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Bounding interval hierarchy 21 Operations Construction To construct any space partitioning structure some form of heuristic is commonly used. For this the surface area heuristic, commonly used with many partitioning schemes, is a possible candidate. Another, more simplistic heuristic is the "global" heuristic described by [4] which only requires an axis-aligned bounding box, rather than the full set of primitives, making it much more suitable for a fast construction. The general construction scheme for a BIH: • calculate the scene bounding box • use a heuristic to choose one axis and a split plane candidate perpendicular to this axis • sort the objects to the left or right child (exclusively) depending on the bounding box of the object (note that objects intersecting the split plane may either be sorted by its overlap with the child volumes or any other heuristic) • calculate the maximum bounding value of all objects on the left and the minimum bounding value of those on the right for that axis (can be combined with previous step for some heuristics) • store these 2 values along with 2 bits encoding the split axis in a new node • continue with step 2 for the children Potential heuristics for the split plane candidate search: • Classical: pick the longest axis and the middle of the node bounding box on that axis • Classical: pick the longest axis and a split plane through the median of the objects (results in a leftist tree which is often unfortunate for ray tracing though) • Global heuristic: pick the split plane based on a global criterion, in the form of a regular grid (avoids unnecessary splits and keeps node volumes as cubic as possible) • Surface area heuristic: calculate the surface area and amount of objects for both children, over the set of all possible split plane candidates, then choose the one with the lowest costs (claimed to be optimal, though the cost function poses unusual demands to proof the formula, which can not be fulfilled in real life. also an exceptionally slow heuristic to evaluate) Ray traversal The traversal phase closely resembles a kd-tree traversal: One has to distinguish 4 simple cases, where the ray • just intersects the left child • just intersects the right child • intersects both children • intersects none of both (the only case not possible in a kd traversal) For the third case, depending on the ray direction (negative or positive) of the component (x, y or z) equalling the split axis of the current node, the traversal continues first with the left (positive direction) or the right (negative direction) child and the other one is pushed onto a stack. Traversal continues until a leaf node is found. After intersecting the objects in the leaf, the next element is popped from the stack. If the stack is empty, the nearest intersection of all pierced leafs is returned. It is also possible to add a 5th traversal case, but which also requires a slightly complicated construction phase. By swapping the meanings of the left and right plane of a node, it is possible to cut off empty space on both sides of a node. This requires an additional bit that must be stored in the node to detect this special case during traversal. Handling this case during the traversal phase is simple, as the ray • just intersects the only child of the current node or • intersects nothing
Bounding interval hierarchy 22 Properties Numerical stability All operations during the hierarchy construction/sorting of the triangles are min/max-operations and comparisons. Thus no triangle clipping has to be done as it is the case with kd-trees and which can become a problem for triangles that just slightly intersect a node. Even if the kd implementation is carefully written, numerical errors can result in a non-detected intersection and thus rendering errors (holes in the geometry) due to the missed ray-object intersection. Extensions Instead of using two planes per node to separate geometry, it is also possible to use any number of planes to create a n-ary BIH or use multiple planes in a standard binary BIH (one and four planes per node were already proposed in [4] and then properly evaluated in [5] ) to achieve better object separation. References Papers [1] Nam, Beomseok; Sussman, Alan. A comparative study of spatial indexing techniques for multidimensional scientific datasets (http:/ / ieeexplore. ieee. org/ Xplore/ login. jsp?url=/ iel5/ 9176/ 29111/ 01311209. pdf) [2] Zachmann, Gabriel. Minimal Hierarchical Collision Detection (http:/ / zach. in. tu-clausthal. de/ papers/ vrst02. html) [3] Wald, Ingo; Boulos, Solomon; Shirley, Peter (2007). Ray Tracing Deformable Scenes using Dynamic Bounding Volume Hierarchies (http:/ / www. sci. utah. edu/ ~wald/ Publications/ 2007/ / / BVH/ download/ / togbvh. pdf) [4] Wächter, Carsten; Keller, Alexander (2006). Instant Ray Tracing: The Bounding Interval Hierarchy (http:/ / ainc. de/ Research/ BIH. pdf) [5] Wächter, Carsten (2008). Quasi-Monte Carlo Light Transport Simulation by Efficient Ray Tracing (http:/ / vts. uni-ulm. de/ query/ longview. meta. asp?document_id=6265) Forums • http:/ / ompf. org/ forum (http:/ / ompf. org/ forum) External links • BIH implementations: Javascript (http:/ / github. com/ imbcmdth/ jsBIH).
