2159:
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.
645:
1959:, 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
417:
2148:
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.
2021:
2045:
2033:
20:
2207:
640:{\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}}}}}
1902:
2203:
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
2158:
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
2229:
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
2222:
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
2147:
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.
1778:
1493:
1398:
1298:
2836:
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
2083:, 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.
2167:
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:
1785:
1164:
1597:
2911:
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,
1672:
947:
164:
1199:) 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
1086:
1038:
890:
1533:
1683:
990:
2056:
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.
1407:
1318:
2998:
Matusik, Wojciech; Ajdin, Boris; Gu, Jinwei; Lawrence, Jason; Lensch, Hendrik P. A.; Pellacini, Fabio; Rusinkiewicz, Szymon (2009-12-01). "Printing spatially-varying reflectance".
1221:
3117:
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".
765:
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325:
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234:
207:
75:
48:
1186:
791:
259:
2827:
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.
835:
813:
2404:"Photovoltaic System Performance Enhancement with Nontracking Planar Concentrators: Experimental Results and Bidirectional Reflectance Function (BDRF)-Based Modeling"
394:
345:
1897:{\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}
371:
2245:
1215:
703:
667:
95:
1103:
2940:
2110:, a specular-microfacet model with an elliptical-Gaussian distribution function dependent on surface tangent orientation (in addition to surface normal).
1538:
1614:
3107:
3084:
2548:
2378:
895:
112:
2952:
Weyrich, Tim; Peers, Pieter; Matusik, Wojciech; Rusinkiewicz, Szymon (2009). "Fabricating microgeometry for custom surface reflectance".
2507:
2974:
2639:
2334:
Duvenhage, Bernardt (2013). "Numerical verification of bidirectional reflectance distribution functions for physical plausibility".
2351:"Photovoltaic system performance enhancement with non-tracking planar concentrators: Experimental results and BDRF based modelling"
2490:
2350:
2125:
Fitted
Lafortune model, a generalization of Phong with multiple specular lobes, and intended for parametric fits of measured data.
1043:
995:
847:
3167:
2850:
1498:
1196:
2092:
2012:
W. Matusik et al. found that interpolating between measured samples produced realistic results and was easy to understand.
1773:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})=f_{\text{r}}(\omega _{\text{r}},\,\omega _{\text{i}})}
1921:
2924:
2113:
2953:
2119:
Ashikhmin–Shirley model, allowing for anisotropic reflectance, along with a diffuse substrate under a specular surface.
2223:
affects their final appearance, as a result this novel method can help us print images even more realistically.
1535:: that is, it will only emit light at wavelength equal to the incoming light. In this case it can be parameterized as
952:
348:
2357:
2941:
https://www.photonicsspectra-digital.com/photonicsspectra/september 2020/MobilePagedReplica.action?pm=2&folio=56
2275:
2155:. The standard algorithm is to measure the BRDF point cloud from images and optimize it by one of the BRDF models.
2152:
1488:{\displaystyle f_{\text{r}}(\lambda _{\text{i}},\,\omega _{\text{i}},\,\lambda _{\text{r}},\,\omega _{\text{r}})=0}
841:
2098:
Torrance–Sparrow model, a general model representing surfaces as distributions of perfectly specular microfacets.
1393:{\displaystyle f_{\text{r}}(\lambda _{\text{i}},\,\omega _{\text{i}},\,\lambda _{\text{r}},\,\omega _{\text{r}})}
844:
and not directly as a quotient between the undifferentiated quantities, is because irradiating light other than
1293:{\displaystyle S(\mathbf {x} _{\text{i}},\,\omega _{\text{i}},\,\mathbf {x} _{\text{r}},\,\omega _{\text{r}})}
2867:
2754:
Nayar, S. K.; Oren, M. (1995). "Generalization of the
Lambertian Model and Implications for Machine Vision".
3182:
2095:, resembling Phong, but allowing for certain quantities to be interpolated, reducing computational overhead.
