The Implementation of Ray Tracing Algorithm with OpenMP Parallelization

Ray tracing is a computer graphics method that renders images realistically. As the name suggests, this technique primarily traces the path of light rays interacting with objects in a scene [1], permitting the calculation of lighting and reflecting impact [2]. As ray tracing is a time-consuming process, the need for parallelization to solve this problem arises. One downside of this solution is the existence of race conditions. In this work, we explore and experiment with a different, well-known solution for this race condition. Starting with the introduction and the background section, a brief overview of the topic is followed by a detailed part of how the race conditions may occur in the case of the ray tracing algorithm. Continuing with the methods and results section, we have used OpenMP to parallelize the Ray tracing algorithm with the different compiler directives critical, atomic, and first-private. Hence, it concluded that both critical and atomic are not efficient solutions to produce a good-quality picture, but first-private succeeded in producing a high-quality picture.

Point cloud-based environment reconstruction and ray tracing simulations for railway tunnel channels

Radio propagation environment plays a critical role in the performance of wireless communication systems,and understanding channel characteristics is vital for ensuring reliable communication links and optimizing system performance.Ray tracing is an effective method to investigate propagation characteristics in a complex environment,and how to quickly and accurately obtain environmental information needs to be solved.This paper presents dynamic environment reconstruction and ray tracing simulation in railway tunnel environment based on Simultaneous Localization and Mapping(SLAM)algorithm and Poisson reconstruction algorithm.Accurate channel parameters are obtained and analyzed based on ray tracing simulation.Both straight and curved tunnels are considered and investigated,and the results show the channel characteristics in complex railway tunnel environments.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

Key technologies for wireless network digital twin towards smart railways

An emerging railway technology called smart railway promises to deliver higher transportation efficiency,enhanced comfort in services,and greater eco-friendliness.The smart railway is expected to integrate fifth-generation mobile communication(5G),Artificial Intelligence(AI),and other technologies,which poses new problems in the construction,operation and maintenance of railway wireless networks.Wireless Digital Twins(DTs),which have recently emerged as a new paradigm for the design of wireless networks,can address these problems and enable the whole lifecycle management of railway wireless networks.However,there are still many scientific issues and challenges for railway-oriented wireless DT.Relevant key technologies to solve these problems are introduced and described,including characterization of materials'physical-EM properties,autonomous reconstruction of Three-dimensional(3D)environment model,AI-empowered environmental cognition,Ray-Tracing(RT),model-based and AIbased RT acceleration,and generation of multi-spectra sensing data.Moreover,this paper presents our research results for each key technology and describes the wireless network planning and optimization system based on highperformance RT developed by our laboratory.This paper outlines the framework for realizing the wireless DT of smart railways,providing the direction for future research.

Target-oriented Gaussian beam migration using a modif ied ray tracing scheme

For large-scale 3D seismic data,target-oriented reservoir imaging is more attractive than conventional full-volume migration,in terms of computation efficiency.Gaussian beam migration(GBM)is one of the most robust depth imaging method,which not only keeps the advantages of ray methods,such as high efficiency and flexibility,but also allows us to solve caustics and multipathing problems.But conventional Gaussian beam migration requires slant stack for prestack data,and ray tracing from beam center location to subsurface,which is not easy to be directly applied for target-oriented imaging.In this paper,we modify the conventional Gaussian beam migration scheme,by shooting rays from subsurface image points to receivers to implement wavefield back-propagation.This modification helps us to achieve a better subsurface illumination in complex structure and allows simple implementation for target reservoir imaging.Significantly,compared with the wavefi eld-based GBM,our method does not reconstruct the subsurface snapshots,which has higher efficiency.But the proposed method is not as efficient as the conventional Gaussian beam migration.Synthetic and field data examples demonstrate the validity and the target-oriented imaging capability of our method.

