Beam Tracing Algorithm Research Articles

Optimizing Urban LiDAR Flight Path Planning Using a Genetic Algorithm and a Dual Parallel Computing Framework

This paper introduces a genetic algorithm (GA) and a beam tracing algorithm incorporated within a dual parallel computing framework to optimize urban aerial laser scanning (ALS) missions to maximize vertical façade data capture, as needed for many three-dimensional reconstruction and modeling workflows. The optimization employs a low-density point cloud from the site of interest as a spatial representation of the urban scene. The GA is suitable for LiDAR flight path optimization due to its capability of handling open-ended problems that have many solutions. However, GAs require evaluating a very large number of candidates. The use of an initial point cloud allows realistic modeling of the urban environment in the optimization at the cost of high data input volumes. To cope with the computational and data demands, a dual parallel computing framework was devised. The parallel computing framework consists of two layers of parallelization. In the upper layer, multiple evaluators work in parallel and in conjunction with a main multi-threading GA optimizer to perform GA operations and evaluate the flight paths. In the lower layer, to evaluate assigned flight paths, each evaluator distributes its data and computation to multiple executors, which can reside on multiple physical nodes of a distributed-memory computing cluster. In addition to parallelism, the data partitioning on the lower layer allows out-of-core computation. Namely, data partitions are efficiently transferred between disks and memory so that only relevant subsets of data are kept in the main memory. The objective of the proposed method is threefold: (1) search for flight paths that yield the highest numbers of vertical points, (2) create a means to explicitly consider the detailed spatial configuration of urban environments, and (3) assure that the proposed optimization strategy is fast and can scale to large problem sizes. Multiple experiments were conducted and demonstrated the success of the proposed method. Converged results were achieved after dozens of generations within two hours. Two flight paths identified by the GA as the most and the least optimal candidates were deployed in real flight missions. The optimal flight path captured 16% more vertical points than the least optimal one, slightly higher than the 13% predicted. Both layers of parallelization were efficient: 13.1/16 for the lower layer and 3.2/4 for the upper layer. The two complementary layers of parallelization allowed flexible and efficient use of distributed computing resources to reduce the runtime. The scalability of the proposed approach was successfully demonstrated up to a data size of 460 million points. The optimization results were realistic and aligned well with the test flight results.

Modified Beam-Splitting 1 (MBS-1) Algorithm for Solving the Problem of Light Scattering by Nonconvex Atmospheric Ice Particles

A new algorithm for solving the problem of light scattering by nonconvex crystals typical for cirrus clouds is presented. It is based on the beam tracing algorithm for convex particles (Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences). The new algorithm is applied for solving the problem of light scattering by hollow-column particles and aggregates of hexagonal ice columns. It is an opensource freely available algorithm.

A hybrid numerical–asymptotic boundary element method for high frequency scattering by penetrable convex polygons

We present a novel hybrid numerical–asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated transmission boundary value problem as a direct boundary integral equation for the unknown Cauchy data, but with a nonstandard numerical discretization which efficiently captures the high frequency oscillatory behaviour. The Cauchy data is represented as a sum of the classical geometrical optics approximation, computed by a beam tracing algorithm, plus a contribution due to diffraction, computed by a Galerkin boundary element method using oscillatory basis functions chosen according to the principles of the Geometrical Theory of Diffraction. We demonstrate with a range of numerical experiments that our boundary element method can achieve a fixed accuracy of approximation using only a relatively small, frequency-independent number of degrees of freedom. Moreover, for the scattering scenarios we consider, the inclusion of the diffraction term provides an order of magnitude improvement in accuracy over the geometrical optics approximation alone.