1307:
of light has been ignored. In reality, the BRDF is wavelength dependent, and to account for effects such as
2336:
Proceedings of the South
African Institute for Computer Scientists and Information Technologists Conference
2260:
2086:
1980:
1972:
1971:
BRDFs can be measured directly from real objects using calibrated cameras and lightsources; however, many
3162:
3147:
2068:
1677:
1200:
743:
716:
303:
272:
212:
185:
53:
26:
3025:
Lan, Yanxiang; Dong, Yue; Pellacini, Fabio; Tong, Xin (2013-07-01). "Bi-scale appearance fabrication".
3126:
2672:
2528:
2308:
3177:
2218:
In order to generate spatially varying BRDF (svBRDF) it has been proposed to use gamut mapping and
2198:
2116:, a "directed-diffuse" microfacet model, with perfectly diffuse (rather than specular) microfacets.
2104:, a specular-microfacet model (Torrance–Sparrow) accounting for wavelength and thus color shifting.
2189:
Optimize the continuity and smoothness of the surface with respect to the manufacturing procedure.
1169:
774:
242:
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2810:
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2423:
2384:
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2250:
2144:
2107:
2005:
1949:
1937:
1925:
2663:
Torrance, K.; Sparrow, E. (1967). "Theory for Off-Specular
Reflection from Roughened Surfaces".
2101:
818:
796:
166:, is a function of four real variables that defines how light from a source is reflected off an
1607:
Physically realistic BRDFs for reciprocal linear optics have additional properties, including,
3103:
3080:
3042:
2970:
2635:
2544:
2467:
2374:
1998:
1983:
model frequently assumed in computer graphics. Some useful features of recent models include:
1917:
237:
175:
379:
330:
3134:
3034:
3007:
2962:
2896:
2895:
Church E., Takacs P., Leonard T., The prediction of BSDFs from surface profile measurements
2802:
2763:
2736:
2711:
2680:
2627:
2594:
2536:
2415:
2366:
2316:
2255:
2080:
167:
396:, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr, with
356:
3172:
3099:
2928:
2854:
2494:
2074:
1945:
1933:
1929:
674:
179:
1300:
in which light entering the surface may scatter internally and exit at another location.
3130:
2676:
2624:
Proceedings of the 4th annual conference on
Computer graphics and interactive techniques
2532:
2312:
16:
Function of four real variables that defines how light is reflected at an opaque surface
2880:
2622:
James F. Blinn (1977). "Models of light reflection for computer synthesized pictures".
2487:
2299:
Nicodemus, Fred (1965). "Directional reflectance and emissivity of an opaque surface".
1976:
1956:
768:
688:
682:
652:
80:
3156:
2790:
2564:
1401:
351:
2984:
2848:
Image-based modelling of material reflective properties of flat objects (In
Russian)
2814:
2427:
2388:
1159:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}},\,\mathbf {x} )}
3054:
2806:
2775:
2649:
2608:
2193:
Many approaches have been proposed for manufacturing the BRDF of the target :
1312:
374:
2847:
2419:
2270:
2122:
HTSG (He, Torrance, Sillion, Greenberg), a comprehensive physically based model.
1988:
1913:
1592:{\displaystyle f_{\text{r}}(\lambda ,\,\omega _{\text{i}},\,\omega _{\text{r}})}
1308:
1203:. The functions defined by the BTF at each point on the surface are thus called
678:
401:
2522:
23:
Diagram showing vectors used to define the BRDF. All vectors are unit length.
3138:
2939:
Eckhardt S, Lunda K., Digital Age Sees New Demand for the Venerable Conoscope
2921:
2370:
2265:
2179:
1941:
1304:
706:
297:
3046:
2540:
2441:
412:
The BRDF was first defined by Fred Nicodemus around 1965. The definition is:
3038:
3011:
2966:
2175:
Sample this distribution to discretize it and make the fabrication feasible.
397:
2684:
1667:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})\geq 0}
2740:
2731:
Ward, Gregory J. (1992). "Measuring and modeling anisotropic reflection".