Influence of Cy berKnife Prescription Isodose Line on the Discrepancy of Dose Results Calculated by the Ray Tracing and Monte Carlo Algorithms for Head and Lung Plans: A Phantom Study

Incorporation of the Monte Carlo(MC)algorithm in optimizing CyberKnife(CK)plans is cumbersome,and early models unconfigured MC calculations,therefore,this study investigated algorithm-based dose calculation discrepancies by selecting different prescription isodose lines(PIDLs)in head and lung CK plans.CK plans were based on anthropomorphic phantoms.Four shells were set at 2-60 mm from the target,and the constraint doses were adjusted according to the design stratcgy.After optimization,30%-90%PIDL plans were generated by ray tracing(RT).In the evaluation module,CK plans were recalculated using the MC algorithm.Therefore,the dosimetric parameters of different PIDL plans based on the RT and MC algorithms were obtained and analyzed.The discrepancies(mean+SD)were 3.72%+0.31%,3.40%+0.11%,3.47%+0.32%,0.17%+0.11%,0.64%+3.60%,7.73%+1.60%,14.62%+3.21%and 10.10%+1.57%for Djs,Dmeam),Dys,and coverage of the PTV,DGI,V,,V;and V,in the head plans and-6.32%+1.15%,-13.46%+0.98%,-20.63%+2.25%,-34.78%+25.03%,12248%+175.60%,-12.92%+5.41%,3.19%+4.67%and 7.13%+1.56%in the lung plans,respectively.The following parameters were significantly correlated with PIDL:dp98%at the 0.05 level and dpal,dys and dv3 at the 0.01 level for the head plans;dp98e%at the 0.05 level and do1e%,dpmeam,Ccoweange,dool,dvs and dv;at the 0.01 level for the lung plans.RT may be used to calculate the dose in CK head plans,but when the dose of organs at risk is close to the limit,it is necessary to refer to the MC results or to further optimize the CK plan to reduce the dose.For lung plans,the MC algorithm is recommended.For early models without the MC algorithm,a lower PIDL plan is recommended;otherwise,a large PIDL plan risks serious underdosage in the target area.

RAY TRACING BEZIER SURFACE

A new algorithm for ray tracing bicubic Bezier surface intersection is presented. In order to find the intersected patches more effectively, a quadtree representation for surface patches is utilized. The introduction of the alternative binary tree subdivision of Bezier surface effectively improves the performance of the ray surface intersection, with the benefit of avoiding the problem that the binary tree subdivision would produce long narrow patches and speeding the intersection finding process. The algorithm has been programmed in FORTRAN-77 and on prime-550 II computer. The result shows that its structure is simple and it is easy to implement with good performance.

Ray tracing/correlation approach to estimation of surface-based duct parameters from radar clutter

This paper describes a technique to estimate surface-based duct parameters by using a simple ray tracing/correlation method. The approach is novel in that it incorporates the Spearman rank-order correlation scheme between the observed surface clutter and the surface ray density for a given propagation path. The simulation results and the real data results both demonstrate the ability of this method to estimate surface-based duct parameters. Compared with the results obtained by a modified genetic algorithm combined with the parabolic wave equation, the results retrieved from the ray tracing/correlation scheme show a minor reduction in accuracy but a great improvement on computation time. Therefore the ray tracing/correlation method might be used as a precursor to more sophisticated and slower techniques, such as genetic algorithm and particle filters, by narrowing the parameter search space and providing a comprehensive and more efficient estimation algorithm.

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameteri- zation in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in trans- versely homogeneous elliptically anisotropic media. Seis- mic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in ellipti- cally anisotropic media with an irregular surface.

Locating flaws in anisotropic and inhomogeneous weldments using ray tracing method

Ultrasonic inspections on nickel-based alloy weldments meets some difficulties due to the curvilinear propagating paths will appear in both anisotropic and inhomogeneons welded joints. Thus, it is difficult to determine the exact location of flaws using the traditional ultrasonic testing method which is based on the assumption that the sound beam will propagate in straight lines. In order to overcome this problem, we provide a new model-based inspection approach to locate the flaws in the nickel-based alloy weldments. Furthermore, some experimental examinations are carried out to compare the locating accuracy between the traditional and the modeled-based approach. It shows that the provided model-based inspection method is more accurate than the traditional method in inspection of the nickel-based alloy weldments.