Areawide dynamic traffic noise simulation in urban built-up area using beam tracing approach

Modeling areawide traffic noise in both space and time domain is a tedious work, especially in urban built-up area. A smart, accurate and rapid method was developed specifically for fixed grid sources and receivers(S-R), which consisted of the precomputed S-R attenuations in off-line, dynamic traffic noise simulation in real time and a database to connect two parts together. In off-line part, beam tracing approach was used to simulate sound propagation among buildings, taking multiple reflections and diffractions into consideration. Firstly, the spatial subdivision was used to subdivide 2D space into a series of order triangles, and then beam tracing algorithm recursively traced beams through these triangles, which was represented by beam tree data structure. In real-time part, the dynamic simulation of traffic provides time-variant input of traffic flow parameters to vehicle emission model, which was then assigned to the nearest source. After deducing S-R attenuations from database, dynamic immissions at grid receivers are obtained by summing up sources inside their circular viewport. Therefore, the outputs (Ln, Leq and LNP) were available to assess the noise pollution levels on a spatial and temporal scale. A part of Zhujiang New Town in Guangzhou was chosen as a validation area, measurement results were in general good agreement with simulations.

Hybrid numerical-asymptotic approximation for high-frequency scattering by penetrable convex polygons

We consider time-harmonic scattering by penetrable convex polygons, a Helmholtz transmission problem. Standard numerical schemes based on piecewise polynomial approximation spaces become impractical at high frequencies due to the requirement that the number of degrees of freedom in any approximation must grow at least linearly with respect to frequency in order to represent the oscillatory solution. High frequency asymptotic methods on the other hand are non-convergent and may be insufficiently accurate at low to medium frequencies. Here, we design a hybrid numerical-asymptotic boundary element approximation space that combines the best features of both approaches. Specifically, we compute the classical geometrical optics solution using a beam tracing algorithm, and then we approximate the remaining diffracted field using an approximation space enriched with carefully chosen oscillatory basis functions. We demonstrate via numerical simulations that this approach permits the accurate and efficient representation of the boundary solution and the far field pattern.

浅海水声信道动态响应建模与仿真研究<br>Dynamic Response Modeling and Simulation in Shallow Water Acoustic Channel

水声通信系统必须与海洋通信信道相匹配才能达到良好的通信性能，如何对这样一个复杂多变的信道环境进行建模和仿真成为了一个研究的热点。本文主要研究浅海水声信道的仿真建模方法。利用BELLHOP高斯射线束跟踪法，对浅海信道的多途特性进行了建模；针对传统声线模型在信道动态响应建模上的不足，提出了一种新型的动态响应信道建模方法，仿真了信道的多途多普勒效应。分析了不同条件下信号的频谱规律。仿真结果与理论值相符，证明了模型的有效性。 Underwater acoustic communication system must match the communication channel in order to achieve a good performance. How to simulate for such a complex channel has become a hot research. This paper studied the shallow water acoustic channel modeling and simulation method. Using BELLHOP Gauss-ray beam tracing algorithm, modeled the multipath characteristics of the Shallow Water Acoustic Channel. Aiming at the lack of the traditional ray beam method, modeled a dynamic response channel. Simulated and analyzed the Doppler effect of the spectrum. The result showed that the Doppler shift was consistent with the theoretical value, which proved the effectiveness of the design.

Prediction of urban sound propagation via adaptive beam tracing.

Prediction of urban sound propagation is an integral part for the assessment of noise levels in cities. Several propagation modeling methods exist to predict sound propagation in city environments including parabolic equation, diffusion equation, radiosity, ray tracing, image source, modal analysis, and transmission line matrix methods. For this study, adaptive beam tracing as a geometrical acoustic prediction method is applied in the context of predicting sound propagation in complex urban environments. Adaptive beam tracing is advantageous compared to the ray tracing and image source methods by eliminating aliasing errors and spurious image sources, respectively. A model of diffraction [Svensson et al., J. Acoust. Soc. Am. 106, 2331–2344 (1999)] is integrated with the adaptive beam tracing algorithm in order to enhance the prediction capability of the proposed method. The effects of facade roughness, street canyon shielding, and building spacing are investigated. Comparison of the proposed method is mad...

