2170:
is limited by the camera being used; this can be as low as 8 bits for older image sensors or as high as 32 bits for the newer automotive image sensors. The other disadvantage is that for BRDF measurements the beam must pass from an external light source, bounce off a pellicle and pass in reverse through the first few elements of the conoscope before being scattered by the sample. Each of these elements is antireflection-coated, but roughly 0.3% of the light is reflected at each air-glass interface. These reflections will show up in the image as a spurious signal. For scattering surfaces with a large signal, this is not a problem, but for
Lambertian surfaces it is.
656:
1970:, NASA uses a BRDF model to characterise surface reflectance anisotropy. For a given land area, the BRDF is established based on selected multiangular observations of surface reflectance. While single observations depend on view geometry and solar angle, the MODIS BRDF/Albedo product describes intrinsic surface properties in several spectral bands, at a resolution of 500 meters. The BRDF/Albedo product can be used to model surface
2032:
2056:
2044:
31:
428:
2218:
2159:
Unfortunately, using such a device to densely measure the BRDF is very time-consuming. One of the first improvements on these techniques used a half-silvered mirror and a digital camera to take many BRDF samples of a planar target at once. Since this work, many researchers have developed other devices for efficiently acquiring BRDFs from real world samples, and it remains an active area of research.
651:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})\,=\,{\frac {\mathrm {d} L_{\text{r}}(\omega _{\text{r}})}{\mathrm {d} E_{\text{i}}(\omega _{\text{i}})}}\,=\,{\frac {\mathrm {d} L_{\text{r}}(\omega _{\text{r}})}{L_{\text{i}}(\omega _{\text{i}})\cos \theta _{\text{i}}\mathrm {d} \omega _{\text{i}}}}}
1913:
2214:
This procedure starts with sampling the BRDF distribution and generating it with microfacet geometry then the surfaced is optimized in terms of smoothness and continuity to meet the limitations of the milling machine. The final BRDF distribution is the convolution of the substrate and the geometry of
2169:
A fast way to measure BRDF or BTDF is a conoscopic scatterometer The advantage of this measurement instrument is that a near-hemispheric measurement can be captured in a fraction of a second with resolution of roughly 0.1°. This instrument has two disadvantages. The first is that the dynamic range
2240:
In addition to color and specularity, real-world objects also contain texture. A 3D printer can be used to manufacture the geometry and cover the surface with a suitable ink; by optimally creating the facets and choosing the ink combination, this method can give us a higher degree of freedom in
2233:
to achieve the targeted BRDF. Given a set of metallic inks with known BRDF an algorithm proposed to linearly combine them to produce the targeted distribution. So far printing only means gray-scale or color printing but real-world surfaces can exhibit different amounts of specularity that
2158:
employ one or more goniometric arms to position a light source and a detector at various directions from a flat sample of the material to be measured. To measure a full BRDF, this process must be repeated many times, moving the light source each time to measure a different incidence angle.
1789:
1504:
1409:
1309:
2847:
E. Lafortune, S. Foo, K. Torrance, and D. Greenberg, Non-linear approximation of reflectance functions. In Turner
Whitted, editor, SIGGRAPH 97 Conference Proceedings, Annual Conference Series, pp. 117–126. ACM SIGGRAPH, Addison Wesley, August
2094:, physically motivated approximation of the radiative transfer solution for a porous, irregular, and particulate surface. Often used in astronomy for planet/small body surface reflection simulations. Multiple versions and modifications exist.
2178:
BRDF fabrication refers to the process of implementing a surface based on the measured or synthesized information of a target BRDF. There exist three ways to perform such a task, but in general, it can be summarized as the following steps:
1796:
1175:
1608:
2922:
Marschner S.R., Westin S.H., Lafortune E.P.F., Torrance K.E., Greenberg D.P. (1999) Image-Based BRDF Measurement
Including Human Skin. In: Lischinski D., Larson G.W. (eds) Rendering Techniques’ 99. Eurographics. Springer,
1683:
958:
175:
1210:) is appropriate for modeling non-flat surfaces, and has the same parameterization as the SVBRDF; however in contrast, the BTF includes non-local scattering effects like shadowing, masking, interreflections or
1097:
1049:
901:
1544:
1694:
1001:
2067:
Three elemental components that can be used to model a variety of light-surface interactions. The incoming light ray is shown in black, the reflected ray(s) modeled by the BRDF in gray.
1418:
1329:
3009:
Matusik, Wojciech; Ajdin, Boris; Gu, Jinwei; Lawrence, Jason; Lensch, Hendrik P. A.; Pellacini, Fabio; Rusinkiewicz, Szymon (2009-12-01). "Printing spatially-varying reflectance".
1232:
3128:
Schaepman-Strub, G.; M. E. Schaepman; T. H. Painter; S. Dangel; J. V. Martonchik (2006-07-15). "Reflectance quantities in optical remote sensing: definitions and case studies".
776:
749:
336:
305:
245:
218:
86:
59:
1197:
802:
270:
2838:
X. He, K. Torrance, F. Sillon, and D. Greenberg, A comprehensive physical model for light reflection, Computer
Graphics 25 (1991), no. Annual Conference Series, 175–186.
846:
824:
2415:"Photovoltaic System Performance Enhancement with Nontracking Planar Concentrators: Experimental Results and Bidirectional Reflectance Function (BDRF)-Based Modeling"
405:
356:
1908:{\displaystyle \forall \omega _{\text{i}},\,\int _{\Omega }f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})\,\cos {\theta _{\text{r}}}d\omega _{\text{r}}\leq 1}
382:
714:
678:
106:
1114:
2951:
2121:, a specular-microfacet model with an elliptical-Gaussian distribution function dependent on surface tangent orientation (in addition to surface normal).