2716:
2699:
2631:
2599:
2582:
2210:
The final BRDF is the aggregated effect of the geometry and ink selection.
2020:
19:
2219:
2183:
670:
266:
2320:
2206:
2044:
2032:
2767:
2486:
Wojciech Matusik, Hanspeter Pfister, Matt Brand, and Leonard McMillan.
3148:
An intuitive introduction to the concept of reflection model and BRDF.
2900:
2240:
2071:, representing perfectly diffuse (matte) surfaces by a constant BRDF.
1960:
942:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}
171:
159:{\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}
2403:
2882:
A Study of Scattering Characteristics for Microscale Rough Surface
2205:
1212:
Bidirectional Surface Scattering Reflectance Distribution Function
949:, might illuminate the surface which would unintentionally affect
18:
1098:
Spatially Varying Bidirectional Reflectance Distribution Function
1400:. Note that in the typical case where all optical elements are
2402:
Andrews, Rob W.; Pollard, Andrew; Pearce, Joshua M. (2015).
2349:
Andrews, Rob W.; Pollard, Andrew; Pearce, Joshua M. (2013).
2089:, a phenomenological model akin to plastic-like specularity.
1081:{\displaystyle \mathrm {d} E_{\text{i}}(\omega _{\text{i}})}
1033:{\displaystyle \mathrm {d} L_{\text{r}}(\omega _{\text{r}})}
885:{\displaystyle \mathrm {d} E_{\text{i}}(\omega _{\text{i}})}
182:
algorithms. The function takes an incoming light direction,
2359:
2013 IEEE 39th Photovoltaic Specialists Conference (PVSC)
1940:. BRDF has also been used for modeling light trapping in
2178:
Design a geometry that produces this distribution (with
840:
The reason the function is defined as a quotient of two
2885:(Master's thesis). Rose-Hulman Institute of Technology.
2527:(2 ed.). Cambridge University Press. p. 323.
2468:"A Survey of BRDF Representation for Computer Graphics"
2172:
Measuring or synthesizing the target BRDF distribution.
1528:{\displaystyle \lambda _{\text{i}}=\lambda _{\text{r}}}
2151:
There is an alternative way to measure BRDF based on
2128:
Lebedev model for analytical-grid BRDF approximation.
1994:
editable using a small number of intuitive parameters
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2961:. New York, New York, USA: ACM Press. pp. 1–6.
2868:
Approximated Scatter Models for Stray Light Analysis
1315:
the dependence on wavelength must be made explicit:
2846:Ilyin A., Lebedev A., Sinyavsky V., Ignatenko, A.,
1218:), is a further generalized 8-dimensional function
2565:"Fundamentals of the Planetary Spectrum Generator"
1896:
1772:
1666:
1591:
1527:
1487:
1392:
1292:
1188:describes a 2D location over an object's surface.
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69:
42:
2524:Theory of Reflectance and Emittance Spectroscopy
985:{\displaystyle L_{\text{r}}(\omega _{\text{r}})}
2143:Traditionally, BRDF measurement devices called
103:bidirectional reflectance distribution function
2583:"Illumination for computer generated pictures"
8:
815:indicates incident light, whereas the index
2793:(2000). "An Anisotropic Phong BRDF Model".
2700:"A reflectance model for computer graphics"
2497:. ACM Transactions on Graphics. 22(3) 2002.
265:-axis), and returns the ratio of reflected
2230:design and more accurate BRDF fabrication.
1303:In all these cases, the dependence on the
2715:
2665:Journal of the Optical Society of America
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28:
3071:Lubin, Dan; Robert Massom (2006-02-10).
2857:. In: GraphiCon'2009.; 2009. p. 198-201.
2756:International Journal of Computer Vision
236:(taken in a coordinate system where the
3079:(1st ed.). Springer. p. 756.
2291:
300:incident on the surface from direction
1599:, with only one wavelength parameter.
1100:(SVBRDF) is a 6-dimensional function,
1963:depending on atmospheric scattering.