Framework for Real-Time Auralization in Architectural Acoustics

Auralization is the process of making audible the acoustics of complex virtual architectural spaces in a realistic and accurate manner. This paper presents a novel real-time auralization software environment comprising a room acoustic modeler, a spatial renderer for auralization, and a visualization and scene graph unit for interactivity. The computation of early reflection paths within the geometric model is based on an efficient beam tracing algorithm capable of real-time detection of specular reflection paths in a static geometry with one or several moving listener(s). For “simple" rooms, the real-time performance is maintained even with dynamic geometries and sources. Results of the room acoustic model consisting of visible reflection paths and their accumulated material attenuation are sent to the audio renderer. From this geometrical and acoustical data, listener position-relative 3D room impulse responses are generated using a hierarchical-order Ambisonics approach. Finally, the spatialized audio output is presented to the listener via multiple loudspeakers or binaurally rendered over headphones. As higher order reflections are more diffuse in nature, they are encoded using lower Ambisonic orders, thereby reducing computational load. The environment combines high quality audio with visual rendering realized using the open source platforms Pure Data and VirChor respectively. This open source auralization framework provides direct audio-visual interaction in real-time and is suitable for VR environments.

Accelerated beam tracing algorithm

Determining early specular reflection paths is essential for room acoustics modeling. Beam tracing algorithms have been used to calculate these paths efficiently, thus allowing modeling of acoustics in real-time with a moving listener in simple, or complex but densely occluded, environments with a stationary sound source. In this paper, it is shown that beam tracing algorithms can still be optimized by utilizing the spatial coherence in path validation with a moving listener. Since the precalculations required for the presented technique are relatively fast, the acoustic reflection paths can be calculated even for a moving source in simple cases. Simulations were performed to show how the accelerated algorithm compares with the basic algorithm with varying scene complexity and occlusion. Up to two-orders of magnitude speed-up was achieved.

Acoustic modeling apparatus and method using accelerated beam tracing techniques

An acoustic modeling system and an acoustic modeling method use beam tracing techniques that accelerate computation of significant acoustic reverberation paths in a distributed virtual environment. The acoustic modeling system and method perform a priority-driven beam tracing to construct a beam tree data structure representing “early” reverberation paths between avatar locations by performing a best-first traversal of a cell adjacency graph that represents the virtual environment. To further accelerate reverberation path computations, the acoustic modeling system and method according to one embodiment perform a bi-directional beam tracing algorithm that combines sets of beams traced from pairs of avatar locations to efficiently find viable acoustic reverberation paths.

Beam-tracing model for predicting sound fields in rooms with multilayer bounding surfaces

This paper presents the development of a wave-based room-prediction model for predicting steady-state sound fields in empty rooms with specularly reflecting, multilayer surfaces. A triangular beam-tracing model with phase, and a transfer-matrix approach to model the surfaces, were involved. Room surfaces were modeled as multilayers of fluid, solid, or porous materials. Biot theory was used in the transfer-matrix formulation of the porous layer. The new model consisted of the transfer-matrix model integrated into the beam-tracing algorithm. The transfer-matrix model was validated by comparing predictions with those by theory, and with experiment. The test surfaces were a glass plate, double drywall panels, double steel panels, a carpeted floor, and a suspended-acoustical ceiling. The beam-tracing model was validated in the cases of three idealized room configurations—a small office, a corridor, and a small industrial workroom—with simple boundary conditions. The number of beams, the reflection order, and the frequency resolution required to obtain accurate results were investigated. Beam-tracing predictions were compared with those by a method-of-images model with phase. The model will be used to study sound fields in rooms with local- or extended-reaction multilayer surfaces.

Interactive and aliasing-free acoustic modeling of reflections and diffractions in architectural environments

A primary challenge in geometrical acoustic modeling is computation of reverberation paths from sound sources fast enough for real-time auralization. This paper describes an aliasing-free beam tracing algorithm based on precomputed spatial subdivision and beam tree data structures that enables real-time acoustic modeling and auralization for sound sources in interactive applications. The proposed method traces convex polyhedral beams from the location of each sound source and receiver through a precomputed spatial subdivision data structure, constructing a beam tree representing the regions of space reachable by potential sequences of transmissions, diffractions, and specular reflections at surfaces of a 3D polygonal model. By computing beam trees asynchronously (off-line), our system can generate reverberation paths between sources and receivers at interactive rates and spatialize audio signals in real-time as sources and receivers move under interactive user control. Unlike previous geometrical acoustic modeling work, our beam tracing method: (1) supports evaluation of early reverberated paths at interactive rates, (2) scales well for large, densely occluded architectural environments, and (3) computes paths of diffraction without aliasing using the uniform theory of diffraction. This system is being used to develop interactive applications in which a user experiences a virtual environment immersively via simultaneous auralization and visualization.

