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Abstract GPU-Assisted Raycasting for Cosmological Adaptive Mesh Refinement Simulations

Volume Graphics (2006) T. M?ller, R. Machiraju, T. Ertl, M. Chen (Editors)

GPU-Assisted Raycasting for Cosmological Adaptive Mesh Re?nement Simulations
Ralf Kaehler1 , John Wise2 , Tom Abel2 and Hans-Christian Hege1
1 Zuse Institute Berlin, Germany Institute for Particle Astrophysics and Cosmology/Stanford University, USA

2 Kavli

Abstract In the recent years the advent of powerful graphics hardware with ?exible, programmable fragment shaders enabled interactive raycasting implementations which perform the ray-integration on a per-pixel basis. Unlike slicebased volume rendering these approaches do not suffer from rendering artifacts caused by varying sample distances along different ray-directions or limited frame-buffer precision. They further allow a direct realization of sophisticated optical models. In this paper we investigate the applicability of GPU-assisted raycasting to block-structured, locally re?ned grids. We present an interactive algorithm for artifact-free, high-quality rendering of data de?ned on this type of grid structure and apply it to render data of time-dependent, three-dimensional galaxy and star formation simulations. We use a physically motivated emission-absorption model to map the computed temperature and density ?elds to color and opacity. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation–Vieweing Algorithms I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism– Raytracing

1. Introduction Nowadays astrophysics, in particular cosmology, probably like no other scienti?c area, is more and more depending on time-dependent, numerical 3D simulations, since for the most relevant research problems explicit analytical solutions do not exist and direct experiments are unfeasible. In order to interpret and verify such simulations, it is important to compare the results to observed image data. Interactive, photorealistic visualization thus becomes an important tool. It allows the scientist to change parameters, e. g. the viewpoint as well as the shading model, on the ?y to get an intuitive impression of the overall structure of the data. Furthermore it supports meaningful visual comparisons of different simulations. Adaptive techniques are vital in this type of simulation since many length scales must be considered to accurately model the physical phenomena, which can range from several 10,000 light years (dynamics of the proto-galaxies) to several light hours for evolving stellar objects in certain rec The Eurographics Association 2006.

gions. A speci?c adaptive approach for solving partial differential equations that is popular in astrophysics is called AMR (Adaptive Mesh Re?nement). It was introduced by Berger et al. in the ’80s [BO84]. The basic idea is to combine the simplicity of structured grids and the advantages of local re?nement by recursively overlaying regions of a coarse initial structured grid with grid patches of increasing resolution. In this paper we present an interactive GPU-assisted raycasting algorithm for high-quality volume rendering of block-structured, locally re?ned grids like octrees or AMR hierarchies. In contrast to hardware accelerated, slice-based approaches our algorithm does not suffer from rendering artifacts due to limited frame-buffer precision or varying slice distances at boundaries of different resolution levels. We apply it to render three-dimensional galaxy and star formation simulations, which follow the hydrodynamics and gravity of gas and dark matter from the density ?uctuation 400,000 years after the big bang. Based on these simulation data the

