Ray Tracing Problem Research Articles

Incorporating topographic effects in surface wave tomography based on shortest-path ray tracing

SUMMARY We propose a new method to obtain 3-D shear wave velocity structures for regions with undulating topography based on surface wave dispersion data. In our method, we assume that surface waves propagate along a curved free surface, and the dispersion effects of these waves can be modelled as a frequency-dependent ray tracing problem. We use the shortest-path method to address off-great-circle propagation arising from inhomogeneous elastic parameters and topographic variations. We then apply our method to both synthetic and real-data inversions and demonstrate that ignoring topographic effects may significantly distort the inverted images. Finally, we analysed the accuracy of our method and provided a rule-of-thumb principle to quantitatively assess the need to account for topographic effects in surface wave tomography for a region.

RTIndeX: Exploiting Hardware-Accelerated GPU Raytracing for Database Indexing

Data management on GPUs has become increasingly relevant due to a tremendous rise in processing power and available GPU memory. Similar to main-memory systems, there is a need for performant GPU-resident index structures to speed up query processing. Unfortunately, mapping indexes efficiently to the highly parallel and hard-to-program hardware is challenging and often fails to yield the desired performance and flexibility. Instead of proposing yet another hand-tailored index, we investigate whether we can exploit an indexing mechanism that is already built into modern GPUs: The raytracing hardware accelerator provided by NVIDIA RTX GPUs. To do so, we re-phrase the database indexing problem as a raytracing problem, where we express the dataset to be indexed as objects in a 3D scene, and point/range lookups as rays across the scene. In this combination, coined RX in the following, lookups are performed as intersection tests in hardware by dedicated raytracing cores. To analyze the pros, cons, and usefulness of the raytracing pipeline for database indexing, we carefully evaluate RX along fourteen dimensions and demonstrate its competitiveness and potential in a large variety of situations.

Quantum Ray Tracing with Simulation

Rendering is a computer graphics process that generates images from a three-dimensional scene including models, lights and cameras. Ray tracing is a category of rendering algorithms that calculates pixel colors by simulating the physical movements of light rays such as reflections, refractions and scatterings. The core problem of ray tracing is a high-dimensional numerical integration, and the classical Monte Carlo ray tracing requires a big number of rays to reduce error. By leveraging the inherent parallelism of quantum computing, we propose a framework of quantum ray tracing algorithm, and do simulation experiments to prove that it has a quadratically faster error convergence than classical Monte Carlo ray tracing.

Leveraging ray tracing cores for particle‐based simulations on GPUs

AbstractNeighbor searching is an essential and computationally heavy step in particle‐based numerical methods such as discrete element method (DEM), molecular dynamics, peridynamics, and smooth particle hydrodynamics. This article presents a novel approach to accelerate particle‐based simulations by leveraging ray tracing (RT) cores in addition to CUDA cores on RTX GPUs. The neighbor search problem is first numerically converted into a general ray tracing problem so that it can be possible to utilize the hardware acceleration of RT cores. A new, general‐purpose RT‐based neighbor search algorithm is then proposed and benchmarked with a prevailing cell‐based one. As a showcase, both algorithms are implemented into a GPU‐based DEM code for simulating large‐scale granular problems including packing, column collapse and debris flow. The overall simulation performance is examined with varying problem sizes and GPU specs. It demonstrates that the RT‐based simulations are 10%–60% faster than the cell‐based ones, depending on the simulated problems and GPU specs. This study offers a new recipe for next‐generation high‐performance computing of large‐scale engineering problems using particle‐based numerical methods.

Solving ultrasonic ray tracing in parts with multiple material layers through Root-Finding methods

Ultrasonic testing has been used for material analysis and inspection since 1930′s. Nevertheless, the applicability of ultrasonic waves to new complex cases is still growing, thanks to the availability of powerful electronics and software. However, the complication that slows down the deployment of ultrasonic inspection to geometric complex parts and structures arises from the wave refraction phenomenon. A clear understanding of the ultrasound wave propagation, impacted by refractions, is crucial to interpret the data obtained from the inspection of multi-layered/multi-medium test subjects as it is not always possible to assume that mechanical waves travel in straight lines. This work presents suitable approaches for solving the ray-tracing problem in multi-layered structures. Accurate benchmarking shows that the use of the Newton-Raphson root-finding method allows a threefold reduction of the computation time, when compared to the bisection-based root-finding methods. An effective combination of the Newton-Raphson methods with bisection-type iterations is also proposed and discussed. Although the work repeatedly refers to the field of ultrasonic inspection, the presented findings are relevant and applicable to areas beyond material inspection.