Priority‐Driven Acoustic Modeling for Virtual Environments

Geometric acoustic modeling systems spatialize sounds according to reverberation paths from a sound source to a receiver to give an auditory impression of a virtual 3D environment. These systems are useful for concert hall design, teleconferencing, training and simulation, and interactive virtual environments. In many cases, such as in an interactive walkthrough program, the reverberation paths must be updated within strict timing constraints ‐ e.g., as the sound receiver moves under interactive control by a user. In this paper, we describe a geometric acoustic modeling algorithm that uses a priority queue to trace polyhedral beams representing reverberation paths in best‐first order up to some termination criteria (e.g., expired time‐slice). The advantage of this algorithm is that it is more likely to find the highest priority reverberation paths within a fixed time‐slice, avoiding many geometric computations for lower‐priority beams. Yet, there is overhead in computing priorities and managing the priority queue. The focus of this paper is to study the trade‐offs of the priority‐driven beam tracing algorithm with different priority functions. During experiments computing reverberation paths between a source and a receiver in a 3D building environment, we find that priority functions incorporating more accurate estimates of source‐to‐receiver path length are more likely to find early reverberation paths useful for spatialization, especially in situations where the source and receiver cannot reach each other through trivial reverberation paths. However, when receivers are added to the environment such that it becomes more densely and evenly populated, this advantage diminishes.

Beam-tracing-based inverse scattering for general aperture antennas

Iterative techniques are presented for two-dimensional inverse scattering from electrically large regions. The region is illuminated by transmitters with arbitrary profiles; this is an escalation in complexity from the line-source and the plane-wave excitations considered in many previous inverse-scattering studies. Imaging algorithms require an accurate and efficient forward model. Here a Gaussian-beam algorithm is utilized as a forward solver and is incorporated into an iterative-Born inversion scheme. General antenna profiles are incorporated into the algorithm by use of the matched-pursuits technique, by which the aperture fields are matched to the beam-tracing algorithm. Results are presented for several cases in which the simple Born approximation fails. Issues addressed include the types of profiles that can be successfully imaged, suitable antenna distributions, and the range of parameters over which the scheme is effective. Performance of the algorithm in the presence of noisy data is also tested.

LDV measurement of turbulent liquid velocity field in channels with curved wall

This paper reports the use of a beam tracing algorithm and a beam steering device to measure, by two-component laser Doppler velocimetry, the velocity field in isothermal turbulent flow of liquid Refrigerant-113 through a vertical pyrex glass tube. Measurement of the mean velocity field in isothermal and heated turbulent flow of the same liquid through a vertical concentric annular channel is also reported. Satisfactory data are obtained and the measurement method is deemed suitable for further detailed measurements.

Geometric beam tracing

Despite their approximate nature, ray methods continue to play an important role in ocean acoustic modeling−sometimes there is no practical alternative, for instance, in modeling impulses or high-frequency sources in 3-D environments. Unfortunately, ray methods are prone to implementation difficulties which often degrade their accuracy. Problems include the failure to locate an eigenray (leading to artificial drop-outs), errors in tracking the phase change through a caustic or singularities at caustics. Gaussian beam methods have been proposed as a remedy; they lead to particularly simple codes free of these problems. However, the promise of Gaussian beam methods remains partially unfulfilled since the optimal choice of beam initial conditions is still being debated. A modified beam tracing algorithm is described that preserves the appealing structural simplicity of Gaussian beam tracing but sacrifices the caustic correction to obtain a robust algorithm. Plots of transmission loss show that the resulting model yields excellent agreement with more computationally intensive full-wave models.