1549:
1625:
2256:
1226:
906:
123:
2963:
Weyrich, Tim; Peers, Pieter; Matusik, Wojciech; Rusinkiewicz, Szymon (2009). "Fabricating microgeometry for custom surface reflectance".
2518:
2345:
Duvenhage, Bernardt (2013). "Numerical verification of bidirectional reflectance distribution functions for physical plausibility".
2362:"Photovoltaic system performance enhancement with non-tracking planar concentrators: Experimental results and BDRF based modelling"
2501:
2361:
2136:
Fitted
Lafortune model, a generalization of Phong with multiple specular lobes, and intended for parametric fits of measured data.
1054:
1006:
858:
3118:
3095:
2861:
2559:
2389:
1509:
2023:
W. Matusik et al. found that interpolating between measured samples produced realistic results and was easy to understand.
1784:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})=f_{\text{r}}(\omega _{\text{r}},\,\omega _{\text{i}})}
2935:
2964:
2130:
Ashikhmin–Shirley model, allowing for anisotropic reflectance, along with a diffuse substrate under a specular surface.
2234:
affects their final appearance, as a result this novel method can help us print images even more realistically.
1546:: that is, it will only emit light at wavelength equal to the incoming light. In this case it can be parameterized as
963:
2985:
2650:
2368:
2118:
2952:
https://www.photonicsspectra-digital.com/photonicsspectra/september 2020/MobilePagedReplica.action?pm=2&folio=56
2166:. The standard algorithm is to measure the BRDF point cloud from images and optimize it by one of the BRDF models.
1499:{\displaystyle f_{\text{r}}(\lambda _{\text{i}},\,\omega _{\text{i}},\,\lambda _{\text{r}},\,\omega _{\text{r}})=0}
2109:
Torrance–Sparrow model, a general model representing surfaces as distributions of perfectly specular microfacets.
1404:{\displaystyle f_{\text{r}}(\lambda _{\text{i}},\,\omega _{\text{i}},\,\lambda _{\text{r}},\,\omega _{\text{r}})}
855:
and not directly as a quotient between the undifferentiated quantities, is because irradiating light other than
3178:
1207:
1304:{\displaystyle S(\mathbf {x} _{\text{i}},\,\omega _{\text{i}},\,\mathbf {x} _{\text{r}},\,\omega _{\text{r}})}
2878:
2765:
Nayar, S. K.; Oren, M. (1995). "Generalization of the
Lambertian Model and Implications for Machine Vision".
2103:
1932:
2106:, resembling Phong, but allowing for certain quantities to be interpolated, reducing computational overhead.
1318:
of light has been ignored. In reality, the BRDF is wavelength dependent, and to account for effects such as
2347:
Proceedings of the South
African Institute for Computer Scientists and Information Technologists Conference
2124:
1982:
BRDFs can be measured directly from real objects using calibrated cameras and lightsources; however, many
359:
3158:
754:
727:
314:
283:
223:
196:
64:
37:
3036:
Lan, Yanxiang; Dong, Yue; Pellacini, Fabio; Tong, Xin (2013-07-01). "Bi-scale appearance fabrication".
2286:
2163:
852:
2229:
In order to generate spatially varying BRDF (svBRDF) it has been proposed to use gamut mapping and
2127:, a "directed-diffuse" microfacet model, with perfectly diffuse (rather than specular) microfacets.
2115:, a specular-microfacet model (Torrance–Sparrow) accounting for wavelength and thus color shifting.
2200:
Optimize the continuity and smoothness of the surface with respect to the manufacturing procedure.
1180:
785:
253:
3193:
2674:
Torrance, K.; Sparrow, E. (1967). "Theory for Off-Specular
Reflection from Roughened Surfaces".
829:
807:
177:, is a function of four real variables that defines how light from a source is reflected off an
2271:
2097:
1991:
1983:
1618:
Physically realistic BRDFs for reciprocal linear optics have additional properties, including,
2478:
1994:
model frequently assumed in computer graphics. Some useful features of recent models include:
3173:
2079:
1688:
1211:
390:
341:
2906:
Church E., Takacs P., Leonard T., The prediction of BSDFs from surface profile measurements
3137:
2683:
2539:
2319:
407:, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr, with
367:
17:
8:
3188:
2209:
1311:
in which light entering the surface may scatter internally and exit at another location.
3141:
2687:
2635:
Proceedings of the 4th annual conference on
Computer graphics and interactive techniques
2543:
2323:
27:
Function of four real variables that defines how light is reflected at an opaque surface
3061:
2991:
2891:
2821:
2782:
2656:
2633:
James F. Blinn (1977). "Models of light reflection for computer synthesized pictures".
2615:
2498:
2434:
2395:
2310:
Nicodemus, Fred (1965). "Directional reflectance and emissivity of an opaque surface".
2291:
2261:
2155:
2016:
1960:
1948:
1936:
699:
663:
91:
3114:
3091:
3053:
2981:
2646:
2575:
2555:
2385:
2112:
2009:
1928:
248:
186:
3127:
2995:
2859:
Image-based modelling of material reflective properties of flat objects (In
Russian)
2825:
2438:
2399:
1170:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}},\,\mathbf {x} )}
3145:
3065:
3045:
3018:
2973:
2907:
2817:
2813:
2786:
2774:
2747:
2722:
2691:
2660:
2638:
2619:
2605:
2547:
2426:
2377:
2327:
2266:
2204:
Many approaches have been proposed for manufacturing the BRDF of the target :
2091:
178:
2858:
3183:
3110:
2939:
2865:
2505:
2430:
2085:
1956:
1944:
1940:
685:
190:
2133:
HTSG (He, Torrance, Sillion, Greenberg), a comprehensive physically based model.