Indirect-approach method for specified-end points seismic ray tracing in three dimen-sional inhomogeneous media

Generally speaking, the factors of both medium and tectonic that give rise to heterogeneity of the earth crust and mantle structures should be taken into account simultaneously in three dimensional seismic ray tracing. In this paper, the three dimensional structure models are constructed with the model similar to generation system in computer aid design and manufacturing (CAD/CAM). Based on the algorithm proposed by Cerveny et al . for complete seismic ray tracing in complex three dimensional structures, a new technique called the indirect approach method for two point seismic ray tracing in three dimensional laterally heterogeneous media has been put forward, and its numerical computing examples were given.

Ray Tracing for Doppler Backscattering System in the Experimental Advanced Superconducting Tokamak

The Doppler backscattering system has been widely used for turbulence measurements,and the microwave beam will be backscattered near the cut-off layer when the Brag condition is fulfilled.In tokamak,the ray-tracing code is used to obtain the radial position and perpendicular wave number of the scattering layer for turbulence velocity measurement and the WKB（Wentzel-Kramers-Brillouin） approximation should be satisfied for optical propagation.To calculate the backscattering location and wave number at the cut-off layer only,a single ray tracing in the cross section is enough,while for spatial and wave number resolution calculation,multiple rays reflecting the microwave beam size should be used.Considering the angle between the wave vector and the magnetic field,a three-dimension quasi-optical Gaussian ray tracing is sometimes needed.

Ray-tracing simulations of whistler-mode wave propagation in different rescaled dipole magnetic fields

Kinetic simulation is a powerful tool to study the excitation and propagation of whistler-mode waves in the Earth’s inner magnetosphere.This method typically applies a scaled-down dipole magnetic field to save computational time.However,it remains unknown whether whistler wave propagation in the scaled-down dipole field is consistent with that in the realistic dipole field.In this work,we develop a ray-tracing code with a scalable dipole magnetic field to address this concern.The simulation results show that parallel whistler waves at different frequencies gradually become oblique after leaving the equator and propagate in different raypaths in a dipole magnetic field.During their propagation,the higher frequency waves tend to have larger wave normal angles at the same latitude.Compared with the wave propagation in a realistic dipole field,the wave raypath and wave normal remain the same,whereas the wave amplification or attenuation is smaller because of the shorter propagation time in a scaled-down dipole field.Our study provides significant guidance for kinetic simulations of whistler-mode waves.

Measurement and verification of concentration-dependent diffusion coefficient:Ray tracing imagery of diffusion process

Ray tracing method is used to study the propagation of collimated beams in a liquid-core cylindrical lens(LCL),which has dual functions of diffusion cell and image formation.The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations,the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution.Guided by the calculation conditions,the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper.The spatial and temporal concentration profile Ce(z,t)of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL;Then,the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C)=D0×(1+α1C+α2C2+α3C3+…).The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn(z,t).The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn(z,t)with Ce(z,t).Finally,the obtained polynomial D(C)is used to calculate the refractive index profiles nn(z,t)s of diffusion solution in the used LCL.Based on the ray propagation law in inhomogeneous media and the calculated n(z,t),the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C).The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.

A Ray-Tracing Analysis of ICRH in Tokamaks

Power deposition profiles generated by Ion Cyclotron Resonance Heating （ICRH） in non-circular tokamaks are studied using a ray-tracing technique. The simulation results for the Experimental Advanced Superconductor Tokamak （EAST） D-shaped plasma are presented. It is indicated that the spatial distributions of plasma parameters （plasma density, species temperature, minority ion concentration, etc.） have an significant influence on the power deposition profiles. The findings may be highly useful to the planned plasma heating and experiments in EAST.

A Fast Algorithm for Ray Tracing

A fast algorithm for ray tracing is presented, with which the specular reflection term of global illumination model is improved. A hybrid technique combining hierarchical bounding volumes and constant size box partitioning is presented and a fast box traversal algorithm is used. By this technique multiple ray intersections with objects that are in more than one box can be avoided. As a result, the speed of ray tracing is considerably increased.