7:
3094:Matt, Pharr; Greg Humphreys (2004).
1916:concept, and accordingly is used in
681:-in-the-direction-of-a-ray per unit
77:points toward the viewer (camera).
2626:. Vol. 11. pp. 192–198.
1811:
1789:
1048:
1000:
852:
760:{\displaystyle \omega _{\text{i}}}
733:{\displaystyle \theta _{\text{i}}}
620:
545:
503:
470:
320:{\displaystyle \omega _{\text{i}}}
289:{\displaystyle \omega _{\text{r}}}
229:{\displaystyle \omega _{\text{r}}}
202:{\displaystyle \omega _{\text{i}}}
70:{\displaystyle \omega _{\text{r}}}
43:{\displaystyle \omega _{\text{i}}}
14:
2446:NASA, Goddard Space Flight Center
1979:have been proposed including the
2227:Combination of Ink and Geometry:
2043:
2031:
2019:
1263:
1233:
1174:
1149:
779:
247:
50:points toward the light source.
2698:Cook, R.; Torrance, K. (1981).
2488:A Data-Driven Reflectance Model
2077:, lunar and Martian reflection.
892:, which are of no interest for
170:surface. It is employed in the
2807:10.1080/10867651.2000.10487522
2704:ACM SIGGRAPH Computer Graphics
1853:
1826:
1767:
1740:
1724:
1697:
1655:
1628:
1586:
1552:
1476:
1421:
1387:
1332:
1287:
1228:
1193:Bidirectional Texture Function
1153:
1117:
1075:
1062:
1027:
1014:
979:
966:
936:
909:
879:
866:
600:
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572:
559:
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517:
497:
484:
458:
431:
153:
126:
1:
3119:Remote Sensing of Environment
2508:"mental ray Layering Shaders"
2408:IEEE Journal of Photovoltaics
1924:of synthetic scenes (see the
3027:ACM Transactions on Graphics
3000:ACM Transactions on Graphics
2420:10.1109/JPHOTOV.2015.2478064
1955:In the context of satellite
1181:{\displaystyle \mathbf {x} }
786:{\displaystyle \mathbf {n} }
254:{\displaystyle \mathbf {n} }
837:indicates reflected light.
685:-perpendicular-to-the-ray,
3199:
3096:Physically Based Rendering
1912:The BRDF is a fundamental
830:{\displaystyle {\text{r}}}
808:{\displaystyle {\text{i}}}
209:, and outgoing direction,
3139:10.1016/j.rse.2006.03.002
2795:Journal of Graphics Tools
2587:Communications of the ACM
2371:10.1109/PVSC.2013.6744136
2134:K-correlation (ABC) model
1404:, the function will obey
2955:ACM SIGGRAPH 2009 papers
2541:10.1017/CBO9781139025683
1922:photorealistic rendering
174:of real-world light, in
3039:10.1145/2461912.2461989
3012:10.1145/1618452.1618474
2967:10.1145/1576246.1531338
2733:Proceedings of SIGGRAPH
2276:Schlick's approximation
2087:Phong reflectance model
1948:) or low concentration
389:{\displaystyle \theta }
340:{\displaystyle \omega }
2866:Richard N. Pfisterer,
2685:10.1364/JOSA.57.001105
2365:. pp. 0229–0234.
2261:Photometry (astronomy)
2211:
2081:Hapke scattering model
1981:Lambertian reflectance
1898:
1774:
1668:
1603:Physically based BRDFs
1593:
1529:
1489:
1394:
1294:
1182:
1160:
1082:
1034:
986:
943:
886:
831:
809:
787:
761:
734:
699:
663:
641:
390:
367:
341:
321:
290:
255:
230:
203:
160:
98:
97:is the surface normal.
91:
71:
44:
3168:Astrophysics concepts
3077:Atmosphere and Oceans
2879:Won, Yonghee (2014).