1603:{\displaystyle f_{\text{r}}(\lambda ,\,\omega _{\text{i}},\,\omega _{\text{r}})}
1214:. The functions defined by the BTF at each point on the surface are thus called
2533:
1987:
1967:
779:
693:
34:
Diagram showing vectors used to define the BRDF. All vectors are unit length.
3149:
2950:
Eckhardt S, Lunda K., Digital Age Sees New Demand for the Venerable Conoscope
2932:
2381:
3167:
3057:
2801:
2551:
2452:
1412:
423:
The BRDF was first defined by Fred Nicodemus around 1965. The definition is:
362:
3049:
3022:
2977:
2186:
Sample this distribution to discretize it and make the fabrication feasible.
2695:
1678:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})\geq 0}
1323:
385:
2751:
2742:
Ward, Gregory J. (1992). "Measuring and modeling anisotropic reflection".
2727:
2710:
2642:
2610:
2593:
2221:
The final BRDF is the aggregated effect of the geometry and ink selection.
2281:
1999:
1924:
1319:
689:
412:
2331:
2778:
2497:
Wojciech Matusik, Hanspeter Pfister, Matt Brand, and Leonard McMillan.
2276:
2190:
1952:
1315:
717:
308:
3159:
An intuitive introduction to the concept of reflection model and BRDF.
2911:
2082:, representing perfectly diffuse (matte) surfaces by a constant BRDF.
953:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}
408:
170:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}
2414:
2230:
2194:
681:
277:
2893:
A Study of Scattering Characteristics for Microscale Rough Surface
1223:
Bidirectional Surface Scattering Reflectance Distribution Function
960:, might illuminate the surface which would unintentionally affect
1109:
Spatially Varying Bidirectional Reflectance Distribution Function
2962:
2251:
2031:
1971:
1411:. Note that in the typical case where all optical elements are
182:
30:
2217:
2055:
2043:
2413:
Andrews, Rob W.; Pollard, Andrew; Pearce, Joshua M. (2015).
2360:
Andrews, Rob W.; Pollard, Andrew; Pearce, Joshua M. (2013).
2100:, a phenomenological model akin to plastic-like specularity.
1092:{\displaystyle \mathrm {d} E_{\text{i}}(\omega _{\text{i}})}
1044:{\displaystyle \mathrm {d} L_{\text{r}}(\omega _{\text{r}})}
896:{\displaystyle \mathrm {d} E_{\text{i}}(\omega _{\text{i}})}
193:
algorithms. The function takes an incoming light direction,
2370:
2013 IEEE 39th Photovoltaic Specialists Conference (PVSC)
1951:. BRDF has also been used for modeling light trapping in
2189:
Design a geometry that produces this distribution (with
851:
The reason the function is defined as a quotient of two
2896:(Master's thesis). Rose-Hulman Institute of Technology.
2538:(2 ed.). Cambridge University Press. p. 323.
2479:"A Survey of BRDF Representation for Computer Graphics"
2183:
Measuring or synthesizing the target BRDF distribution.
1539:{\displaystyle \lambda _{\text{i}}=\lambda _{\text{r}}}
3008:
2162:
There is an alternative way to measure BRDF based on
2139:
Lebedev model for analytical-grid BRDF approximation.
2005:
editable using a small number of intuitive parameters
1799:
1697:
1628:
1552:
1512:
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1235:
1183:
1117:
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256:
226:
199:
126:
94:
67:
40:
3035:
2972:. New York, New York, USA: ACM Press. pp. 1–6.
2879:
Approximated Scatter Models for Stray Light Analysis
2412:
2359:
1326:
the dependence on wavelength must be made explicit:
2857:Ilyin A., Lebedev A., Sinyavsky V., Ignatenko, A.,
1229:), is a further generalized 8-dimensional function
3104:
3081:
2576:"Fundamentals of the Planetary Spectrum Generator"
1907:
1783:
1677:
1602:
1538:
1498:
1403:
1303:
1199:describes a 2D location over an object's surface.
1191:
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995:
952:
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399:
376:
350:
330:
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264:
239:
212:
169:
100:
80:
53:
3165:
2799:
2535:Theory of Reflectance and Emittance Spectroscopy
996:{\displaystyle L_{\text{r}}(\omega _{\text{r}})}
2673:
2154:Traditionally, BRDF measurement devices called
114:bidirectional reflectance distribution function
2632:
2594:"Illumination for computer generated pictures"
2667:
2511:
2338:
2303:
2708:
2476:
826:indicates incident light, whereas the index
2804:(2000). "An Anisotropic Phong BRDF Model".
2711:"A reflectance model for computer graphics"
2508:. ACM Transactions on Graphics. 22(3) 2002.
276:-axis), and returns the ratio of reflected
2241:design and more accurate BRDF fabrication.
1314:In all these cases, the dependence on the
2764:
2735:
2726:
2676:Journal of the Optical Society of America
2609:
2344:
2309:
1867:
1853:
1816:
1767:
1724:
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1613:
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1572:
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1462:
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1359:
1287:
1271:
1257:
1158:
1144:
936:
551:
547:
476:
472:
458:
153:
3082:Lubin, Dan; Robert Massom (2006-02-10).
2868:. In: GraphiCon'2009.; 2009. p. 198-201.