Kaehler et al. / GPU-Assisted Raycasting for Cosmological AMR Simulations

in?uence of the ?rst stellar objects within these galaxies on the surrounding gas is computed in a preprocessing step. The resulting temperature and density ?elds are processed by the GPU-assisted volume rendering algorithm that computes emission and absorption coef?cients at each location within the data volume and allows to interactively adjust the relevant rendering parameters. In the next Section we will review related work in the ?eld. In Section 3 we sketch the grid structure on which the ?eld variables are de?ned. Next will describe the GPUassisted raycasting approach for locally re?ned structured grids (Section 4). In Section 5 we give some details about the cosmological simulations and specify the emissionabsorption model we used to render the simulation data. We end with a comparison of the method to hardwareaccelerated slice-based approaches in terms of image quality and rendering performance. 2. Related Work Slice-based hardware-assisted volume rendering using 3D textures hardware was introduced by Cullip and Neumann in 1993 [CN93]. The underlying idea is to map the data volume to a 3D-texture, respectively a stack of 2D-textures and exploit graphics hardware to extract and blend a set of axesor viewpoint-aligned slices to approximate the volume rendering integral. The basic algorithm has been extended for multiresolution data in [LHJ99, WWH? 00, KH02]. Other acceleration techniques and also sophisticated optical models have been realized for slice-based approaches, see e. g. [KPHE02, EKE01, GWGS02]. Though slice-based approaches allow for interactive rendering of even larger data volumes, they suffer from several disadvantages, that might lead to visible artifacts: ?rst the slice distance for perspective projection varies along different directions. Further currently hardware accelerated blending is only supported for 16-bit (or less) ?oat render targets and thus the rendering performance is reduced drastically if 32-bit render targets are used, see e.g. [YNCP05]. This is especially problematic for adaptive grids, since in these cases usually wide viewing angles are required and a large number of highly transparent slices have to be blended. Though the precision problem should be solved for future generations of graphics hardware, another source of artifacts for slice-based rendering of adaptive grids remains. It is due to small regions at slice edges at level boundaries, where the sample distance changes from one slice to another. Weiler et al. addressed this problem in detail in [WWH? 00]. They presented an algorithm to detect these problematic regions and render the corresponding slice parts with the correct opacity that corresponds to the actual sample distance in these regions. However, since this approach requires connectivity information between adjacent cells and the resolution

of adjacent blocks might differ by an arbitrary number of re?nement levels the proposed solution is cumbersome for AMR data. With the advent of programmable graphics hardware that supports ?exible fragment programs, it became feasible to perform a ray-integration on a per-pixel based at interactive frame rates, as described in [RGW? 03,KW03,SSKE05]. In this approach the data volume is converted to a 3D texture and a fragment program is executed for each pixel that is covered by the projected bounding box of the data volume. The ray is parameterized in texture coordinates and the integral can be computed as for software implementations. This approach has been adopted for the rendering of large datasets, see for example [HQK05]. In this approach the data domain is decomposed into subvolumes that are sorted and processed front-to-back according the actual viewpoint. GPU-assisted raycasting is very attractive for adaptive grids, since it does not suffer from the rendering artifacts mentioned above, which limits the achievable image quality for this kind of data using slice-based methods. A software-based raycasting approach for AMR data has been proposed in [WOK? 03]. Photorealistic volume visualization of planetary and re?ection nebulae has been presented in [MHLH05]. In this approach the aim was to model the 3D shape of nebulae based on 2D image data, rather than to render simulation data of the galactic nebula formations. In particular the authors present an approximation for multiple scattering events based on a multi-resolution method. 3. The Grid Structure The basic idea of AMR is to combine the simplicity of structured grids with the advantages of local grid adaption. In this approach the computational domain is covered by a set of 3 coarse, structured subgrids Γ0 l=0...n ? R . The union of these 0 := n 0 subgrids is called the root level Λ m=0 Γm .




Figure 1: Re?nement process for AMR schemes: Cells that require re?nement are determined using local error criteria (a) and clustered into separate subgrids (b), which cover the regions with higher resolution. This process is recursively continued until each cell ful?lls the error criteria (c). During the computation, local error estimators are utilized to detect cells that require higher resolution. These cells are covered by a set of rectangular subgrids. Unlike in ?nite element approaches, these subgrids do not replace but rather
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Kaehler et al. / GPU-Assisted Raycasting for Cosmological AMR Simulations

overlay the re?ned regions of the coarse base grid. The equations are advanced on the ?ner subgrids and this re?nement procedure recursively continues until all cells ful?ll the considered error criterion, giving rise to a hierarchy of nested re?nement levels, as shown in Figure 1.
Γ0 0 h0 1 h1 1 Γ1 1 Γ1 0