A Survey on Bounding Volume Hierarchies for Ray Tracing

AbstractRay tracing is an inherent part of photorealistic image synthesis algorithms. The problem of ray tracing is to find the nearest intersection with a given ray and scene. Although this geometric operation is relatively simple, in practice, we have to evaluate billions of such operations as the scene consists of millions of primitives, and the image synthesis algorithms require a high number of samples to provide a plausible result. Thus, scene primitives are commonly arranged in spatial data structures to accelerate the search. In the last two decades, the bounding volume hierarchy (BVH) has become the de facto standard acceleration data structure for ray tracing‐based rendering algorithms in offline and recently also in real‐time applications. In this report, we review the basic principles of bounding volume hierarchies as well as advanced state of the art methods with a focus on the construction and traversal. Furthermore, we discuss industrial frameworks, specialized hardware architectures, other applications of bounding volume hierarchies, best practices, and related open problems.

Eigenrays in 3D heterogeneous anisotropic media, Part I: Kinematics

ABSTRACTWe present a new ray bending approach, referred to as the Eigenray method, for solving two‐point boundary‐value kinematic and dynamic ray tracing problems in 3D smooth heterogeneous general anisotropic elastic media. The proposed Eigenray method is aimed to provide reliable stationary ray path solutions and their dynamic characteristics, in cases where conventional initial‐value ray shooting methods, followed by numerical convergence techniques, become challenging. The kinematic ray bending solution corresponds to the vanishing first traveltime variation, leading to a stationary path between two fixed endpoints (Fermat's principle), and is governed by the nonlinear second‐order Euler–Lagrange equation. The solution is based on a finite‐element approach, applying the weak formulation that reduces the Euler–Lagrange second‐order ordinary differential equation to the first‐order weighted‐residual nonlinear algebraic equation set. For the kinematic finite‐element problem, the degrees of freedom are discretized nodal locations and directions along the ray trajectory, where the values between the nodes are accurately and naturally defined with the Hermite polynomial interpolation. The target function to be minimized includes two essential penalty (constraint) terms, related to the distribution of the nodes along the path and to the normalization of the ray direction. We distinguish between two target functions triggered by the two possible types of stationary rays: a minimum traveltime and a saddle‐point solution (due to caustics). The minimization process involves the computation of the global (all‐node) traveltime gradient vector and the traveltime Hessian matrix. The traveltime Hessian is used for the minimization process, analysing the type of the stationary ray, and for computing the geometric spreading of the entire resolved stationary ray path. The latter, however, is not a replacement for the dynamic ray tracing solution, since it does not deliver the geometric spreading for intermediate points along the ray, nor the analysis of caustics. Finally, we demonstrate the efficiency and accuracy of the proposed method along three canonical examples.

Transfer operator approach to ray-tracing in circular domains

The computation of wave-energy distributions in the mid-to-high frequency regime can be reduced to ray-tracing calculations. Solving the ray-tracing problem in terms of an operator equation for the energy density leads to an inhomogeneous equation which involves a Perron–Frobenius operator defined on a suitable Sobolev space. Even for fairly simple geometries, let alone realistic scenarios such as typical boundary value problems in room acoustics or for mechanical vibrations, numerical approximations are necessary. Here we study the convergence of approximation schemes by rigorous methods. For circular billiards we prove that convergence of finite-rank approximations using a Fourier basis follows a power law where the power depends on the smoothness of the source distribution driving the system. The relevance of our studies for more general geometries is illustrated by numerical examples.

