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.

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.

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.

Fluoro-ruby retrograde tracing and three-dimensional visualization of the corticospinal tract in the guinea pig

Fluoro-ruby was injected into the posterior funiculus of the spinal cord in the cervical （C5-T2） and lumbar （L3-6） segments of adult guinea pigs. The spinal cord was cut into serial frozen sections. The Fluoro-ruby labeling was clearly delineated from the surrounding structure. The labeling traversed the cervical, thoracic and lumbar segments, and was located on the ventral portion of the posterior funiculus on the injected side, proximal to the intermediate zone of the dorsal gray matter. The fluorescence area narrowed rostro-caudally. The spinal cord, spinal cord gray matter and corticospinal tract were reconstructed using 3D-DOCTOR 4.0 software, resulting in a robust three-dimensional profile. Using functionality provided by the reconstruction software, free multi-angle observation and sectioning could be conducted on the spinal cord and corticospinal tract. Our experimental findings indicate that the Fluoro-ruby retrograde fluorescent tracing technique can accurately display the anatomical location of corticospinal tract in the guinea pig and that three-dimensional reconstruction software can be used to provide a three-dimensional image of the corticospinal tract.

A minimum traveltime ray tracing global algorithm on a triangular net for propagating plane waves

To address the problem of subdividing inflexible rectangular grid models and their poor definition of velocity interfaces,we propose a complex structure triangular net for a minimum traveltime ray tracing global algorithm.Our procedure is：（1） Subdivide a triangle grid based on the Delaunay triangular subdivision criterion and the relationships of the points,lines,and the surfaces in the subdividing area.（2） Define the topology relationships and related concepts of triangular unit ray tracing.（3） The source point and wave arrival points at any time compose the propagating plane wave and the minimum traveltime and secondary source positions are calculated during the plane wave propagation.We adopt the hyperbolic approximation global algorithm for secondary source retrieving.（4） By minimum traveltime ray tracing,collect the path from receiver to source points with the neighborhood point＇s traveltime and the direction of the secondary source.Numerical simulation examples are given to test the algorithm.The results show that the triangular net ray tracing method demonstrates model subdivision flexibility,precise velocity discontinuity interfaces,and accurate computations.

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.

Extension of e^N method to general three-dimensional boundary layers

In order to extend the eN method to general three-dimensional boundary layers, the conservation law of the imaginary parts for the wave parameters with a fixed wave vector is deduced. The compatibility relationship （CR） and the general theory of ray tracing （RT）, which have been extensively used in conservative systems, are applied to a general three-dimensional boundary layer belonging to non-conservative systems. Two kinds of eN methods, i.e., the eN-CR method and the eN-RT method, are established. Both the two kinds of methods can wavenumber and the amplitude of the be used to predict the evolutions of the spanwise disturbances in general three-dimensional boundary layers. The reliability of the proposed methods is verified and validated by performing a direct numerical simulation （DNS） in a hypersonic general three-dimensional boundary layer over an aircraft model. The results are also compared with those obtained by other eN methods, indicating that the proposed methods have great potential applications in improving the transition prediction accuracy in general three-dimensional boundary layers.

Marine Mobile Wireless Channel Modeling Based on Improved Spatial Partitioning Ray Tracing

In 5G era,it is expected to achieve wireless network coverage including offshore areas.Modeling of marine wireless channels is the basis of constructing a marine communication system.In this paper,a communication scene between an unmanned aerial vehicle(UAV)and a boat is simulated to study the marine wireless channel.Firstly,an improved spatial partitioning ray tracing algorithm is proposed to track the propagation path of electromagnetic waves at sea surface.Secondly,a mobile channel is simulated and modeled based on the track results.Finally,a loss measurement is carried out in the coastal waters based on the simple wireless channel loss measuring platform,and a path loss propagation model is built.Then we compare the actual measurement data with the simulation results and find that the two are have good consistency,which further verifies the reliability of the simulation.

Fast ray tracing method in 3-D structure and its proof of positive definiteness

Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.

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.

A Preliminary Ray Tracing Approach to Computational Electromagnetics for Reverberation Chambers

This paper summarizes a theoretical design analysis for the implementation of an electromagnetic modeling tool, focusing on the simulation of electromagnetic field propagation inside reverberation chambers. The simulation algorithms which have been developed rely on a ray tracing technique, adapted in such a way as to maximize compatibility with the specific requirements and parameters, as applicable for reverberation chambers. The most significant example of a typical parameter is the high rate of wave reflections inside the chambers’ cavity. An implementation of the algorithms was used for simulation of several theoretically predictable cases. Study of the results of these test cases showed that some of the design decisions and algorithms used need to be reviewed in order to optimize the computational aspects of the application, such as resource management (memory, CPU time). Results of typical sample cases are re- viewed in this paper as well, in order to identify possible pitfalls and objectives for future research.

Global heat transfer model and dynamic ray tracing algorithm for complex multiple turbine blades of Nibased superalloys in directional solidification process

High-quality solidification microstructure during directional solidification relies on precise temperature gradient control, so accurate calculation of the temperature field is critical. In this study, a 3D transient global heat transfer model of directional solidification by the Bridgman method based on the finite difference method is developed. The radiation heat in this model is calculated by the discrete transfer method, and a modified method of external surface area for irregular geometric models is proposed to reduce the zigzag shape caused by finite difference grids. Considering the radiative heat transfer between any surface elements of all materials in the directional solidification furnace, a dynamic ray tracing algorithm is developed to simulate the entire process of directional solidification. Then, the simulated results are compared with the theoretical results and experimental results, respectively. Finally, based on the present model and method, the simulation program developed is applied to the directional solidification of actual castings. The simulated results are in good agreement with the experimental results, which indicate that the model and method developed in this study is effective and practical.

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.

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.

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.

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.