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.

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.

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.

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 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.

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.

A rapid and accurate two-point ray tracing method in horizontally layered velocity model

A rapid and accurate method for two-point ray tracing in horizontally layered velocity model is presented in this paper. Numerical experiments show that this method provides stable and rapid convergence with high accuracies, regardless of various 1-D velocity structures, takeoff angles and epicentral distances. This two-point ray tracing method is compared with the pseudobending technique and the method advanced by Kim and Baag (2002). It turns out that the method in this paper is much more efficient and accurate than the pseudobending technique, but is only applicable to 1-D velocity model. Kim's method is equivalent to ours for cases without large takeoff angles, but it fails to work when the takeoff angle is close to 90°. On the other hand, the method presented in this paper is applicable to cases with any takeoff angles with rapid and accurate convergence. Therefore, this method is a good choice for two-point ray tracing problems in horizontally layered velocity model and is efficient enough to be applied to a wide range of seismic problems.

A Receiver Model for Ultrasonic Ray Tracing in an Inhomogeneous Anisotropic Weld

In this paper, a receiver model for ultrasonic ray tracing simulation is described. This is a complementary part of an existing simulation model and is the next step towards a numerical solution to the inverse problem and thus a NDT methodology for characterization of the dendrite orientation in a weld. The establishment of the receiver model is based on the electromechanical reciprocity principle. A concise retrospect of the weld model and the 2D model is made. The reciprocity principle is applied in an original way to handle the model problem including the back wall. Experimental qualitative validations for both P and SV waves on a specific weld are also made for C-scans included in this paper. Two different cases are studied. The first is a direct incidence of an ultrasonic ray towards the weld, and the second is a reflection from the back surface in the base material followed by an incidence to the weld. Even though mode-converted rays are excluded in the simulations, both the P and SV probe-models show the same behavior as the experimental results. The qualitative validation though reveals that it even if a thorough time-gating of received information would enable exclusion of mode-conversion in the model, inaccuracy of experimental results is affecting the evaluation of the weld model.

ACCELERATING RAY TRACING THROUGH POLYGON PROJECTION

An algorithm for accelerating ray tracing through polygon projection is proposed.Ray tracing,as it is well known,invokes large amount of computation,more than 70 percent of total rendering time is spent in calculating the intersections between rays and objects.Bounding volume is a commonly used technique for reducing the computation time, but this necessitates intersecting rays with bounding volumes.Our new algorithm avoids the initial intersection tests between primary rays and bounding volumes by polygon projection with little extra overhead.With this technique,the bounding volumes can be constructed as tightly as one wishes.Experiments show that the new algorithm is very efficient.

Ray tracing particle image velocimetry-Challenges in the application to a packed bed

Ray tracing Particle Image Velocimetry(RT-PIV)is an optical technique for high resolution velocity measurements in challenging optical systems,such as transparent packed beds,that uses ray tracing to correct for distortions introduced by transparent geometries in the light paths.The ray tracing based correction is a post processing step applied to the raw PIV particle images before classical PIV evaluation.In this study,RT-PIV is performed in the top layer of a body centred cubic(bcc)sphere packing with gaseous flow,where optical access is obtained by the use of transparent N-BK7 glass balls with a diameter of d=40 mm.RT-PIV introduces new experimental and numerical challenges,for example a limited field of view,illumination difficulties,a very large required depth of field and high sensitivity to geometric parameters used in the ray tracing correction.These challenges and their implications are the main scope and discussed in the present work.Further,the validation of the ray tracing reconstruction step is presented and examples for the obtained corrected vector fields in a packed bed are given.The results show the strength of the method in reconstructing velocity fields behind transparent spheres that would not have been accessible by optical measurement techniques without the ray tracing correction.

Multi-point temperature measurements in packed beds using phosphor thermometry and ray tracing simulations

Packed bed reactors are commonly found in the process industry,for example in flame-assisted calci-nation for cement production.Understanding the heat transfer inside the bed is essential for process control,product quality and energy efficiency.Here we propose a technique to determine the internal temperature distribution of packed beds based on a combination of lifetime-based phosphor ther-mometry,ray tracing simulations,and assimilation of temperature data using finite element heat transfer simulations.To establish and validate the technique,we considered a reproducible regular packing of 6 mm diameter aluminum spheres,with one of the spheres in the top layer being electrically heated.If a sphere inside the packing is coated with thermographic phosphors and excitation light is directed to-wards the packing,luminescence from the coated sphere exits the packed bed after multiple reflection and the sphere's temperature can be determined.Isothermal measurements showed that the temper-ature obtained by phosphor thermometry is independent of the luminescent sphere location.When imaging the luminescence on a camera,the luminescence distribution in recorded image depended,however,on the position of the sphere.Therefore,in setups with multiple phosphor-coated spheres,their signals can be separated using a least squares fit.We demonstrate the approach using a setup with three luminescent spheres and validated the temperature readings against thermocouple measurements.To obtain the spatial signatures for individual sphere positions required for the least squares fit,ray tracing simulations were used.These provide an efficient alternative to single sphere measurements that are only practical for regular spherical packed beds.Multi-point measurements were used as input to a finite element heat transfer simulations to determine parameters such as particle-to-particle air gap distance.With these,the full temperature distribution inside the bed could be assimilated from the measured values.

Fast Ray Tracing NURBS Surfaces

In this paper, a new algorithm with extrapolation process for computingthe ray/surface intersection is presented. Also, a ray is defined to be the in-tersection of two planes, which are nonorthogonal in general, in such a waythat the number of multiplication operations is reduced. In the preprocessingstep, NURBS surfaces are subdivided adaptively into rational Bezier patches.Parallelepipeds are used to enclose the respective patches as tightly as possible.Therefore, for each ray that hits the enclosure (i.e., parallelepiped) of a patchthe intersection points with the parallelepiped's faces can be used to vield agood starting poiat for the following iteration. The improved Newton iterationwith extrapolation process saves CPU time by reducing the number of iterationsteps. The intersection scheme is faster than previous methods for which published performance data allow reliable comparison. The method may also beused to speed up tracing the intersection of two parametric surfaces and otheroperations that need Newton iteration.