with blocks consisting of cells from the same resolution level. Rendering the separate subgrids directly would result in severe rendering artifacts. This is because of facts: In the AMR approach the patches of ?ner subgrids do not replace but rather overlap regions of coarser levels, so re?ned regions of the data volume would be rendered multiple times. It is further not possible in general to traverse the subgrids separately in a view-consistent order, due to the nesting of the re?nement levels and the fact that subsets of the grids might form visibility cycles. We therefore decompose the data domain into axisaligned blocks Bl ? Λl with m (Bl ∩ Blj ) = 0 ∨ (Bl ∩ Blj ) ? (? Bl ∪ ? Blj ) for i = j / i i i that consist either of cells that are re?ned by subgrids, or of cells which are not further re?ned. Each block is processed separately during the rendering phase, so it has to be ensured that no subsets of the blocks build visibility cycles for any viewpoint. In [KH02] a decomposition scheme is proposed that ful?lls these constraints. In particular the resulting blocks are arranged in a kD-tree structure, allowing an ef?cient determination of the view-consistent order for each viewpoint. The resulting decomposition consists of three types of nodes: ? nodes representing areas of the computational domain which cover only cells that are further re?ned, ? nodes that contain only cells that are unre?ned and represent leaves of the decomposition tree ? and nodes that contain re?ned and unre?ned cells; these nodes are used to traverse the tree in a view-consistent order. Notice that no data from the original AMR hierarchy is copied, but only bounding box information and pointers to the original data are stored in the kD-tree. Once a node is rendered for the ?rst time, see next subsection, a 3D-texture is allocated on-the-?y for the subgrid the node refers to and the texture name is stored for later rendering passes. This ensures that only those textures needed for the actual viewpoint are generated. Furthermore it allows to keep the data of the original hierarchy out-of-core and just load it once it is required for the rendering. We employ nearest-neighbor interpolation for cellcentered AMR data and trilinear interpolation for vertexcentered data. In the ?rst case the texels are aligned with the centers of the cells, while in the second one they are aligned with the vertices of the grid. To avoid artifacts originating from discontinuities between adjacent subgrids for trilinear interpolation, adjacent texture-blocks share a row of data samples at their common boundary faces and the data at dangling nodes has to be replaced to the interpolated texel values of the abutting, coarse texture.

Γ2 0

x01 ?00 x00

x11 Γ1 2 x10

Figure 2: Two-dimensional example of a structured AMR grid. The root level Γ0 is re?ned by three subgrids Γ1 , Γ1 , Γ1 0 1 2 0 that generate the re?nement level Λ1 . Λ1 itself is re?ned by one subgrid Γ2 . 0 The mesh spacings of the ?ner grids are recursively de?ned by hl := (hl?1 /r, hl?1 /r, hl?1 /r). The positive integer r 0 1 2 denotes the so-called re?nement factor, and h0 = (h0 , h0 , h0 ) 0 1 2 is the mesh spacing of the root grid. In principle this factor r can differ for each direction and each level, but in order to simplify the notation we assume that it is constant. In the AMR approach, cells are either completely re?ned by cells of the next ?ner grid or remain completely unre?ned. Each coarse cell can be decomposed into a set of r3 cells of the next ?ner discretization. In the following the union of all l level l subgrids Γl m=0,1,2... is called re?nement level Λ or just level l, compare Figure 2. By construction these levels are nested: Λl+1 ? Λl ? Λ0 . 4. The GPU-assisted Raycasting Approach The outline of the GPU-assisted raycaster for structured adaptive mesh re?nement data is as follows: ? First the hierarchy of nested re?nement levels is decomposed into blocks of disjoint, axis-aligned blocks that cover only cells from the same level of resolution. ? The blocks are traversed front-to-back in a viewconsistent order and rendered separately into an offscreen render buffer. The resulting contribution from each block to the ?nal image is stored in a offscreen render target. ? After all blocks are processed the offscreen target is rendered into the frame-buffer. In the next subsections the single steps are discussed in more detail. 4.1. Space Partitioning In order to take advantage of the GPU-assisted raycasting approaches the data volume should be processed block-wise,
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Kaehler et al. / GPU-Assisted Raycasting for Cosmological AMR Simulations

Figure 3: Three time-steps from a star formation simulation rendered with the optical model presented in Sect. 5.1, that maps density and temperature ?elds to emission and absorption coef?cients. The dark regions in the middle image result from non-illuminated gas that absorbs large amounts of light from behind it.