2767:International Journal of Computer Vision
2216:
247:(taken in a coordinate system where the
29:
3090:(1st ed.). Springer. p. 756.
311:incident on the surface from direction
14:
3166:
1610:, with only one wavelength parameter.
1111:(SVBRDF) is a 6-dimensional function,
2591:
2531:
1974:depending on atmospheric scattering.
3105:Matt, Pharr; Greg Humphreys (2004).
2741:
1927:concept, and accordingly is used in
1102:
692:-in-the-direction-of-a-ray per unit
2889:
2173:
88:points toward the viewer (camera).
24:
3075:
2637:. Vol. 11. pp. 192–198.
1822:
1800:
1059:
1011:
863:
771:{\displaystyle \omega _{\text{i}}}
744:{\displaystyle \theta _{\text{i}}}
631:
556:
514:
481:
331:{\displaystyle \omega _{\text{i}}}
300:{\displaystyle \omega _{\text{r}}}
240:{\displaystyle \omega _{\text{r}}}
213:{\displaystyle \omega _{\text{i}}}
81:{\displaystyle \omega _{\text{r}}}
54:{\displaystyle \omega _{\text{i}}}
25:
3205:
2457:NASA, Goddard Space Flight Center
1990:have been proposed including the
2238:Combination of Ink and Geometry:
2073:
2054:
2042:
2030:
1274:
1244:
1185:
1160:
790:
258:
61:points toward the light source.
3029:
3002:
2956:
2944:
2926:
2916:
2900:
2883:
2871:
2851:
2841:
2832:
2793:
2758:
2709:Cook, R.; Torrance, K. (1981).
2702:
2626:
2585:
2568:
2499:A Data-Driven Reflectance Model
2088:, lunar and Martian reflection.
1918:
903:, which are of no interest for
181:surface. It is employed in the
2818:10.1080/10867651.2000.10487522
2715:ACM SIGGRAPH Computer Graphics
2525:
2491:
2470:
2445:
2406:
2353:
2149:
1864:
1837:
1778:
1751:
1735:
1708:
1666:
1639:
1597:
1563:
1487:
1432:
1398:
1343:
1298:
1239:
1204:Bidirectional Texture Function
1164:
1128:
1086:
1073:
1038:
1025:
990:
977:
947:
920:
890:
877:
611:
598:
583:
570:
541:
528:
508:
495:
469:
442:
164:
137:
13:
1:
3130:Remote Sensing of Environment
2519:"mental ray Layering Shaders"
2419:IEEE Journal of Photovoltaics
2297:
1935:of synthetic scenes (see the
418:
3038:ACM Transactions on Graphics
3011:ACM Transactions on Graphics
2431:10.1109/JPHOTOV.2015.2478064
1966:In the context of satellite
1192:{\displaystyle \mathbf {x} }
797:{\displaystyle \mathbf {n} }
265:{\displaystyle \mathbf {n} }
7:
2245:
848:indicates reflected light.
696:-perpendicular-to-the-ray,
10:
3210:
3107:Physically Based Rendering
1923:The BRDF is a fundamental
841:{\displaystyle {\text{r}}}
819:{\displaystyle {\text{i}}}
220:, and outgoing direction,
3150:10.1016/j.rse.2006.03.002
2806:Journal of Graphics Tools
2598:Communications of the ACM
2382:10.1109/PVSC.2013.6744136
2145:K-correlation (ABC) model
1977:
1415:, the function will obey
2966:ACM SIGGRAPH 2009 papers
2552:10.1017/CBO9781139025683
1933:photorealistic rendering
185:of real-world light, in
3050:10.1145/2461912.2461989
3023:10.1145/1618452.1618474
2978:10.1145/1576246.1531338
2744:Proceedings of SIGGRAPH
2287:Schlick's approximation
2098:Phong reflectance model
1959:) or low concentration
400:{\displaystyle \theta }
351:{\displaystyle \omega }
2877:Richard N. Pfisterer,
2696:10.1364/JOSA.57.001105
2376:. pp. 0229–0234.
2272:Photometry (astronomy)
2222:
2092:Hapke scattering model
1992:Lambertian reflectance
1909:
1785:
1679:
1614:Physically based BRDFs
1604:
1540:
1500:
1405:
1305:
1193:
1171:
1093:
1045:
997:
954:
897:
842:
820:
798:
772:
745:
710:
674:
652:
401:
378:
352:
332:
301:
266:
241:
214:
171:
109:
108:is the surface normal.
102:
82:
55:
3179:Astrophysics concepts
3088:Atmosphere and Oceans
2890:Won, Yonghee (2014).
2752:10.1145/133994.134078
2728:10.1145/965161.806819
2643:10.1145/563858.563893
2611:10.1145/360825.360839
2592:Phong, B. T. (1975).
2532:Hapke, Bruce (2012).
2220:
2015:being well-suited to
1910:
1786:
1689:Helmholtz reciprocity
1680:
1605:
1541:
1501:
1406:
1306:
1212:subsurface scattering
1194:
1172:
1094:
1046:
998:
955:
898:
843:
821:
799:
773:
751:is the angle between
746:
711:
675:
653:
411:(sr) being a unit of
402:
379:
377:{\displaystyle \phi }
353:
333:
302:
267:
242:
215:
172:
103:
83:
56:
33:
3084:Polar Remote Sensing
2800:Ashikhmin, Michael;
2746:. pp. 265–272.
