A Review of Spatial Sound for Virtual Environments and Games with Graphics Processing Units <s> Geometric-Based Modeling <s> A set of analytical expressions has been developed which will predict the absorption of sound in air at 20°C. The results agree within 3% of previous work in the frequency range of 100 Hz 1 MHz for all humidities. Below 100 Hz accuracy cannot be judged because of lack of knowledge about the vibration‐vibration energy transfer between CO2 and O2. <s> BIB001 </s> A Review of Spatial Sound for Virtual Environments and Games with Graphics Processing Units <s> Geometric-Based Modeling <s> It is shown how the information contained in an energy histogram obtained by ray tracing can be converted into an equivalent impulse response which, after binaural processing, is ready for auralization sufficient for the auralization process. Furthermore the steps are discussed which are needed to transform this information into a binaural impulse response ready for a convolution with music signals <s> BIB002 </s> A Review of Spatial Sound for Virtual Environments and Games with Graphics Processing Units <s> Geometric-Based Modeling <s> The creation of photorealistic images of three-dimensional models is central to computer graphics. Photon mapping, an extension of ray tracing, makes it possible to efficiently simulate global illumination in complex scenes. Photon mapping can simulate caustics (focused light, like shimmering waves at the bottom of a swimming pool), diffuse inter-reflections (e.g., the bleeding of colored light from a red wall onto a white floor, giving the floor a reddish tint), and participating media (such as clouds or smoke). This book is a practical guide to photon mapping; it provides both the theory and the practical insight necessary to implement photon mapping and simulate all types of direct and indirect illumination efficiently. <s> BIB003 </s> A Review of Spatial Sound for Virtual Environments and Games with Graphics Processing Units <s> Geometric-Based Modeling <s> We present a modified photon mapping algorithm capable of running entirely on GPUs. Our implementation uses breadth-first photon tracing to distribute photons using the GPU. The photons are stored in a grid-based photon map that is constructed directly on the graphics hardware using one of two methods: the first method is a multipass technique that uses fragment programs to directly sort the photons into a compact grid. The second method uses a single rendering pass combining a vertex program and the stencil buffer to route photons to their respective grid cells, producing an approximate photon map. We also present an efficient method for locating the nearest photons in the grid, which makes it possible to compute an estimate of the radiance at any surface location in the scene. Finally, we describe a breadth-first stochastic ray tracer that uses the photon map to simulate full global illumination directly on the graphics hardware. Our implementation demonstrates that current graphics hardware is capable of fully simulating global illumination with progressive, interactive feedback to the user. <s> BIB004 </s> A Review of Spatial Sound for Virtual Environments and Games with Graphics Processing Units <s> Geometric-Based Modeling <s> The modeling of room acoustics and simulation of sound wave propagation remain a difficult and computationally expensive task. Two main techniques have evolved, with one focusing on a real physical - wave-oriented - sound propagation, while the other approximates sound waves as rays using raytracing techniques. Due to many advances in computer science, and especially computer graphics over the last decade, interactive 3D sound simulations for complex and dynamic environments are within reach. Inthispaperweanalyzesoundpropagationintermsofacoustic energy and explore the possibilities to map these concepts to radiometry and graphics rendering equations. Although we concentrate on ray-based techniques, we also partially consider wavebased sound propagation effects. The implemented system exploits modern graphics hardware and rendering techniques and is able to efficiently simulate 3D room acoustics, as well as to measure simplified personal HRTFs through acoustic raytracing. <s> BIB005