4.2. Raycasting the Subgrids The GPU-accelerated raycasting of the separate blocks is based on the single-pass approach described in [SSKE05]. In this approach ?rst the 3D data texture and colortable texture are generated, respectively bound to different texture units. Next the front faces of the block’s bounding box are rendered into an offscreen 2D RGB-?oating point texture. The texture coordinates of the vertices are set identical to the vertex coordinates in order to access object space coordinates in the fragment shader. Within the fragment shader the ray direction in object space coordinates is computed for each pixel. Next the ray-entry point and the direction vector are transformed to texture coordinate space and the raycasting is performed. The data values are obtained via texture lookups and mapped to color and opacity via the colortable. Finally the resulting color and opacity of the each ray-segment are blended according to the front-to-back blending equation Cdst = Cdst + (1 ? αdst )αsrcCsrc , αdst = αdst + (1 ? αdst )αsrc . In order to meed the requirements for rendering the multiresolution block-structured data, we modi?ed this approach. To prevent multiple computation of the ray direction for pixels that are contained in the projected screen space of multiple subgrids, we initially render the front-faces of the enclosing bounding box of the rendered subgrids, compute the ray direction for these pixels and store them in a separate texture that is used to lookup the ray directions when the separate subgrids are processed. When processing a block, for each ray the blended color and opacity from the last ray-segment are required as initial values. According to the speci?cation of the OpenGL framebuffer_object extension [FBO] reading from the texture that is bound as a texture target is currently unde?ned. However, it worked in our scenario, so we additionally bound the texture render target onto a texture unit, in order to access it within the fragment shader.

Alternatively one could copy the area required from the render buffer in a separate rendering pass by binding the previous texture target, rendering the front-faces of the bounding box and loading a fragment shader that just copies the color and opacity information into a separate buffer. This buffer would be additionally bound as a texture in the raycasting pass to provide the initial values for each raysegment. In order to increase the rendering performance the sample distance along the ray is adapted to the actual resolution of the precessed block. Therefore corrected opacity values are precomputed according for the step size that is used for each re?nement level according to αi (l) = 1 ? (1 ? αi (0)) rl .


Here αi (0) are the opacity values used for the root level and r is re?nement factor of the hierarchy. These values are stored as l separate 1D-RGBA-textures, one for each level of re?nement. In general the last interval for each ray-segment will only be a fraction of the actual interval extension used for the integration. Artifacts due to wrong opacity values for these intervals are avoided by computing the correct value for the last integration interval on-the-?y. More details about the implementation of the renderer will be given at the end of subsection 5.1. 5. The Application Scenario Recently several studies (see [ABN02, BCL02]) established that the ?rst stars in the universe were massive, about 100 solar masses, and were formed when the universe was only 200 million years old. These stars form isolated in their host gas cloud, in contrast to stars in clusters that we see in the local universe. Due to their large mass, these ?rst stars are very luminous, which lead to intense heating and ionization of the adjacent regions. The ?rst star calculations are ab initio,
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Kaehler et al. / GPU-Assisted Raycasting for Cosmological AMR Simulations

Figure 4: The image sequence shows the effect of wavelength dependent absorption used in the optical model. From left to right the absolute amount of absorption was increased, resulting in a reddening of the resulting color.