TURTLE: A C library for an optimistic stepping through a topography

TURTLE is a C library providing utilities allowing to navigate through a topography described by a Digital Elevation Model (DEM). The library has been primarily designed for the Monte Carlo transport of particles scattering over medium to long ranges, e.g. atmospheric muons. But, it can also efficiently handle ray tracing problems with very large DEMs (109 nodes or more), e.g. for neutrino simulations. The TURTLE library was built on an optimistic ray tracing algorithm, detailed in the present paper. This algorithm proceeds by trials and errors, approximating the topography within the modelling uncertainties of the DEM data. This allows to traverse a topography in constant time, i.e. independently of the number of grid nodes, and with no added memory. Detailed performance studies are provided by comparison to other ray tracing algorithms and as an application to muon transport in a Monte Carlo simulation. Program summaryProgram Title: The TURTLE libraryProgram Files doi:http://dx.doi.org/10.17632/pbnsctnbk8.1Licensing provisions: LGPL-3.0Programming language: C99Nature of problem: Transport long range Monte Carlo particles through a topography described by a high resolution Digital Elevation Model (DEM).Solution method: Mapping the ground surface on the fly using a heuristic requiring only the original DEM data.

ТОМОГРАФИЯ, ОСНОВАННАЯ НА ПРЕДСТАВЛЕНИИ МОДЕЛИ ПОЛИНОМАМИ ЧЕБЫШЕВА: ПРИМЕРЫ ИСПОЛЬЗОВАНИЯ

The paper deals with the three-dimensional travel-time tomography of the first arrivals. The model is represented by Chebyshev polynomials. This allows one to use a priori information about the model effectively and reduce the number of recoverable parameters to the required minimum. Also, such a model representation makes it possible to obtain a very efficient algorithm for solving the two-point ray-tracing problem for three-dimensional media, which is necessary for tomography. Examples of solving the three-dimensional cross-well tomography, as well as examples using tomography for the reconstruction of stress fields in the coal-rock mass are presented.

Gravitational wave effects on astrometric observables

Observational data from the ESA astrometric mission Gaia determining the positions of celestial objects within an accuracy of few microarcseconds will be soon fully available. Other satellite-based space missions are currently planned to significantly improve such precision in the next years. The data reduction process needs high-precision general relativistic models, allowing one to solve the inverse ray-tracing problem in the gravitational field of the Solar System up to the requested level of accuracy and leading then to the estimate of astrometric parameters. Besides a satisfactory description of the background field due to the planets (which should include their multipolar structure), one should consider also other effects which may induce modifications to the light propagation. For instance, the interaction of the light signal with the superposed gravitational field of a gravitational wave emitted by a distant source would cause a shift in the apparent positions of the stars. We compute here the main astrometric observables needed for data reduction of satellite-based missions in the presence of a passing plane gravitational wave. We also take into account the effect of the mass quadrupole moment of the planets, improving previous results obtained for Gaia.

Application of the optimization method to the point-to-point radio wave ray-tracing problem

Point-to-point ray tracing is an important problem in many fields of science. In direct variational methods, some trajectory is transformed to an optimal trajectory. While these methods are routinely used in calculations of pathways of seismic waves, chemical reactions, diffusion processes, etc., these approaches are not widely known in ionospheric point-to-point ray tracing. A two-dimensional representation of the optical path functional is developed, and used to gain insight into the fundamental difference between high and low ionospheric rays. We conclude that high and low rays are minima and saddle points of the optical path functional, respectively. An optimization method for point-to-point ionospheric ray tracing, based on the direct variational principle for the optical path, is proposed. This is applied to calculations of high, trans-ionospheric, and multi-hop rays.

Photorealistic volume scattering model in the bidirectional stochastic ray tracing problem

This paper is devoted to the development of physically correct rendering model of scenes containing volume scattering objects. The solution of the rendering equation is based on the Monte-Carlo bidirectional ray tracing. Two efficient approaches to the solution of the rendering equation for different parameters of the volume scattering medium (typically, concentration of scattering particles) are developed. Examples illustrate how the proposed models can be used for photorealistic visualization of scenes containing volume scattering objects and for the simulation of illuminators based on the volume scattering effect. Possible limitations of the application field of the proposed models are considered.

The ray tracing analytical solution within the RAMOD framework. The case of a Gaia-like observer

This paper presents the analytical solution of the inverse ray tracing problem for photons emitted by a star and collected by an observer located in the gravitational field of the Solar System. This solution has been conceived to suit the accuracy achievable by the ESA Gaia satellite (launched on 19 December 2013) consistently with the measurement protocol in General Relativity adopted within the RAMOD framework. The aim of this study is to provide a general relativistic tool for the science exploitation of such a revolutionary mission, whose main goal is to trace back star directions from within our local curved space-time, therefore providing a three-dimensional map of our Galaxy. The calculations are performed assuming that the massive bodies of the Solar System move uniformly and have monopole and quadrupole structures. The results are useful for a thorough comparison and cross-checking validation of what already exists in the field of relativistic astrometry. Moreover, the analytical solutions presented here can be extended to model other measurements that require the same order of accuracy as that expected for Gaia.