1797:
1695:
1626:
1550:
1510:
1419:
1330:
1233:
1181:
1115:
1055:
1051:is only affected by
1007:
964:
907:
859:
830:
808:
786:
755:
728:
720:, or power per unit
700:
664:
429:
391:
368:
342:
315:
284:
254:
224:
197:
124:
92:
65:
38:
3142:2006RSEnv.103...27S
2688:1967JOSA...57.1105T
2544:2012tres.book.....H
2349:. pp. 200–208.
2332:10.1364/AO.4.000767
2324:1965ApOpt...4..767N
2215:the milled surface.
2156:gonioreflectometers
2113:Cook–Torrance model
2017:Monte Carlo methods
1793:conserving energy:
189:algorithms, and in
2938:2011-07-06 at the
2864:2011-07-06 at the
2779:10.1007/BF01679684
2504:2018-07-21 at the
2292:Specular highlight
2262:Gonioreflectometer
2227:Printing the BRDF:
2223:
1961:solar photovoltaic
1949:object recognition
1937:rendering equation
1905:
1781:
1675:
1600:
1536:
1496:
1401:
1301:
1189:
1167:
1089:
1041:
993:
950:
893:
838:
816:
794:
768:
741:
706:
670:
648:
397:
374:
348:
328:
297:
262:
237:
210:
167:
110:
98:
78:
51:
3120:978-0-12-553180-1
3097:978-3-540-43097-1
2933:BRDFRecon project
2912:10.1117/12.962842
2561:978-0-521-88349-8
2477:Rusinkiewicz, S.
2391:978-1-4799-3299-3
2104:Blinn–Phong model
2012:at grazing angles
1939:), as well as in
1929:computer graphics
1896:
1882:
1861:
1847:
1834:
1810:
1775:
1761:
1748:
1732:
1718:
1705:
1663:
1649:
1636:
1594:
1580:
1560:
1533:
1520:
1484:
1470:
1456:
1442:
1429:
1395:
1381:
1367:
1353:
1340:
1295:
1281:
1265:
1251:
1152:
1138:
1125:
1103:Related functions
1083:
1070:
1035:
1022:
987:
974:
944:
930:
917:
887:
874:
836:
814:
765:
738:
709:{\displaystyle E}
673:{\displaystyle L}
646:
642:
627:
608:
595:
580:
567:
545:
538:
525:
505:
492:
466:
452:
439:
338:. Each direction
325:
294:
234:
207:
187:computer graphics
161:
147:
134:
101:{\displaystyle n}
75:
48:
16:(Redirected from
3201:
3153:
3124:
3113:. p. 1019.
3109:(1st ed.).
3101:
3070:
3069:
3033:
3027:
3026:
3006:
3000:
2999:
2971:
2960:
2954:
2948:
2942:
2930:
2924:
2920:
2914:
2904:
2898:
2897:
2887:
2881:
2875:
2869:
2855:
2849:
2845:
2839:
2836:
2830:
2829:
2797:
2791:
2790:
2762:
2756:
2755:
2739:
2733:
2732:
2730:
2706:
2700:
2699:
2682:(9): 1105–1114.
2671:
2665:
2664:
2630:
2624:
2623:
2613:
2589:
2583:
2582:
2580:
2572:
2566:
2565:
2529:
2523:
2522:
2515:
2509:
2495:
2489:
2488:
2486:
2485:
2474:
2468:
2467:
2465:
2463:
2449:
2443:
2442:
2425:(6): 1626–1635.
2410:
2404:
2403:
2375:
2366:
2357:
2351:
2350:
2342:
2336:
2335:
2307:
2267:Opposition spike
2174:BRDF fabrication
2125:Oren–Nayar model
2080:Lambertian model
2058:
2046:
2034:
1984:phenomenological
1955:(e.g. using the
1945:inverse problems
1914:
1912:
1911:
1906:
1898:
1897:
1894:
1885:
1884:
1883:
1880:
1863:
1862:
1859:
1849:
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1845:
1836:
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1812:
1811:
1808:
1790:
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1777:
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1773:
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1707:
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1703:
1684:
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1665:
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1647:
1638:
1637:
1634:
1609:
1607:
1606:
1601:
1596:
1595:
1592:
1582:
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1578:
1562:
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1545:
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1542:
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1535:
1534:
1531:
1522:
1521:
1518:
1505:
1503:
1502:
1497:
1486:
1485:
1482:
1472:
1471:
1468:
1458:
1457:
1454:
1444:
1443:
1440:
1431:
1430:
1427:
1410:
1408:
1407:
1402:
1397:
1396:
1393:
1383:
1382:
1379:
1369:
1368:
1365:
1355:
1354:
1351:
1342:
1341:
1338:
1310:
1308:
1307:
1302:
1297:
1296:
1293:
1283:
1282:
1279:
1277:
1267:
1266:
1263:
1253:
1252:
1249:
1247:
1198:
1196:
1195:
1190:
1188:
1176:
1174:
1173:
1168:
1163:
1154:
1153:
1150:
1140:
1139:
1136:
1127:
1126:
1123:
1098:
1096:
1095:
1090:
1085:
1084:
1081:
1072:
1071:
1068:
1062:
1050:
1048:
1047:
1042:
1037:
1036:
1033:
1024:
1023:
1020:
1014:
1002:
1000:
999:
994:
989:
988:
985:
976:
975:
972:
959:
957:
956:
951:
946:
945:
942:
932:
931:
928:
919:
918:
915:
902:
900:
899:
894:
889:
888:
885:
876:
875:
872:
866:
847:
845:
844:
839:
837:
834:
825:
823:
822:
817:
815:
812:
803:
801:
800:
795:
793:
777:
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774:
769:
767:
766:
763:
750:
748:
747:
742:
740:
739:
736:
715:
713:
712:
707:
679:
677:
676:
671:
657:
655:
654:
649:
647:
645:
644:
643:
640:
634:
629:
628:
625:
610:
609:
606:
597:
596:
593:
586:
582:
581:
578:
569:
568:
565:
559:
553:
546:
544:
540:
539:
536:
527:
526:
523:
517:
511:
507:
506:
503:
494:
493:
490:
484:
478:
468:
467:
464:
454:
453:
450:
441:
440:
437:
406:
404:
403:
398:
383:
381:
380:
375:
360:parameterized by
357:
355:
354:
349:
337:
335:
334:
329:
327:
326:
323:
306:
304:
303:
298:
296:
295:
292:
271:
269:
268:
263:
261:
246:
244:
243:
238:
236:
235:
232:
219:
217:
216:
211:
209:
208:
205:
176:
174:
173:
168:
163:
162:
159:
149:
148:
145:
136:
135:
132:
107:
105:
104:
99:
87:
85:
84:
79:
77:
76:
73:
60:
58:
57:
52:
50:
49:
46:
21:
3209:
3208:
3204:
3203:
3202:
3200:
3199:
3198:
3164:
3163:
3121:
3111:Morgan Kaufmann
3098:
3078:
3076:Further reading
3073:
3034:
3030:
3007:
3003:
2988:
2969:
2961:
2957:
2949:
2945:
2940:Wayback Machine
2931:
2927:
2921:
2917:
2905:
2901:
2888:
2884:
2876:
2872:
2866:Wayback Machine
2856:
2852:
2846:
2842:
2837:
2833:
2798:
2794:
2763:
2759:
2740:
2736:
2707:
2703:
2672:
2668:
2653:
2631:
2627:
2590:
2586:
2578:
2574:
2573:
2569:
2562:
2530:
2526:
2517:
2516:
2512:
2506:Wayback Machine
2496:
2492:
2483:
2481:
2475:
2471:
2461:
2459:
2451:
2450:
2446:
2411:
2407:
2392:
2373:
2364:
2358:
2354:
2343:
2339:
2308:
2304:
2300:
2248:
2176:
2152:
2086:Lommel–Seeliger
2076:
2071:
2070:
2069:
2068:
2064:
2063:
2062:
2059:
2051:
2050:
2047:
2039:
2038:
2035:
2010:Fresnel effects
2008:accounting for
1988:analytic models
1980:
1957:OPTOS formalism
1941:computer vision
1921:
1893:
1889:
1879:
1875:
1874:
1858:
1854:
1844:
1840:
1831:
1827:
1821:
1817:
1807:
1803:
1798:
1795:
1794:
1772:
1768:
1758:
1754:
1745:
1741:
1729:
1725:
1715:
1711:
1702:
1698:
1696:
1693:
1692:
1660:
1656:
1646:
1642:
1633:
1629:
1627:
1624:
1623:
1616:
1591:
1587:
1577:
1573:
1557:
1553:
1551:
1548:
1547:
1530:
1526:
1517:
1513:
1511:
1508:
1507:
1481:
1477:
1467:
1463:
1453:
1449:
1439:
1435:
1426:
1422:
1420:
1417:
1416:
1392:
1388:
1378:
1374:
1364:
1360:
1350:
1346:
1337:
1333:
1331:
1328:
1327:
1292:
1288:
1278:
1273:
1272:
1262:
1258:
1248:
1243:
1242:
1234:
1231:
1230:
1184:
1182:
1179:
1178:
1159:
1149:
1145:
1135:
1131:
1122:
1118:
1116:
1113:
1112:
1105:
1080:
1076:
1067:
1063:
1058:
1056:
1053:
1052:
1032:
1028:
1019:
1015:
1010:
1008:
1005:
1004:
984:
980:
971:
967:
965:
962:
961:
941:
937:
927:
923:
914:
910:
908:
905:
904:
884:
880:
871:
867:
862:
860:
857:
856:
833:
831:
828:
827:
811:
809:
806:
805:
789:
787:
784:
783:
762:
758:
756:
753:
752:
735:
731:
729:
726:
725:
701:
698:
697:
665:
662:
661:
639:
635:
630:
624:
620:
605:
601:
592:
588:
587:
577:
573:
564:
560:
555:
554:
552:
535:
531:
522:
518:
513:
512:
502:
498:
489:
485:
480:
479:
477:
463:
459:
449:
445:
436:
432:
430:
427:
426:
421:
392:
389:
388:
369:
366:
365:
343:
340:
339:
322:
318:
316:
313:
312:
291:
287:
285:
282:
281:
272:lies along the
257:
255:
252:
251:
231:
227:
225:
222:
221:
204:
200:
198:
195:
194:
191:computer vision
158:
154:
144:
140:
131:
127:
125:
122:
121:
93:
90:
89:
72:
68:
66:
63:
62:
45:
41:
39:
36:
35:
28:
23:
22:
15:
12:
11:
5:
3207:
3197:
3196:
3194:Remote sensing
3191:
3186:
3181:
3176:
3162:
3161:
3155:
3154:
3125:
3119:
3102:
3096:
3077:
3074:
3072:
3071:
3028:
3001:
2986:
2955:
2943:
2925:
2915:
2899:
2882:
2870:
2850:
2840:
2831:
2802:Shirley, Peter
2792:
2773:(3): 227–251.
2757:
2734:
2721:(3): 301–316.
2701:
2666:
2651:
2625:
2604:(6): 311–317.
2584:
2567:
2560:
2524:
2510:
2490:
2469:
2444:
2405:
2390:
2352:
2337:
2318:(7): 767–775.