i.e. without any assumptions, and follow the hydrodynamics, gravity, and chemistry in a cosmological environment. The simulations end at the birth of the ?rst star and do not follow its impact on the host gas cloud. It was argued that radiative transfer in a cosmological sense would best split the highly anisotropic point sources, such as stars, from diffuse sources, such as recombinations of electrons and ions in dense regions. For the point sources, ray tracing is an effective way of accurately calculating the evolution of ionized regions. Abel et al. [AWB06] have successfully coupled an adaptive ray tracing scheme [AW02] into the AMR code enzo [BL97]. By doing so, they were able to precisely follow the radiation of the ?rst star, whose radiation drives a shock through the surrounding gas that effectively expels the majority of it. At the end of the star’s life, this gas is traveling outward at 30 km/s, and the gas up to 5,000 light years away have been ionized by this one star. The adaptive ray tracing scheme splits rays in the framework of HEALPix as they venture farther from its source to guarantee each grid cell in the hydrodynamic simulation contains at least 5 rays. This ensures that all relevant cells are sampled well. Furthermore it results in ef?cient ray tracing close to the source when not many rays are needed for a consistent calculation. We use the GPU-assisted raycaster presented above to interactively render the output of this raytracing step. It is basically the resulting temperature and density distribution of the gaseous matter within the proto-galaxy. In the next subsection we describe the physically motivated optical model that was used to map the data to emission and absorption coef?cients. 5.1. The Optical Model In order to render the datasets, we must map the temperature to physical colors in the same manner as observational data. In telescopic observations, light is passed through various ?lc The Eurographics Association 2006.

ters with a transmission function Ti (ν) and post-processed to create color images. The most common ?lters, Johnson U, B, V, R, and I, are shown in Figure 5; however any other choice of ?lters is possible. We can utilize the temperature ?eld to create a realistic colormap. A parcel of gas with a temperature T emits a blackbody spectrum, Bν (ν, T ) = 1 2hν 3 , c2 exp(hν/kT ) ? 1 (2)

where ν is frequency, h = 6.673 × 10?27 erg·s is the Planck constant, c is the speed of light, and k = 1.38 × 10?16 erg K?1 is Boltzmann’s constant. Now we can convolve Bν with a choice of three ?lters that correspond to RGB values. The ?ux Fi in the ith ?lter, where i ∈ [1,2,3], is Fi = Bν Ti dν.

i ? We normalize Fi by evaluating Fi = max(FF,F ,F ) so that 1 2 3 the ?lter with the maximum ?ux has a value of 1. For example, to represent realistic colors to the human eye, we choose the R, V, and B ?lters to represent RGB so that ? ? ? RGB = [F0 (R), F1 (V ), F2 (B)]. To get the ?nal emission coef?cient we scale this term by the normalized gas density ρ ρmax present at the voxel location.

In addition to emission, the scattering of light by particles larger than its wavelength λ can affect the incoming light. For the correct absorption properties detailed models are needed that must be adapted exactly to the type of simulations considered. E.g. the ionized regions need to be treated differently than non-ionized regions. For the latter one wavelength independent Compton scattering is appropriate. Such level of detail is beyond the scope of the current work. We rather use Rayleigh scattering for the whole computational domain as an attempt towards physical based rendering. This is motivated by the fact at the time when the ?rst stars formed there was no dust present in the intergalactic medium. It was not produced until the ?rst generation stars ended in supernova explosions. As a result, in our ap-

Kaehler et al. / GPU-Assisted Raycasting for Cosmological AMR Simulations #sub-grids 65 670 4100 GPU-Raycasting 19 fps 7 fps 1 fps Slice-based 59 fps 23 fps 4 fps

Data I Data II Data III

Table 1: The ?rst column denotes number of subgrids, the second one frame-rates for the GPU-assisted raycasting and the last one the frame-rate for the slice-based approach.

Figure 5: Transmission functions T for Johnson U, B, V, R, I ?lters. These ?lters are most common when conducting astronomical observations.

