3D graphics eBook - Course Materials Repository
3D graphics eBook - Course Materials Repository 3D graphics eBook - Course Materials Repository
OrenNayar reflectance model 89 Analysis of this phenomenon has a long history and can be traced back almost a century. Past work has resulted in empirical models designed to fit experimental data as well as theoretical results derived from first principles. Much of this work was motivated by the non-Lambertian reflectance of the moon. The Oren-Nayar reflectance model, developed by Michael Oren and Shree K. Nayar in 1993 [1] , predicts reflectance from rough diffuse surfaces for the entire hemisphere of source and sensor directions. The model takes into account complex physical phenomena such as masking, shadowing and interreflections between points on the surface facets. It can be viewed as a generalization of Lambert’s law. Today, it is widely used in computer graphics and animation for rendering rough surfaces. It also has important implications for human vision and computer vision problems, such as shape from shading, photometric stereo, etc. Formulation The surface roughness model used in the derivation of the Oren-Nayar model is the microfacet model, proposed by Torrance and Sparrow [2] , which assumes the surface to be composed of long symmetric V-cavities. Each cavity consists of two planar facets. The roughness of the surface is specified using a probability function for the distribution of facet slopes. In particular, the Gaussian distribution is often used, and thus the variance of the Gaussian distribution, , is a measure of the roughness of the surfaces (ranging from 0 to 1). In the Oren-Nayar reflectance model, each facet is assumed to be Lambertian in Aggregation of the reflection from rough surfaces Diagram of surface reflection reflectance. As shown in the image at right, given the radiance of the incoming light , the radiance of the reflected light , according to the Oren-Nayar model, is where , ,
OrenNayar reflectance model 90 , , and is the albedo of the surface, and is the roughness of the surface (ranging from 0 to 1). In the case of (i.e., all facets in the same plane), we have , and , and thus the Oren-Nayar model simplifies to the Lambertian model: Results Here is a real image of a matte vase illuminated from the viewing direction, along with versions rendered using the Lambertian and Oren-Nayar models. It shows that the Oren-Nayar model predicts the diffuse reflectance for rough surfaces more accurately than the Lambertian model. Plot of the brightness of the rendered images, compared with the measurements on a cross section of the real vase. Here are rendered images of a sphere using the Oren-Nayar model, corresponding to different surface roughnesses (i.e. different values):
- 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
- 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: OrenNayar reflectance model 88 Oren
- 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 and 108: Phong reflection model 102 Visual i
- Page 109 and 110: Phong reflection model 104 Because
- 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 135 and 136: Quaternions and spatial rotation 13
- Page 137 and 138: Quaternions and spatial rotation 13
- Page 139 and 140: Quaternions and spatial rotation 13
- Page 141 and 142: Quaternions and spatial rotation 13
- Page 143 and 144: Quaternions and spatial rotation 13
OrenNayar reflectance model 90<br />
,<br />
,<br />
and is the albedo of the surface, and is the roughness of the surface (ranging from 0 to 1). In the case of<br />
(i.e., all facets in the same plane), we have , and , and thus the Oren-Nayar model simplifies to the<br />
Lambertian model:<br />
Results<br />
Here is a real image of a matte vase illuminated from the viewing direction, along with versions rendered using the<br />
Lambertian and Oren-Nayar models. It shows that the Oren-Nayar model predicts the diffuse reflectance for rough<br />
surfaces more accurately than the Lambertian model.<br />
Plot of the brightness of the rendered images, compared with the<br />
measurements on a cross section of the real vase.<br />
Here are rendered images of a sphere<br />
using the Oren-Nayar model,<br />
corresponding to different surface<br />
roughnesses (i.e. different values):
Change language