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Phong reflection model 103 When the color is represented as RGB values, as often is the case in computer graphics, this equation is typically modeled separately for R, G and B intensities, allowing different reflections constants and for the different color channels. Computationally more efficient alterations When implementing the Phong reflection model, there are a number of methods for approximating the model, rather than implementing the exact formulas, which can speed up the calculation; for example, the Blinn–Phong reflection model is a modification of the Phong reflection model, which is more efficient if the viewer and the light source are treated to be at infinity. Another approximation [3] also addresses the computation of the specular term since the calculation of the power term may be computationally expensive. Considering that the specular term should be taken into account only if its dot product is positive, it can be approximated by realizing that for , for a sufficiently large, fixed integer (typically 4 will be enough), where is a real number (not necessarily an integer). The value can be further approximated as ; this squared distance between the vectors and is much less sensitive to normalization errors in those vectors than is Phong's dot-product-based . The value can be chosen to be a fixed power of 2, where is a small integer; then the expression can be efficiently calculated by squaring times. Here the shininess parameter is , proportional to the orignal parameter . This method substitutes a few multiplications for a variable exponentiation. Inverse Phong reflection model The Phong reflection model in combination with Phong shading is an approximation of shading of objects in real life. This means that the Phong equation can relate the shading seen in a photograph with the surface normals of the visible object. Inverse refers to the wish to estimate the surface normals given a rendered image, natural or computer-made. The Phong reflection model contains many parameters, such as the surface diffuse reflection parameter (albedo) which may vary within the object. Thus the normals of an object in a photograph can only be determined, by introducing additive information such as the number of lights, light directions and reflection parameters. For example we have a cylindrical object for instance a finger and like to calculate the normal on a line on the object. We assume only one light, no specular reflection, and uniform known (approximated) reflection parameters. We can then simplify the Phong equation to: With a constant equal to the ambient light and a constant equal to the diffusion reflection. We can re-write the equation to: Which can be rewritten for a line through the cylindrical object as: For instance if the light direction is 45 degrees above the object we get two equations with two unknowns.
Phong reflection model 104 Because of the powers of two in the equation there are two possible solutions for the normal direction. Thus some prior information of the geometry is needed to define the correct normal direction. The normals are directly related to angles of inclination of the line on the object surface. Thus the normals allow the calculation of the relative surface heights of the line on the object using a line integral, if we assume a continuous surface. If the object is not cylindrical, we have three unknown normal values . Then the two equations still allow the normal to rotate around the view vector, thus additional constraints are needed from prior geometric information. For instance in face recognition those geometric constraints can be obtained using principal component analysis (PCA) on a database of depth-maps of faces, allowing only surface normals solutions which are found in a normal population. [4] Applications As already implied, the Phong reflection model is often used together with Phong shading to shade surfaces in 3D computer graphics software. Apart from this, it may also be used for other purposes. For example, it has been used to model the reflection of thermal radiation from the Pioneer probes in an attempt to explain the Pioneer anomaly. [5] References [1] B. T. Phong, Illumination for computer generated pictures, Communications of ACM 18 (1975), no. 6, 311–317. [2] University of Utah School of Computing, http:/ / www. cs. utah. edu/ school/ history/ #phong-ref [3] Lyon, Richard F. (August 2, 1993). "Phong Shading Reformulation for Hardware Renderer Simplification" (http:/ / dicklyon. com/ tech/ Graphics/ Phong_TR-Lyon. pdf). . Retrieved 7 March 2011. [4] Boom, B.J. and Spreeuwers, L.J. and Veldhuis, R.N.J. (September 2009). "Model-Based Illumination Correction for Face Images in Uncontrolled Scenarios". Lecture Notes in Computer Science 5702 (2009): 33–40. doi:10.1007/978-3-642-03767-2. [5] F. Francisco, O. Bertolami, P. J. S. Gil, J. Páramos. "Modelling the reflective thermal contribution to the acceleration of the Pioneer spacecraft". arXiv:1103.5222.
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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
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
Page 77 and 78: Level of detail 72 Well known appro
Page 79 and 80: Level of detail 74 Hierarchical LOD
Page 81 and 82: Newell's algorithm 76 Newell's algo
Page 83 and 84: Non-uniform rational B-spline 78 Us
Page 85 and 86: Non-uniform rational B-spline 80 of
Page 87 and 88: Non-uniform rational B-spline 82 ar
Page 89 and 90: Non-uniform rational B-spline 84 Ex
Page 91 and 92: Normal mapping 86 How it works To c
Page 93 and 94: OrenNayar reflectance model 88 Oren
Page 95 and 96: OrenNayar reflectance model 90 , ,
Page 97 and 98: Painter's algorithm 92 The algorith
Page 99 and 100: Parallax mapping 94 • Parallax Ma
Page 101 and 102: Particle system 96 A cube emitting
Page 103 and 104: Path tracing 98 History Further inf
Page 105 and 106: Path tracing 100 Scattering distrib
Page 107: Phong reflection model 102 Visual i
Page 111 and 112: Phong shading 106 Visual illustrati
Page 113 and 114: Photon mapping 108 Rendering (2nd p
Page 115 and 116: Photon tracing 110 Advantages and d
Page 117 and 118: Potentially visible set 112 • Can
Page 119 and 120: Potentially visible set 114 Externa
Page 121 and 122: Procedural generation 116 increases
Page 123 and 124: Procedural generation 118 • Softi
Page 125 and 126: Procedural generation 120 Reference
Page 127 and 128: Procedural texture 122 Self-organiz
Page 129 and 130: Procedural texture 124 References [
Page 131 and 132: 3D projection 126 The distance of t
Page 133 and 134: Quaternions and spatial rotation 12
Page 145 and 146: Radiosity 140 Overview of the radio
Page 147 and 148: Radiosity 142 This is sometimes kno
Page 149 and 150: Radiosity 144 References [1] " Mode
Page 151 and 152: 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
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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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