plication area the particle diameter of the medium is very small compared to the wavelength of the light that is scattered, respectively absorbed. So Raleigh scattering applies in our case (instead of Mie scattering which would become 1 relevant if the particles would be bigger than 10 of the light wavelength). According to the Rayleigh law the intensity of the scattered light is proportional to density and λ ?4 . Thus blue light is scattered more strongly than red light. A prime example of this process is the atmosphere scattering the Sun’s radiation and causing the sky to be blue. To consider scattering, we correct the incoming blackbody emission by the scattering light intensity in the line of sight of the observer for the three different dominant wavelengths. Multiple scattering would change the appearance of our rendered objects as soon as it starts to scatter signi?cant amounts of photons into the line of the sight. In the low density, dust free environment of the ?rst proto-galaxies multiple scattering events have a low probability and thus we do not take them into account. We precompute the color emission (without the density weighting) and the absorption coef?cients for each level and stored them in 1D ?oating point textures. The densityweighting is performed on-the-?y. Since 6 ?oats have to be stored after the integration of each segment in order to accumulate the 3 color and 3 absorption values, we use two 32-bit ?oating point 2D RGB-textures as render targets to store the intermediate results of the raycasting passes. The two scalar?elds for density and gas temperature are stored as 2-channel (GL_LUMINANCE_ALPHA) 3D-textures with one byte per channel. 6. Results The algorithms have been implemented as extensions to Amira [SWH05], an object-oriented, expandable 3D data visualization system developed at ZIB.

We tested the presented approaches on a standard PC system (Pentium 4, 3.0 GHz, 2 GByte Main Memory) that was equipped with a NVIDIA GeForce 6800 GT graphics card with 256 MByte of graphics memory. OpenGL was used as the graphics API and the fragments shaders have been implemented with the OpenGL Shading Language. For generating the rendering targets we used the OpenGL framebuffer_object extension [FBO], since it is available on Windows and Linux systems. We compared the performance and image quality of the GPU-assisted raycasting approach with a slice-based volume renderer. In this case we used a standard emissionabsorption model with three color and one alpha channel that is realized via a user de?ned colortable. For the GPUassisted raycasting approach we performed early ray termination, if the alpha component exceeded 0.99. We used three datasets with an increasing number of subgrids for the comparison. The number of cells at the root level was 323 , 643 , respectively 1283 for the examples. The sampling distance was increased for each level of resolution and was about half the actual cell size. Information about the number of subgrids as well as the performance numbers are given in Table 1. For all examples the size of the viewport was 760x700. The performance of the raycasting method was about 30% of the one obtained with the slice-based renderer. Renderings of the datasets are shown in Figure 7. Figure 6 shows a comparison of the image quality of the two approaches. Though opacity corrections according to Equation 1 have been applied, the middle image shows severe rendering artifacts for the re?ned regions. These stem from insuf?cient framebuffer precision during blending the highly-transparent slices and from small regions at slice edges at level boundaries, where the sample distance changes from one slice to another, see Section 2. Since 32bit ?oating-point precision is used in the raycasting approach and the rays are computed on a per-pixel basis, no artifacts are visible in the right image. Examples of the emission-absorption model presented in Section 5.1 are shown in Figure 3 and 4. The ?rst one shows three timesteps of the time-dependent star-formation simulation described in Section 5, while the latter one points out the effect of the wavelength dependent absorption model.
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Kaehler et al. / GPU-Assisted Raycasting for Cosmological AMR Simulations

Figure 6: A comparison of the image quality of slice-based (middle) and GPU-assisted raycasting (right) approaches. The left images shows the bounding boxes of the re?ned region of an adaptive simulation. The middle image show severe rendering artifacts for these regions, due to insuf?cient framebuffer precision to correctly blend the highly-transparent slices. Since ?oating-point precision is used in the raycasting approach, no artifacts are visible in that case.

Figure 7: Galaxy formation simulations that were used to compare the rendering performance of the slice-based and GPUassisted raycasting approach.

7. Conclusions and Future Work In this paper we presented a frame-work for high-quality, interactive volume rendering of data de?ned on locally re?ned, block-structured grids. We chose a GPU-based raycasting approach that does not suffer from the drawbacks affecting the image quality of hardware-accelerated slice-based methods. It has superior image quality compared to slicebased methods and directly supports the implementation of advanced optical models, like the wavelength-dependent emission-absorption model used for rendering the cosmology simulation data. Though the performance of the GPUbased approach is only about 30% of the slice-based method for the tested datasets, this performance penalty is expected to decrease for future generations of graphics hardware. There are several ways the extend the work presented in this paper. Pruning of tree-traversal based on local error criteria as well as empty space leaping should speed up the rendering performance considerably.
c The Eurographics Association 2006.