2312:Applied Optics
2301:
2299:
2296:
2295:
2294:
2289:
2284:
2279:
2274:
2269:
2264:
2259:
2254:
2247:
2244:
2243:
2242:
2235:
2224:
2202:
2201:
2198:
2187:
2184:
2175:
2172:
2151:
2148:
2147:
2146:
2143:
2140:
2137:
2134:
2131:
2128:
2122:
2116:
2110:
2107:
2101:
2095:
2089:
2083:
2075:
2072:
2066:
2065:
2060:
2053:
2052:
2048:
2041:
2040:
2036:
2029:
2028:
2027:
2026:
2025:
2021:
2020:
2013:
2006:
2003:
1998:accommodating
1979:
1976:
1968:remote sensing
1920:
1917:
1916:
1915:
1904:
1901:
1892:
1888:
1878:
1873:
1870:
1866:
1857:
1852:
1843:
1839:
1830:
1824:
1820:
1815:
1806:
1802:
1791:
1780:
1771:
1766:
1757:
1753:
1744:
1740:
1737:
1728:
1723:
1714:
1710:
1701:
1685:
1674:
1671:
1668:
1659:
1654:
1645:
1641:
1632:
1615:
1612:
1599:
1590:
1585:
1576:
1571:
1568:
1565:
1556:
1529:
1525:
1516:
1495:
1492:
1489:
1480:
1475:
1466:
1461:
1452:
1447:
1438:
1434:
1425:
1400:
1391:
1386:
1377:
1372:
1363:
1358:
1349:
1345:
1336:
1300:
1291:
1286:
1276:
1270:
1261:
1256:
1246:
1241:
1238:
1216:Apparent BRDFs
1187:
1166:
1162:
1157:
1148:
1143:
1134:
1130:
1121:
1104:
1101:
1088:
1079:
1075:
1066:
1061:
1040:
1031:
1027:
1018:
1013:
992:
983:
979:
970:
949:
940:
935:
926:
922:
913:
892:
883:
879:
870:
865:
792:
780:surface normal
761:
734:
705:
694:projected-area
669:
638:
633:
623:
619:
616:
613:
604:
600:
591:
585:
576:
572:
563:
558:
550:
543:
534:
530:
521:
516:
510:
501:
497:
488:
483:
475:
471:
462:
457:
448:
444:
435:
420:
417:
396:
373:
347:
321:
290:
280:exiting along
260:
249:surface normal
230:
203:
166:
157:
152:
143:
139:
130:
97:
71:
44:
26:
9:
6:
4:
3:
2:
3206:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3171:
3169:
3160:
3157:
3156:
3151:
3147:
3143:
3139:
3135:
3131:
3126:
3122:
3116:
3112:
3108:
3103:
3099:
3093:
3089:
3085:
3080:
3079:
3067:
3063:
3059:
3055:
3051:
3047:
3043:
3039:
3032:
3024:
3020:
3016:
3012:
3005:
2997:
2993:
2989:
2987:9781605587264
2983:
2979:
2975:
2968:
2967:
2959:
2953:
2947:
2941:
2937:
2934:
2929:
2919:
2913:
2909:
2903:
2895:
2894:
2886:
2880:
2874:
2867:
2863:
2860:
2854:
2844:
2835:
2827:
2823:
2819:
2815:
2811:
2807:
2803:
2796:
2788:
2784:
2780:
2776:
2772:
2768:
2761:
2753:
2749:
2745:
2738:
2729:
2724:
2720:
2716:
2712:
2705:
2697:
2693:
2689:
2685:
2681:
2677:
2670:
2662:
2658:
2654:
2652:9781450373555
2648:
2644:
2640:
2636:
2629:
2621:
2617:
2612:
2607:
2603:
2599:
2595:
2588:
2577:
2571:
2563:
2557:
2553:
2549:
2545:
2541:
2537:
2536:
2528:
2520:
2514:
2507:
2503:
2500:
2494:
2480:
2473:
2458:
2454:
2453:"BRDF/Albedo"
2448:
2440:
2436:
2432:
2428:
2424:
2420:
2416:
2409:
2401:
2397:
2393:
2387:
2383:
2379:
2372:
2371:
2363:
2356:
2348:
2341:
2333:
2329:
2325:
2321:
2317:
2313:
2306:
2302:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2268:
2265:
2263:
2260:
2258:
2255:
2253:
2250:
2249:
2239:
2236:
2232:
2228:
2225:
2219:
2213:
2211:
2207:
2206:
2205:
2199:
2196:
2192:
2188:
2185:
2182:
2181:
2180:
2171:
2167:
2165:
2160:
2157:
2144:
2141:
2138:
2135:
2132:
2129:
2126:
2123:
2120:
2117:
2114:
2111:
2108:
2105:
2102:
2099:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2077:
2074:Some examples
2057:
2045:
2033:
2024:
2018:
2014:
2011:
2007:
2004:
2001:
1997:
1996:
1995:
1993:
1989:
1985:
1975:
1973:
1969:
1964:
1962:
1958:
1954:
1950:
1946:
1942:
1938:
1934:
1930:
1926:
1902:
1899:
1890:
1886:
1876:
1871:
1868:
1855:
1850:
1841:
1828:
1818:
1813:
1804:
1792:
1769:
1764:
1755:
1742:
1738:
1726:
1721:
1712:
1699:
1690:
1686:
1672:
1669:
1657:
1652:
1643:
1630:
1621:
1620:
1619:
1611:
1588:
1583:
1574:
1569:
1566:
1554:
1527:
1523:
1514:
1493:
1490:
1478:
1473:
1464:
1459:
1450:
1445:
1436:
1423:
1414:
1389:
1384:
1375:
1370:
1361:
1356:
1347:
1334:
1325:
1321:
1317:
1312:
1289:
1284:
1268:
1259:
1254:
1236:
1228:
1224:
1219:
1217:
1213:
1209:
1205:
1200:
1155:
1146:
1141:
1132:
1119:
1110:
1100:
1077:
1064:
1029:
1016:
981:
968:
938:
933:
924:
911:
881:
868:
854:
853:differentials
849:
781:
759:
732:
723:
719:
703:
695:
691:
687:
683:
667:
658:
636:
621:
617:
614:
602:
589:
574:
561:
548:
532:
519:
499:
486:
473:
460:
455:
446:
433:
424:
416:
414:
410:
394:
387:
371:
364:
363:azimuth angle
361:
345:
319:
310:
288:
279:
275:
250:
228:
201:
192:
188:
184:
180:
155:
150:
141:
128:
119:
115:
95:
69:
42:
32:
19:
3174:3D rendering
3136:(1): 27–42.
