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Stencil codes 199 Implementation Issues Many simulation codes may be formulated naturally as stencil codes. Since computing time and memory consumption grow linearly wth the number of array elements, parallel implementations of stencil codes are of paramount importance to research. [6] This is challenging since the computations are tightly coupled (because of the cell updates depending on neighboring cells) and most stencil codes are memory bound (i.e. the ratio of memory accesses and calculations is high). [7] Virtually all current parallel architectures have been explored for executing stencil codes efficiently [8] ; at the moment GPGPUs have proven to be most efficient. [9] Libraries Due to both, the importance of stencil codes to computer simulations and their high computational requirements, there are a number of efforts which aim at creating reusable libraries to support scientists in implementing new stencil codes. The libraries are mostly concerned with the parallelization, but may also tackle other challenges, such as IO, steering and checkpointing. They may be classified by their API. Patch-Based Libraries This is a traditional design. The library manages a set of n-dimensional scalar arrays, which the user code may access to perform updates. The library handles the synchronization of the boundaries (dubbed ghost zone or halo). The advantage of this interface is that the user code may loop over the arrays, which makes it easy to integrate legacy codes [10] . The disadvantage is that the library can not handle cache blocking (as this has to be done within the loops [11] ) or wrapping of the code for accelerators (e.g. via CUDA or OpenCL). Notable implementations include Cactus [12] , a physics problem solving environment, and waLBerla [13] . Cell-Based Libraries These libraries move the interface to updating single simulation cells: only the current cell and its neighbors are exposed to the user code, e.g. via getter/setter methods. The advantage of this approach is that the library can control tightly which cells are updated in which order, which is useful not only to implement cache blocking, [9] but also to run the same code on multi-cores and GPUs. [14] This approach requires the user to recompile his source code together with the library. Otherwise a function call for every cell update would be required, which would seriously impair performance. This is only feasible with techniques such as class templates or metaprogramming, which is also the reason why this design is only found in newer libraries. Examples are Physis [15] and LibGeoDecomp [16] . References [1] Roth, Gerald et al. (1997) Proceedings of SC'97: High Performance Networking and Computing. Compiling Stencils in High Performance Fortran. (http:/ / citeseer. ist. psu. edu/ viewdoc/ summary?doi=10. 1. 1. 53. 1505) [2] Sloot, Peter M.A. et al. (May 28, 2002) Computational Science - ICCS 2002: International Conference, Amsterdam, The Netherlands, April 21-24, 2002. Proceedings, Part I. (http:/ / books. google. com/ books?id=qVcLw1UAFUsC& pg=PA843& dq=stencil+ array& sig=g3gYXncOThX56TUBfHE7hnlSxJg#PPA843,M1) Page 843. Publisher: Springer. ISBN 3540435913. [3] Fey, Dietmar et al. (2010) Grid-Computing: Eine Basistechnologie für Computational Science (http:/ / books. google. com/ books?id=RJRZJHVyQ4EC& pg=PA51& dq=fey+ grid& hl=de& ei=uGk8TtDAAo_zsgbEoZGpBQ& sa=X& oi=book_result& ct=result& resnum=1& ved=0CCoQ6AEwAA#v=onepage& q& f=true). Page 439. Publisher: Springer. ISBN 3540797467 [4] Yang, Laurence T.; Guo, Minyi. (August 12, 2005) High-Performance Computing : Paradigm and Infrastructure. (http:/ / books. google. com/ books?id=qA4DbnFB2XcC& pg=PA221& dq=Stencil+ codes& as_brr=3& sig=H8wdKyABXT5P7kUh4lQGZ9C5zDk) Page 221. Publisher: Wiley-Interscience. ISBN 047165471X [5] Micikevicius, Paulius et al. (2009) 3D finite difference computation on GPUs using CUDA (http:/ / portal. acm. org/ citation. cfm?id=1513905) Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units ISBN: 978-1-60558-517-8 [6] Datta, Kaushik (2009) Auto-tuning Stencil Codes for Cache-Based Multicore Platforms (http:/ / www. cs. berkeley. edu/ ~kdatta/ pubs/ EECS-2009-177. pdf), Ph.D. Thesis