2741:10.1145/133994.134078
2717:10.1145/965161.806819
2632:10.1145/563858.563893
2600:10.1145/360825.360839
2581:Phong, B. T. (1975).
2521:Hapke, Bruce (2012).
2209:
2004:being well-suited to
1899:
1775:
1678:Helmholtz reciprocity
1669:
1594:
1530:
1490:
1395:
1295:
1201:subsurface scattering
1183:
1161:
1083:
1035:
987:
944:
887:
832:
810:
788:
762:
740:is the angle between
735:
700:
664:
642:
400:(sr) being a unit of
391:
368:
366:{\displaystyle \phi }
342:
322:
291:
256:
231:
204:
161:
92:
72:
45:
22:
3073:Polar Remote Sensing
2789:Ashikhmin, Michael;
2735:. pp. 265–272.
1786:
1684:
1615:
1539:
1499:
1408:
1319:
1222:
1170:
1104:
1044:
1040:is only affected by
996:
953:
896:
848:
819:
797:
775:
744:
717:
709:, or power per unit
689:
653:
418:
380:
357:
331:
304:
273:
243:
213:
186:
113:
81:
54:
27:
3131:2006RSEnv.103...27S
2677:1967JOSA...57.1105T
2533:2012tres.book.....H
2338:. pp. 200–208.
2321:10.1364/AO.4.000767
2313:1965ApOpt...4..767N
2204:the milled surface.
2145:gonioreflectometers
2102:Cook–Torrance model
2006:Monte Carlo methods
1782:conserving energy:
178:algorithms, and in
2927:2011-07-06 at the
2853:2011-07-06 at the
2768:10.1007/BF01679684
2493:2018-07-21 at the
2281:Specular highlight
2251:Gonioreflectometer
2216:Printing the BRDF:
2212:
1950:solar photovoltaic
1938:object recognition
1926:rendering equation
1894:
1770:
1664:
1589:
1525:
1485:
1390:
1290:
1178:
1156:
1078:
1030:
982:
939:
882:
827:
805:
783:
757:
730:
695:
659:
637:
386:
363:
337:
317:
286:
251:
226:
199:
156:
99:
87:
67:
40:
3109:978-0-12-553180-1
3086:978-3-540-43097-1
2922:BRDFRecon project
2901:10.1117/12.962842
2550:978-0-521-88349-8
2466:Rusinkiewicz, S.
2380:978-1-4799-3299-3
2093:Blinn–Phong model
2001:at grazing angles
1928:), as well as in
1918:computer graphics
1885:
1871:
1850:
1836:
1823:
1799:
1764:
1750:
1737:
1721:
1707:
1694:
1652:
1638:
1625:
1583:
1569:
1549:
1522:
1509:
1473:
1459:
1445:
1431:
1418:
1384:
1370:
1356:
1342:
1329:
1284:
1270:
1254:
1240:
1141:
1127:
1114:
1092:Related functions
1072:
1059:
1024:
1011:
976:
963:
933:
919:
906:
876:
863:
825:
803:
754:
727:
698:{\displaystyle E}
662:{\displaystyle L}
635:
631:
616:
597:
584:
569:
556:
534:
527:
514:
494:
481:
455:
441:
428:
327:. Each direction
314:
283:
223:
196:
176:computer graphics
150:
136:
123:
90:{\displaystyle n}
64:
37:
3190:
3142:
3113:
3102:. p. 1019.
3098:(1st ed.).
3090:
3059:
3058:
3022:
3016:
3015:
2995:
2989:
2988:
2960:
2949:
2943:
2937:
2931:
2919:
2913:
2909:
2903:
2893:
2887:
2886:
2876:
2870:
2864:
2858:
2844:
2838:
2834:
2828:
2825:
2819:
2818:
2786:
2780:
2779:
2751:
2745:
2744:
2728:
2722:
2721:
2719:
2695:
2689:
2688:
2671:(9): 1105–1114.
