily reach meters depending on the distance. This is due to the use of ellipsoid calculations in an approximate way (e.g., using a sphere instead of an ellipsoid). This paper presents the implementation of two algorithms that solve with high accuracy (less than 100 nm) and efficiently (few iterations) two basic geometric calculations on the ellipsoid that are essential to build more complex spatial operators: the intersection of two geodesics and the minimum distance from a point to a geodesic.

Identification of Property Boundaries Using an IFC-Based Cadastral Database

Property boundaries have a significant importance in cadaster as they define the legal extent of the ownership rights. Among 3D data models, Industry Foundation Class (IFC) provides the potential capabilities for modelling property boundaries in a 3D environment. In some jurisdictions, such as Victoria, Australia, some property boundaries are assigned to the faces of building elements which are modelled as solids in IFC. In order to retrieve these property boundaries, boundary identification analysis should be performed, and faces of building elements should be extracted. However, extracting faces of solids from an IFC file is not possible as faces of solids are not considered as a separate object-type. Therefore, this paper aims to develop a spatial query approach for the identification of property boundaries using 3D spatial operators of a database to address this problem. The viability of the developed approach is tested using an IFC-based 3D cadastral database with two real datasets and one test dataset. The proposed methodology not only supports vertical walls and horizontal roofs but can also be used for detecting boundaries in properties surrounded by complex building structures such as oblique and curved walls and roofs.

Convergence analysis of a variational quasi-reversibility approach for an inverse hyperbolic heat conduction problem

We study a time-reversed hyperbolic heat conduction problem based upon the Maxwell–Cattaneo model of non-Fourier heat law. This heat and mass diffusion problem is a hyperbolic type equation for thermodynamics systems with thermal memory or with finite time-delayed heat flux, where the Fourier or Fick law is proven to be unsuccessful with experimental data. In this work, we show that our recent variational quasi-reversibility method for the classical time-reversed heat conduction problem, which obeys the Fourier or Fick law, can be adapted to cope with this hyperbolic scenario. We establish a generic regularization scheme in the sense that we perturb both spatial operators involved in the PDE. Driven by a Carleman weight function, we exploit the natural energy method to prove the well-posedness of this regularized scheme. Moreover, we prove the Hölder rate of convergence in the mixed {L^{2}}–{H^{1}} spaces.

Exact extrapolation and immersive modelling with finite-difference injection

SUMMARY In numerical modelling of wave propagation, the finite-difference (FD) injection method enables the re-introduction of simulated wavefields in model subdomains with machine precision, enabling the efficient calculation of waveforms after localized model alterations. By rewriting the FD-injection method in terms of sets of equivalent sources, we show how the same principles can be applied to achieve on-the-fly wavefield extrapolation using Kirchhoff–Helmholtz (KH)-like integrals. The resulting extrapolation methods are numerically exact when used in conjunction with FD-computed Green’s functions. Since FD injection only relies on the linearity of the wave equation and compactness of FD stencils in space, the methods can be applied to both staggered and non-staggered discretizations with arbitrary-order spatial operators. Examples for both types of discretizations show how these extrapolators can be used to truncate models with exact absorbing or immersive boundary conditions. Such immersive modelling involves the evaluation of KH-type extrapolation and representation integrals in the same simulation, which include the long-range interactions missing from conventional FD injection.

Simulation of a muographic analysis of a volcanic dome in Geant4

Here we present a Monte Carlo simulation of a muographic campaign on Methana volcano, Greece. In order to estimate the absorption parameters and the pattern of muon scattering at various incident energies (GeV to TeV), a radar-derived digital terrain model (DTM) was submitted to irradiation by horizontal muons in Geant4 and the penetrating muons were collected by a hypothetical MicroMegas particle detector on the other side of the DTM. Monte Carlo simulation demonstrated that muon energies at least as high as 10 TeV are required for whole-scale radiography of Methana and one has to reduce the scale of study to smaller structures (e.g. ~ 600 m - wide volcanic domes) in order to exploit the more affluent lower energy muons (~ 600 GeV). Coulomb scattering, on the other hand, brings about deflection of muon trajectories away from the detector, resulting in loss of information. Additionally, scattering adds Gaussian blurring to the scanned objects. With the intention of improving contrast and extract objects in muographic image we recommend the use of spatial operators (filters) employed in image analysis.

Analysis of performance of selected geospatial analyses implemented on the basis of relational and NoSQL databases

Databases are a basic component of every GIS system and many geoinformation applications. They also hold a prominent place in the tool kit of any cartographer. Solutions based on the relational model have been the standard for a long time, but there is a new increasingly popular technological trend – solutions based on the NoSQL database which have many advantages in the context of processing of large data sets. This paper compares the performance of selected spatial relational and NoSQL databases executing queries with selected spatial operators. It has been hypothesised that a non-relational solution will prove to be more effective, which was confirmed by the results of the study. The same spatial data set was loaded into PostGIS and MongoDB databases, which ensured standardisation of data for comparison purposes. Then, SQL queries and JavaScript commands were used to perform specific spatial analyses. The parameters necessary to compare the performance were measured at the same time. The study’s results have revealed which approach is faster and utilises less computer resources. However, it is difficult to clearly identify which technology is better because of a number of other factors which have to be considered when choosing the right tool.

Quantum mechanical MRI simulations: Solving the matrix dimension problem

We propose a solution to the matrix dimension problem in quantum mechanical simulations of MRI (magnetic resonance imaging) experiments on complex molecules. This problem is very old; it arises when Kronecker products of spin operators and spatial dynamics generators are taken—the resulting matrices are far too large for any current or future computer. However, spin and spatial operators individually have manageable dimensions, and we note here that the action by their Kronecker products on any vector may be computed without opening those products. This eliminates large matrices from the simulation process. MRI simulations for coupled spin systems of complex metabolites in three dimensions with diffusion, flow, chemical kinetics, and quantum mechanical treatment of spin relaxation are now possible. The methods described in this paper are implemented in versions 2.4 and later of the Spinach library.