Stencil codes 200 [7] Wellein, G et al. (2009) Efficient temporal blocking for stencil computations by multicore-aware wavefront parallelization (http:/ / ieeexplore. ieee. org/ xpl/ freeabs_all. jsp?arnumber=5254211), 33rd Annual IEEE International Computer Software and Applications Conference, COMPSAC 2009 [8] Datta, Kaushik et al. (2008) Stencil computation optimization and auto-tuning on state-of-the-art multicore architectures (http:/ / portal. acm. org/ citation. cfm?id=1413375), SC '08 Proceedings of the 2008 ACM/IEEE conference on Supercomputing [9] Schäfer, Andreas and Fey, Dietmar (2011) High Performance Stencil Code Algorithms for GPGPUs (http:/ / www. sciencedirect. com/ science/ article/ pii/ S1877050911002791), Proceedings of the International Conference on Computational Science, ICCS 2011 [10] S. Donath, J. Götz, C. Feichtinger, K. Iglberger and U. Rüde (2010) waLBerla: Optimization for Itanium-based Systems with Thousands of Processors (http:/ / www. springerlink. com/ content/ p2583237l2187374/ ), High Performance Computing in Science and Engineering, Garching/Munich 2009 [11] Nguyen, Anthony et al. (2010) 3.5-D Blocking Optimization for Stencil Computations on Modern CPUs and GPUs (http:/ / dl. acm. org/ citation. cfm?id=1884658), SC '10 Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis [12] http:/ / cactuscode. org/ [13] http:/ / www10. informatik. uni-erlangen. de/ Research/ Projects/ walberla/ description. shtml [14] Naoya Maruyama, Tatsuo Nomura, Kento Sato, and Satoshi Matsuoka (2011) Physis: An Implicitly Parallel Programming Model for Stencil Computations on Large-Scale GPU-Accelerated Supercomputers, SC '11 Proceedings of the 2011 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis [15] https:/ / github. com/ naoyam/ physis [16] http:/ / www. libgeodecomp. org External Links [ Physis (https:/ / github. com/ naoyam/ physis)] LibGeoDecomp (http:/ / www. libgeodecomp. org) Subdivision surface A subdivision surface, in the field of 3D computer graphics, is a method of representing a smooth surface via the specification of a coarser piecewise linear polygon mesh. The smooth surface can be calculated from the coarse mesh as the limit of a recursive process of subdividing each polygonal face into smaller faces that better approximate the smooth surface.
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3D Rendering PDF generated using th
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Image-based lighting 64 Image plane
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References Article Sources and Cont
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3D rendering 2 Non real-time Animat
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3D rendering 4 The shaded three-dim
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Ambient occlusion 6 ambient occlusi
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Ambient occlusion 8 • ShadeVis (h
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Anisotropic filtering 10 will only
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Beam tracing 12 Beam tracing Beam t
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Bilinear filtering 14 Are all true.
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Binary space partitioning 16 togeth
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Binary space partitioning 18 Other
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Binary space partitioning 20 [1] Bi
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Bounding interval hierarchy 22 Prop
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Bounding volume 24 bounding boxes b
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Bump mapping 26 Bump mapping Bump m
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CatmullClark subdivision surface 28
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CatmullClark subdivision surface 30
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Conversion between quaternions and
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Cube mapping 34 Advantages Cube map
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Cube mapping 36 Related A large set
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Diffuse reflection 38 2), or, of co
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Displacement mapping 40 Meaning of
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DooSabin subdivision surface 42 Ext
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False radiosity 44 False radiosity
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Geometry pipelines 46 Geometry pipe
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Global illumination 48 Rendering wi
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Gouraud shading 50 Gouraud shading
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Graphics pipeline 52 Graphics pipel
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Graphics pipeline 54 References 1.