Many acoustical modeling approaches adopt the hypothesis of "geometric acoustics" that assumes that sound is a ray phenomenon. The acoustics of an environment is then modeled by tracing (following) these "sound rays" as they propagate through the environment while accounting for any interactions between the sound rays and any objects/surfaces they may encounter (see Fig. 3 ). Mathematical models are used to account for sound source emission patterns, atmospheric scattering, and the medium's absorption of sound ray energy as a function of humidity, temperature, frequency, and distance BIB001 . At the receiver, the RIR is obtained by constructing an echogram which describes the distribution of incident sound energy (rays) over time. The equivalent room impulse response can be obtained by post-processing the echogram BIB002 . Fig. (3) . Ray-based acoustical modeling. Reprinted from BIB005 . Audio-based ray tracing using the GPU was implemented by Jedrzejewski to compute the propagation of acoustical reflections in highly occluded environments and to allow for the sound source and the listener to move throughout the simulation without the need for a long pre-computation phase  . The method consists of six phases, the first four of which constitute a short pre-computation stage. Jedrzejewski takes advantage of the fact that in acoustics, as opposed to graphics, objects other than walls do not contribute significantly to the sound wave modifications and therefore can be ignored during the computation. Because of this, only polygons that represent walls are taken into account. Furthermore, to make the system more e cient, each ray is intersected with a plane rather than a polygon. A comparison of the method implemented on a GPU and a CPU (2GHz AMD CPU and an ATI Radeon 9800 video card) demonstrated that the GPU-based implementation was much more computationally e cient (32 vs. 500 ms to trace a ray of order 10 on the GPU and CPU respectively). Röber et al. BIB005 describe a ray-based acoustical modeling method that employed the GPU to allow for real-time acoustical simulations. Their framework was designed along existing (computer graphics) GPU-based ray tracing systems suitably modified to handle sound wave propagation. The system accepts a 3D polygonal mesh of up to 15,000 polygons and pre-processes it into an accessible structure. All signal processing, including HRTF convolution and delay filtering, is programmed as fragment shaders and for each task a single shader is developed. The 3D scene data along with sounds and frequency band decomposed HRTFs are loaded into tex-ture memory and decomposed into 10 bands that are assigned positions and an emittance pattern within the virtual room. Rays are cast into the scene and the value of acoustic energy received per frequency band is accumulated and stored within cubemaps. Each ray is then filtered and delayed using HRTFs according to its position and wavelength. Using this method every cast ray is traced through the virtual scene and its acoustic energy is accumulated and stored per frequency band. A frame-rate of up to 25 fps was achieved using a detailed model of a living room containing 1,500 polygons (using an NVIDIA GeForce 8800 GTX video card). One problem associated with ray-based approaches involves dealing with the large number of potential interactions between a propagating sound ray and the surfaces it may encounter. A sound incident on a surface may be simultaneously reflected specularly, reflected di usely, be refracted, and be di racted. Typical solutions to modeling such e ects include the generation and emission of multiple "new" rays at each interaction point. Such approaches lead to exponential running times making them computationally intractable except for the most basic environments and only for very short time periods, particularly for traditional (non-GPU) methods. Although this situation is remarkably improved upon with the use of GPU-based acoustic ray tracing techniques, the problem still remains. As with wave-based methods, greater work can be done to take advantage of the human auditory perception system thus avoiding computations that have minimal (if any), perceptual consequences. For example, it is not necessary to account for non-audible reflections. Finally, photon mapping is a popular two-pass "particlebased", probabilistic global illumination method that is independent of the scene geometry BIB003 . Being probabilistic, the solution can be made more accurate by increasing the number of samples at various points of the computation allowing for an accuracy vs. e ciency trade-o . Despite the computational improvements over many other global illumination methods such as ray tracing, software-based photon mapping is still computationally prohibitive for dynamic, interactive virtual environment and game applications. However, a "compute bound" GPU implementation whose performance will continue to improve with improving GPU floating point operations was introduced in by Purcell et al. BIB004 . Although the GPU-based photon mapping has not been applied to acoustical modeling, sonel mapping is the application of the (original) photon mapping method to acoustical modeling and has led to great computational savings  . Future work can include further computational savings to sonel mapping by appropriately modifying and incorporating Purcell's GPU-based solution.