Vectorial approach of determining the wave propagation at metasurfaces

Vector approach often benefits optical engineers and physicists, and a vector formulation of the laws of reflection and refraction has been studied (Tkaczyk, 2012). However, the conventional reflection and refraction laws may be violated in the presence of a metasurface, and reflection and refraction at the metasurface obey generalized laws of reflection and refraction (Yu et al., 2011). In this letter, the vectorial laws of reflection and refraction at the metasurface were derived, and the matrix formulation of these vectorial laws are also obtained. These results enable highly efficient and unambiguous computations in ray-tracing problems that involve a metasurface.

Ray tracing — computing the incomputable?

We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical, error-prone (especially analogue rather than digital) computational systems. We take as a case study the ray-tracing problem, a Turing-machine-incomputable problem that can, in apparent violation of the Church-Turing thesis, nonetheless be said to be solved by certain optical computers; however, we apply the framework of complexity theory so as to formalize the intuition that the purported super-Turing power of these computers in fact vanishes once precision is properly considered.

The Erez–Rosen metric and the role of the quadrupole on light propagation

The gravitational field of a static body with the quadrupole moment is described by an exact solution found by Erez and Rosen. Here, we investigate the role of the quadrupole in the motion, deflection and lensing of a light ray in the above metric. The standard lensing observables such as image positions and magnification have been explicitly obtained in the weak-field and small-quadrupole limit. In this limit, the spacetime metric appears as the natural generalization to quadrupole corrections of the metric form adopted also in current astrometric models. Hence, the corresponding analytical solution of the inverse ray tracing problem and the consistency with other approaches are also discussed.

Polynomial Optics: A Construction Kit for Efficient Ray‐Tracing of Lens Systems

AbstractSimulation of light transport through lens systems plays an important role in graphics. While basic imaging properties can be conveniently derived from linear models (like ABCD matrices), these approximations fail to describe nonlinear effects and aberrations that arise in real optics. Such effects can be computed by proper ray tracing, for which, however, finding suitable sampling and filtering strategies is often not a trivial task. Inspired by aberration theory, which describes the deviation from the linear ray transfer in terms of wavefront distortions, we propose a ray‐space formulation for nonlinear effects. In particular, we approximate the analytical solution to the ray tracing problem by means of a Taylor expansion in the ray parameters. This representation enables a construction‐kit approach to complex optical systems in the spirit of matrix optics. It is also very simple to evaluate, which allows for efficient execution on CPU and GPU alike, including the computation of mixed derivatives of any order. We evaluate fidelity and performance of our polynomial model, and show applications in high‐quality offline rendering and at interactive frame rates.

Seismic ray tomography using L1 integral norm

Seismic ray tomography methods are usually associated with substantial computer processing time. The reason for this is that at each step of the iterative inversion process defined by the tomographic method the two-point ray tracing problem must be solved for each source-receiver pair. In order to resolve this, an Euclidean norm (L2 vector norm), commonly used in error functions which are to be minimized in inversion procedures, is substituted by an L1 integral norm, which enables the estimation of model parameters by minimizing the area between observed and calculated traveltime curves that are interpolated (or adjusted) to the data points. Relatively simple mathematical developments and numerical experiments with two-dimensional compressional seismic wave velocity field models showthat L1 integral norm saves an enormous amount of processing time with no significant loss of accuracy. Occasionally, parameters of the model can be better estimated using L1 integral norm than the L2 vector norm that is traditionally utilized in seismic inversion tomography.

Acceleration of acoustic raytracing using graphics processors.

OpenCL presents an industry standard interface to accelerate computationally expensive algorithms on consumer grade graphics hardware. Presented is a system in which raytracing for room acoustic simulation is accelerated with OpenCL. The system is primarily geared toward realtime applications such as video gaming or virtual reality, but may be extended to higher quality simulations for architectural acoustics. Different methods for mapping the raytracing problem onto the GPU are discussed, as well as strategies for optimizing the algorithm for graphics processors from different manufacturers.