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Hidden surface determination 56 imp
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High dynamic range rendering 58 Hig
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High dynamic range rendering 60 Ton
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High dynamic range rendering 62 Fro
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High dynamic range rendering 64 •
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Irregular Z-buffer 66 Applications
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Lambert's cosine law 68 than would
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Lambertian reflectance 70 Lambertia
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Level of detail 72 Well known appro
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Level of detail 74 Hierarchical LOD
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Newell's algorithm 76 Newell's algo
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Non-uniform rational B-spline 78 Us
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Non-uniform rational B-spline 80 of
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Non-uniform rational B-spline 82 ar
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Non-uniform rational B-spline 84 Ex
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Normal mapping 86 How it works To c
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OrenNayar reflectance model 88 Oren
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OrenNayar reflectance model 90 , ,
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Painter's algorithm 92 The algorith
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Parallax mapping 94 • Parallax Ma
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Particle system 96 A cube emitting
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Path tracing 98 History Further inf
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Path tracing 100 Scattering distrib
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Phong reflection model 102 Visual i
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Phong reflection model 104 Because
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Phong shading 106 Visual illustrati
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Photon mapping 108 Rendering (2nd p
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Photon tracing 110 Advantages and d
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Potentially visible set 112 • Can
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Potentially visible set 114 Externa
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Procedural generation 116 increases
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Procedural generation 118 • Softi
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Procedural generation 120 Reference
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Procedural texture 122 Self-organiz
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Procedural texture 124 References [
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3D projection 126 The distance of t
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Quaternions and spatial rotation 12
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Radiosity 140 Overview of the radio
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Radiosity 142 This is sometimes kno
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Radiosity 144 References [1] " Mode
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Ray casting 146 the light will reac
Page 153 and 154: Ray tracing 148 Typically, each ray
Page 155 and 156: Ray tracing 150 independence of eac
Page 157 and 158: Ray tracing 152 On June 12, 2008 In
Page 159 and 160: Reflection 154 Reflection Reflectio
Page 161 and 162: Reflection 156 Glossy Reflection Fu
Page 163 and 164: Reflection mapping 158 Cube mapping
Page 165 and 166: Render Output unit 160 Render Outpu
Page 167 and 168: Rendering 162 • indirect illumina
Page 169 and 170: Rendering 164 Ray tracing Ray traci
Page 171 and 172: Rendering 166 Academic core The imp
Page 173 and 174: Rendering 168 • 1984 Distributed
Page 175 and 176: Retained mode 170 Retained mode In
Page 177 and 178: Scanline rendering 172 Comparison w
Page 179 and 180: Screen Space Ambient Occlusion 174
Page 181 and 182: Screen Space Ambient Occlusion 176
Page 183 and 184: Shadow mapping 178 Algorithm overvi
Page 185 and 186: Shadow mapping 180 Drawing the scen
Page 187 and 188: Shadow mapping 182 Further reading
Page 189 and 190: Shadow volume 184 There is also a p
Page 191 and 192: Shadow volume 186 The depth fail me
Page 193 and 194: Silhouette edge 188 Silhouette edge
Page 195 and 196: Specular highlight 190 Specular hig
Page 197 and 198: Specular highlight 192 normalized o
Page 199 and 200: Sphere mapping 194 Sphere mapping I
Page 201 and 202: Stencil codes 196 Stencil codes Ste
Page 203: Stencil codes 198 Stencils The shap
Page 207 and 208: Subdivision surface 202 used a four
Page 209 and 210: Subsurface scattering 204 Subsurfac
Page 211 and 212: Subsurface scattering 206 External
Page 213 and 214: Surface normal 208 If a (possibly n
Page 215 and 216: Surface normal 210 Normal in geomet
Page 217 and 218: Texture filtering 212 Texture filte
Page 219 and 220: Texture mapping 214 Texture mapping
Page 221 and 222: Texture mapping 216 constant distan
Page 223 and 224: Texture synthesis 218 • Structure
Page 225 and 226: Texture synthesis 220 Pattern-based
Page 227 and 228: Texture synthesis 222 • Micro-tex
Page 229 and 230: UV mapping 224 A UV map can either
Page 231 and 232: Vertex 226 Polytope vertices are re
Page 233 and 234: Vertex Buffer Object 228 //Make the
Page 235 and 236: Vertex Buffer Object 230 GLuint sha
Page 237 and 238: Vertex Buffer Object 232 vertexes *
Page 239 and 240: Virtual actor 234 Virtual actor A v
Page 241 and 242: Virtual actor 236 exercises, and ev
Page 243 and 244: Volume rendering 238 Volume ray cas
Page 245 and 246: Volume rendering 240 Maximum intens
Page 247 and 248: Volume rendering 242 Image-based me
Page 249 and 250: Volumetric lighting 244 References
Page 251 and 252: Voxel 246 • Outcast, a game made
Page 253 and 254: Z-buffering 248 Z-buffering In comp
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Z-buffering 250 } } display COLOR a
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Z-fighting 252 Z-fighting Z-fightin
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Appendix 3D computer graphics softw
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3D computer graphics software 256
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3D computer graphics software 258
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3D computer graphics software 260 2
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Article Sources and Contributors 26
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Article Sources and Contributors 26
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Image Sources, Licenses and Contrib
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Image Sources, Licenses and Contrib
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