Internally the simulation computes the densities for the different components of the gas separately, so it would be interesting to use this data directly and apply measured extinction curves for the different compoments. Further for other kind of simulations, e.g. scenarios with dust present in the intergalactic medium, the effects of multiple scattering should be investigated, e.g. based on the approach described in [MHLH05].

8. Acknowledgements This work was partially supported by the Max-PlanckInstitute for Gravitational Physics (Albert-Einstein Institute), Potsdam/Germany and the NSF CAREER award AST0239709 from the National Science Foundation. We thank Malte Clasen (Zuse Institute Berlin) for fruitful discussions.

Kaehler et al. / GPU-Assisted Raycasting for Cosmological AMR Simulations

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Lazy Sweep Ray Casting A Fast Scanline Algorithm for Rendering Irregular Grids (Abstract) Cl? udio T. Silva a Joseph S. B. Mitchell y For the ...

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Adaptive Mesh Re nement with Discontinuities for ... Europe Abstract The radiosity method simulates ...raycasting and those patches which obstruct the ...

Abstract A Hybrid GPU-CPU Renderer_图文.pdf

Abstract A Hybrid GPU-CPU Renderer_专业资料。In ... however a mesh is constructed from the image ...For all such marked pixels, a ray is cast in...


The connectivity meshes of the resulting triangles ...The colon surface is rendered by ray-casting the...This surface assisted technique helps to skip most...

A Recursive Taylor Method for Ray-Casting Algebraic Surfaces_....pdf

Abstract In this paper, we propose a recursive Taylor method for ray-casting algebraic surfaces. The performance of this approach is compared with four ...

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Abstract Binary Volumetric Octree Representation for ... ray-casting of volumetric model, raytracing of ... Hardware-Assisted Reli... 6页 免费 GPU 加速...

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ray Clusters with Adaptive Mesh Refinement_专业资料... R.S., Castander, F.J., & Couch, W.J. ...Abstract GPU-Assisted ... 8页 免费 ...

Adaptive Mesh Refinement with Discontinuities for the ....pdf

Adaptive Mesh Refinement with Discontinuities for ...raycasting and those patches which obstruct the ... Abstract GPU-Assisted ... 8页 免费 The ...

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基于GPU Raycasting算法的矢量-栅格混合绘制研究_电子/电路_工程科技_专业资料。Raycasting 第27卷第7期2010年7月 计算机应用研究 Application V01.27No.7Jul....

...Accelerating High-Quality Volume Raycasting on G....pdf

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Abstract GPU-Accelerated Deep Shadow Maps for Direct Volume ....pdf

Abstract GPU-Accelerated Deep Shadow Maps for Direct Volume Rendering_IT认证_...computed via multipass ray-casting from the light source’s point of view....

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Abstract Implicit Adaptive Volume Ray-Casting_专业资料。In this work we ...4 EXPERIMENTS Figure 4: Exception situation in mesh traversal are nearly ...

Memory-Aware and Efficient Ray-Casting Algorithm.pdf

rfarias}@lcg.ufrj.br Abstract Ray-casting ...rst method for ray-casting irregular meshes using...Silva. Gpu-based tiled ray casting using depth ...

Abstract An Analysis Of GPU-based Interactive Raytracing.pdf

Abstract An Analysis Of GPU-based Interactive Raytracing_专业资料。Raytracing...Figure 2. Light rays are cast from the camera and traced around the ...


ABSTRACT This article describes a method for 3D ...(e.g. polygon mesh), which are then rendered ...ADAPTIVE TERMINATION Ray casting with pseudocoloring...

Simple, Fast, and Robust Ray Casting of Irregular Grids.pdf

Simple, Fast, and Robust Ray Casting of ...adaptive meshes, it is becoming increasingly common...Abstract S-RAD A Simpl... 12页 免费 ...


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