2660:
2654:
2653:
2619:
2613:
2612:
2602:
2578:
2572:
2571:
2569:
2561:
2555:
2554:
2518:
2512:
2511:
2504:
2498:
2484:
2478:
2477:
2475:
2474:
2463:
2457:
2456:
2454:
2452:
2438:
2432:
2431:
2414:(6): 1626–1635.
2399:
2393:
2392:
2364:
2355:
2346:
2340:
2339:
2331:
2325:
2324:
2296:
2256:Opposition spike
2163:BRDF fabrication
2114:Oren–Nayar model
2069:Lambertian model
2047:
2035:
2023:
1973:phenomenological
1944:(e.g. using the
1934:inverse problems
1903:
1901:
1900:
1895:
1887:
1886:
1883:
1874:
1873:
1872:
1869:
1852:
1851:
1848:
1838:
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1834:
1825:
1824:
1821:
1815:
1814:
1801:
1800:
1797:
1779:
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1762:
1752:
1751:
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1739:
1738:
1735:
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1709:
1708:
1705:
1696:
1695:
1692:
1673:
1671:
1670:
1665:
1654:
1653:
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1640:
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1636:
1627:
1626:
1623:
1598:
1596:
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1590:
1585:
1584:
1581:
1571:
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1551:
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1526:
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1520:
1511:
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1507:
1494:
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1471:
1461:
1460:
1457:
1447:
1446:
1443:
1433:
1432:
1429:
1420:
1419:
1416:
1399:
1397:
1396:
1391:
1386:
1385:
1382:
1372:
1371:
1368:
1358:
1357:
1354:
1344:
1343:
1340:
1331:
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1327:
1299:
1297:
1296:
1291:
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1285:
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1272:
1271:
1268:
1266:
1256:
1255:
1252:
1242:
1241:
1238:
1236:
1187:
1185:
1184:
1179:
1177:
1165:
1163:
1162:
1157:
1152:
1143:
1142:
1139:
1129:
1128:
1125:
1116:
1115:
1112:
1087:
1085:
1084:
1079:
1074:
1073:
1070:
1061:
1060:
1057:
1051:
1039:
1037:
1036:
1031:
1026:
1025:
1022:
1013:
1012:
1009:
1003:
991:
989:
988:
983:
978:
977:
974:
965:
964:
961:
948:
946:
945:
940:
935:
934:
931:
921:
920:
917:
908:
907:
904:
891:
889:
888:
883:
878:
877:
874:
865:
864:
861:
855:
836:
834:
833:
828:
826:
823:
814:
812:
811:
806:
804:
801:
792:
790:
789:
784:
782:
766:
764:
763:
758:
756:
755:
752:
739:
737:
736:
731:
729:
728:
725:
704:
702:
701:
696:
668:
666:
665:
660:
646:
644:
643:
638:
636:
634:
633:
632:
629:
623:
618:
617:
614:
599:
598:
595:
586:
585:
582:
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571:
570:
567:
558:
557:
554:
548:
542:
535:
533:
529:
528:
525:
516:
515:
512:
506:
500:
496:
495:
492:
483:
482:
479:
473:
467:
457:
456:
453:
443:
442:
439:
430:
429:
426:
395:
393:
392:
387:
372:
370:
369:
364:
349:parameterized by
346:
344:
343:
338:
326:
324:
323:
318:
316:
315:
312:
295:
293:
292:
287:
285:
284:
281:
260:
258:
257:
252:
250:
235:
233:
232:
227:
225:
224:
221:
208:
206:
205:
200:
198:
197:
194:
165:
163:
162:
157:
152:
151:
148:
138:
137:
134:
125:
124:
121:
96:
94:
93:
88:
76:
74:
73:
68:
66:
65:
62:
49:
47:
46:
41:
39:
38:
35:
3198:
3197:
3193:
3192:
3191:
3189:
3188:
3187:
3153:
3152:
3116:
3110:
3100:Morgan Kaufmann
3093:
3087:
3070:
3067:
3065:Further reading
3062:
3024:
3023:
3019:
2997:
2996:
2992:
2977:
2958:
2951:
2950:
2946:
2938:
2934:
2929:Wayback Machine
2920:
2916:
2910:
2906:
2894:
2890:
2878:
2877:
2873:
2865:
2861:
2855:Wayback Machine
2845:
2841:
2835:
2831:
2826:
2822:
2788:
2787:
2783:
2753:
2752:
2748:
2730:
2729:
2725:
2697:
2696:
2692:
2662:
2661:
2657:
2642:
2621:
2620:
2616:
2580:
2579:
2575:
2567:
2563:
2562:
2558:
2551:
2520:
2519:
2515:
2506:
2505:
2501:
2495:Wayback Machine
2485:
2481:
2472:
2470:
2465:
2464:
2460:
2450:
2448:
2440:
2439:
2435:
2401:
2400:
2396:
2381:
2362:
2353:
2348:
2347:
2343:
2333:
2332:
2328:
2298:
2297:
2293:
2289:
2237:
2165:
2141:
2075:Lommel–Seeliger
2065:
2060:
2059:
2058:
2057:
2053:
2052:
2051:
2048:
2040:
2039:
2036:
2028:
2027:
2024:
1999:Fresnel effects
1997:accounting for
1977:analytic models
1969:
1946:OPTOS formalism
1930:computer vision
1910:
1878:
1864:
1843:
1829:
1816:
1806:
1792:
1784:
1783:
1757:
1743:
1730:
1714:
1700:
1687:
1682:
1681:
1645:
1631:
1618:
1613:
1612:
1605:
1576:
1562:
1542:
1537:
1536:
1515:
1502:
1497:
1496:
1466:
1452:
1438:
1424:
1411:
1406:
1405:
1377:
1363:
1349:
1335:
1322:
1317:
1316:
1277:
1261:
1247:
1231:
1220:
1219:
1168:
1167:
1134:
1120:
1107:
1102:
1101:
1094:
1065:
1052:
1042:
1041:
1017:
1004:
994:
993:
969:
956:
951:
950:
926:
912:
899:
894:
893:
869:
856:
846:
845:
817:
816:
795:
794:
773:
772:
747:
742:
741:
720:
715:
714:
687:
686:
651:
650:
624:
609:
590:
577:
576:
562:
549:
543:
520:
507:
501:
487:
474:
468:
448:
434:
421:
416:
415:
410:
378:
377:
355:
354:
329:
328:
307:
302:
301:
276:
271:
270:
261:lies along the
241:
240:
216:
211:
210:
189:
184:
183:
180:computer vision
143:
129:
116:
111:
110:
79:
78:
57:
52:
51:
30:
25:
24:
17:
12:
11:
5:
3196:
3194:
3186:
3185:
3183:Remote sensing
3180:
3175:
3170:
3165:
3155:
3154:
3151:
3150:
3144:
3143:
3114:
3108:
3091:
3085:
3066:
3063:
3061:
3060:
3017:
2990:
2975:
2944:
2932:
2914:
2904:
2888:
2871:
2859:
2839:
2829:
2820:
2791:Shirley, Peter
2781:
2762:(3): 227–251.
2746:
2723:
2710:(3): 301–316.
2690:
2655:
2640:
2614:
2593:(6): 311–317.
2573:
2556:
2549:
2513:
2499:
2479:
2458:
2433:
2394:
2379:
2341:
2326:
2307:(7): 767–775.