Page 1 and 2: 3D Rendering PDF generated using th
Page 3 and 4: Image-based lighting 64 Image plane
Page 5 and 6: References Article Sources and Cont
Page 7 and 8: 3D rendering 2 Non real-time Animat
Page 9 and 10: 3D rendering 4 The shaded three-dim
Page 11 and 12: Ambient occlusion 6 ambient occlusi
Page 13 and 14: Ambient occlusion 8 • ShadeVis (h
Page 15 and 16: Anisotropic filtering 10 will only
Page 17 and 18: Beam tracing 12 Beam tracing Beam t
Page 19 and 20: Bilinear filtering 14 Are all true.
Page 21 and 22: Binary space partitioning 16 togeth
Page 23 and 24: Binary space partitioning 18 Other
Page 25: Binary space partitioning 20 [1] Bi
Page 29 and 30: Bounding volume 24 bounding boxes b
Page 31 and 32: Bump mapping 26 Bump mapping Bump m
Page 33 and 34: CatmullClark subdivision surface 28
Page 35 and 36: CatmullClark subdivision surface 30
Page 37 and 38: Conversion between quaternions and
Page 39 and 40: Cube mapping 34 Advantages Cube map
Page 41 and 42: Cube mapping 36 Related A large set
Page 43 and 44: Diffuse reflection 38 2), or, of co
Page 45 and 46: Displacement mapping 40 Meaning of
Page 47 and 48: DooSabin subdivision surface 42 Ext
Page 49 and 50: False radiosity 44 False radiosity
Page 51 and 52: Geometry pipelines 46 Geometry pipe
Page 53 and 54: Global illumination 48 Rendering wi
Page 55 and 56: Gouraud shading 50 Gouraud shading
Page 57 and 58: Graphics pipeline 52 Graphics pipel
Page 59 and 60: Graphics pipeline 54 References 1.
Page 61 and 62: Hidden surface determination 56 imp
Page 63 and 64: High dynamic range rendering 58 Hig
Page 65 and 66: High dynamic range rendering 60 Ton
Page 67 and 68: High dynamic range rendering 62 Fro
Page 69 and 70: High dynamic range rendering 64 •
Page 71 and 72: Irregular Z-buffer 66 Applications
Page 73 and 74: Lambert's cosine law 68 than would
Page 75 and 76: 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
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Ray tracing 148 Typically, each ray
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Ray tracing 150 independence of eac
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Ray tracing 152 On June 12, 2008 In
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Reflection 154 Reflection Reflectio
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Reflection 156 Glossy Reflection Fu
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Reflection mapping 158 Cube mapping
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Render Output unit 160 Render Outpu
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Rendering 162 • indirect illumina
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Rendering 164 Ray tracing Ray traci
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Rendering 166 Academic core The imp
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Rendering 168 • 1984 Distributed
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Retained mode 170 Retained mode In
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Scanline rendering 172 Comparison w
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Screen Space Ambient Occlusion 174
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Screen Space Ambient Occlusion 176
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Shadow mapping 178 Algorithm overvi
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Shadow mapping 180 Drawing the scen
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Shadow mapping 182 Further reading
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Shadow volume 184 There is also a p
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Shadow volume 186 The depth fail me
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Silhouette edge 188 Silhouette edge
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Specular highlight 190 Specular hig
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Specular highlight 192 normalized o
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Sphere mapping 194 Sphere mapping I
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Stencil codes 196 Stencil codes Ste
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Stencil codes 198 Stencils The shap
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Stencil codes 200 [7] Wellein, G et
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Subdivision surface 202 used a four
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Subsurface scattering 204 Subsurfac
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Subsurface scattering 206 External
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Surface normal 208 If a (possibly n
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Surface normal 210 Normal in geomet
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Texture filtering 212 Texture filte
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Texture mapping 214 Texture mapping
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Texture mapping 216 constant distan
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Texture synthesis 218 • Structure
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Texture synthesis 220 Pattern-based
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Texture synthesis 222 • Micro-tex
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UV mapping 224 A UV map can either
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Vertex 226 Polytope vertices are re
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Vertex Buffer Object 228 //Make the
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Vertex Buffer Object 230 GLuint sha
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Vertex Buffer Object 232 vertexes *
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Virtual actor 234 Virtual actor A v
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Virtual actor 236 exercises, and ev
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Volume rendering 238 Volume ray cas
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Volume rendering 240 Maximum intens
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Volume rendering 242 Image-based me
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Volumetric lighting 244 References
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Voxel 246 • Outcast, a game made
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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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