Ray Tracing Study of Electromagnetic Ion Cyclotron Waves Associated with Bi-Ion Frequencies

Ray tracing study of electromagnetic ion cyclotron （EMIC） waves is conducted based on a realistic plasma density model. The simulation result shows that EMIC waves propagate away from the equatorial source region to higher latitudes basically along geomagnetic field lines, and are reflected at the region where their frequency matches the local bi-ion frequency. H＋ band suffers H＋-He＋ bi-ion frequency reflection at lower latitudes, whereas He＋ band suffers He＋-O＋ bi-ion frequency reflection at higher latitudes. Moreover, the concentration of heavy ions slightly affects the bi-ion frequencies and then slightly determines the reflection location of ray paths of EMIC waves. The current results present the first detailed study on the propagation characteristics of EMIC waves associated with bi-ion frequencies.

A Three-Dimensional Ray Tracing Study on Whistler-Mode Chorus During Geomagnetic Activities

A three-dimensional ray tracing study of a whistler-mode chorus is conducted for different geomagnetic activities by using a global core plasma density model. For the upperband chorus, the initial azimuthal wave angle affects slightly the projection of ray trajectories onto the plane （Z, √（x^2 ＋ y^2））, but controls the longitudinal propagation. The trajectory of the upper-band chorus is strongly associated with the plasmapause and the magnetic local time （MLT） of chorus source region. For the high geomagnetic activity, the chorus trajectory moves inward together with the plasmapause. In the bulge region, the plasmapause extends outward, while the chorus trajectory moves outward together with the plasmapause. For moderately or high geomagnetic activity, the lower-band chorus suffers low hybrid resonance （LHR） reflection before it reaches the plasmapause, leading to a weak correlation with the geomagnetic activity and magnetic local time of the chorus source region. For low geomagnetic activity, the lower-band chorus may be reflected firstly at the plasmapause instead of suffering LHR reflection, exhibiting a propagation characteristic similar to that of the upper-band chorus. The results provide a new insight into the propagation characteristics of the chorus for different geomagnetic activities and contribute to further understanding of the acceleration of energetic electron by a chorus wave.

Focusing behaviors of ultrasonic phased arrays in anisotropic and inhomogeneous weldments

It meets some difficulties in the case of ultrasonic phased arrays testing for the nickel-based alloy welded joint, since the ultrasound will propagate with curvilinear paths in this kind anisotropic joint. Thus, it is hard to calculate the phased array time delays properly according to the traditional focusing approach, which is based on the assumption that the sound beam will propagate in straight lines. In order to focus the phased arrays beam in this kind anisotropic joint, we provide a modified focusing approach by combining the ray tracing method and the bisectional searching optimization. With the help of this focusing approach, the curved ray path connecting each element position in phased arrays to the expected focus point in weldments can be determined, so that it can be used to calculate the proper time delay and control the beam focusing in the anisotropic weldment. Furthermore, some experimental examinations are carried out to compare the focusing behaviors between the traditional and the modified focusing approach. It shows that the provided focusing approach is more accurate than the traditional method in the case of inspection on the nickel-based alloy weldments.

Channel Characteristics Based on Ray Tracing Methods in Indoor Corridor at 300 GHz

With the rapid development of communication technology,people's demand for ultra-high-speed wireless links becomes higher,among which terahertz spectra are considered as one of the most promising spectra.In this paper,we analyze the channel characteristics at 300 GHz in indoor corridor based on ray tracing methods,including the large-scale and small-scale fading parameters.Simulation results show that it is suitable for short distance transmission due to its large path loss(PL).Firstly,compared with line-of-sight(LoS),the correlation of frequency components in non-line-of-sight(NLoS)is much better,but LoS has more abundant circle angular spread(CAS).Then,a stochastic model is well derived to describe the distance-dependent behaviour of root-mean-square delay spread(RMS-DS)as well as root-mean-square CAS(RMS-CAS).Besides,we find that the channel capacity can effectively increase by increasing the transmitted power in both LoS and NLoS.Finally,it can be seen that the RMS-DS can be significantly reduced in LoS and the channel capacity can increase by changing the position of the transceivers.The simulation results will provide references for future indoor communication.