3133:
3129:
3106:
3087:
3086:. Volume I:
3083:
3041:
3037:
3031:
3014:
3010:
3004:
2965:
2958:
2946:
2928:
2918:
2902:
2892:
2885:
2873:
2853:
2843:
2834:
2812:(2): 25–32.
2809:
2805:
2795:
2770:
2766:
2760:
2743:
2737:
2718:
2714:
2704:
2679:
2675:
2669:
2634:
2628:
2601:
2597:
2587:
2570:
2534:
2527:
2513:
2493:
2482:. Retrieved
2472:
2460:. Retrieved
2456:
2447:
2422:
2418:
2408:
2369:
2355:
2346:
2340:
2315:
2311:
2305:
2237:
2226:
2208:
2203:
2177:
2168:
2161:
2153:
2022:
1981:
1965:
1922:
1919:Applications
1622:positivity:
1617:
1506:except when
1324:luminescence
1313:
1222:
1220:
1215:
1203:
1201:
1108:
1106:
850:
804:. The index
722:surface area
721:
659:
425:
422:
386:zenith angle
273:
117:
113:
111:
3044:(4): 1–12.
2282:Reflectance
2150:Acquisition
2000:anisotropic
1953:solar cells
1925:radiometric
1320:iridescence
690:solid-angle
413:solid angle
3189:Radiometry
3168:Categories
3017:(5): 1–9.
2484:2007-09-05
2298:References
2277:Radiometry
2231:halftoning
2195:halftoning
2191:microfacet
2164:HDR images
2119:Ward model
2002:reflection
1316:wavelength
1003:, whereas
718:irradiance
419:Definition
409:steradians
358:is itself
309:irradiance
120:), symbol
3058:0730-0301
2212:the BRDF:
2142:ABg model
1963:systems.
1943:for many
1900:≤
1891:ω
1877:θ
1872:
1856:ω
1842:ω
1823:Ω
1819:∫
1805:ω
1801:∀
1770:ω
1756:ω
1727:ω
1713:ω
1670:≥
1658:ω
1644:ω
1589:ω
1575:ω
1567:λ
1528:λ
1515:λ
1479:ω
1465:λ
1451:ω
1437:λ
1390:ω
1376:λ
1362:ω
1348:λ
1290:ω
1260:ω
1147:ω
1133:ω
1078:ω
1030:ω
982:ω
939:ω
925:ω
882:ω
760:ω
733:θ
688:per unit
637:ω
622:θ
618:
603:ω
575:ω
533:ω
500:ω
461:ω
447:ω
395:θ
372:ϕ
346:ω
320:ω
289:ω
229:ω
202:ω
156:ω
142:ω
70:ω
43:ω
2996:13932018
2936:Archived
2862:Archived
2826:18520447
2502:Archived
2462:March 9,
2439:40828010
2400:32127698
2246:See also
1947:such as
1687:obeying
1177:, where
778:and the
682:radiance
278:radiance
3138:Bibcode
3066:4960068
2787:2367943
2684:Bibcode
2661:8043767
2620:1439868
2540:Bibcode
2320:Bibcode
2210:Milling
2037:Diffuse
307:to the
3184:Optics
3117:
3094:
3064:
3056:
2994:
2984:
2923:Vienna
2824:
2785:
2659:
2649:
2618:
2558:
2437:
2398:
2388:
2252:Albedo
2061:Mirror
2049:Glossy
1978:Models
1972:albedo
1413:linear
1227:BSSRDF
724:, and
660:where
183:optics
179:opaque
3062:S2CID
2992:S2CID
2970:(PDF)
2848:1997.
2822:S2CID
2783:S2CID
2657:S2CID
2616:S2CID
2579:(PDF)
2435:S2CID
2396:S2CID
2374:(PDF)
2365:(PDF)
686:power
684:, or
3115:ISBN
3092:ISBN
3054:ISSN
2982:ISBN
2647:ISBN
2556:ISBN
2464:2017
2386:ISBN
2257:BSDF
1986:and
1931:for
1221:The
1202:The
1107:The
384:and
118:BRDF
112:The
18:BRDF
3146:doi
3134:103
3046:doi
3019:doi
2974:doi
2908:doi
2814:doi
2775:doi
2748:doi
2723:doi
2692:doi
2639:doi
2606:doi
2548:doi
2427:doi
2378:doi
2328:doi
1869:cos
1322:or
1208:BTF
716:is
680:is
615:cos
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2990:.
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