2301:Applied Optics
2290:
2288:
2285:
2284:
2283:
2278:
2273:
2268:
2263:
2258:
2253:
2248:
2243:
2236:
2233:
2232:
2231:
2224:
2213:
2191:
2190:
2187:
2176:
2173:
2164:
2161:
2140:
2137:
2136:
2135:
2132:
2129:
2126:
2123:
2120:
2117:
2111:
2105:
2099:
2096:
2090:
2084:
2078:
2072:
2064:
2061:
2055:
2054:
2049:
2042:
2041:
2037:
2030:
2029:
2025:
2018:
2017:
2016:
2015:
2014:
2010:
2009:
2002:
1995:
1992:
1987:accommodating
1968:
1965:
1957:remote sensing
1909:
1906:
1905:
1904:
1893:
1890:
1881:
1877:
1867:
1862:
1859:
1855:
1846:
1841:
1832:
1828:
1819:
1813:
1809:
1804:
1795:
1791:
1780:
1769:
1760:
1755:
1746:
1742:
1733:
1729:
1726:
1717:
1712:
1703:
1699:
1690:
1674:
1663:
1660:
1657:
1648:
1643:
1634:
1630:
1621:
1604:
1601:
1588:
1579:
1574:
1565:
1560:
1557:
1554:
1545:
1518:
1514:
1505:
1484:
1481:
1478:
1469:
1464:
1455:
1450:
1441:
1436:
1427:
1423:
1414:
1389:
1380:
1375:
1366:
1361:
1352:
1347:
1338:
1334:
1325:
1289:
1280:
1275:
1265:
1259:
1250:
1245:
1235:
1230:
1227:
1205:Apparent BRDFs
1176:
1155:
1151:
1146:
1137:
1132:
1123:
1119:
1110:
1093:
1090:
1077:
1068:
1064:
1055:
1050:
1029:
1020:
1016:
1007:
1002:
981:
972:
968:
959:
938:
929:
924:
915:
911:
902:
881:
872:
868:
859:
854:
781:
769:surface normal
750:
723:
694:
683:projected-area
658:
627:
622:
612:
608:
605:
602:
593:
589:
580:
574:
565:
561:
552:
547:
539:
532:
523:
519:
510:
505:
499:
490:
486:
477:
472:
464:
460:
451:
446:
437:
433:
424:
409:
406:
385:
362:
336:
310:
279:
269:exiting along
249:
238:surface normal
219:
192:
155:
146:
141:
132:
128:
119:
86:
60:
33:
15:
13:
10:
9:
6:
4:
3:
2:
3195:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3161:
3160:
3158:
3149:
3146:
3145:
3140:
3136:
3132:
3128:
3124:
3120:
3115:
3111:
3105:
3101:
3097:
3092:
3088:
3082:
3078:
3074:
3069:
3068:
3064:
3056:
3052:
3048:
3044:
3040:
3036:
3032:
3028:
3021:
3018:
3013:
3009:
3005:
3001:
2994:
2991:
2986:
2982:
2978:
2976:9781605587264
2972:
2968:
2964:
2957:
2956:
2948:
2945:
2942:
2936:
2933:
2930:
2926:
2923:
2918:
2915:
2908:
2905:
2902:
2898:
2892:
2889:
2884:
2883:
2875:
2872:
2869:
2863:
2860:
2856:
2852:
2849:
2843:
2840:
2833:
2830:
2824:
2821:
2816:
2812:
2808:
2804:
2800:
2796:
2792:
2785:
2782:
2777:
2773:
2769:
2765:
2761:
2757:
2750:
2747:
2742:
2738:
2734:
2727:
2724:
2718:
2713:
2709:
2705:
2701:
2694:
2691:
2686:
2682:
2678:
2674:
2670:
2666:
2659:
2656:
2651:
2647:
2643:
2641:9781450373555
2637:
2633:
2629:
2625:
2618:
2615:
2610:
2606:
2601:
2596:
2592:
2588:
2584:
2577:
2574:
2566:
2560:
2557:
2552:
2546:
2542:
2538:
2534:
2530:
2526:
2525:
2517:
2514:
2509:
2503:
2500:
2496:
2492:
2489:
2483:
2480:
2469:
2462:
2459:
2447:
2443:
2442:"BRDF/Albedo"
2437:
2434:
2429:
2425:
2421:
2417:
2413:
2409:
2405:
2398:
2395:
2390:
2386:
2382:
2376:
2372:
2368:
2361:
2360:
2352:
2345:
2342:
2337:
2330:
2327:
2322:
2318:
2314:
2310:
2306:
2302:
2295:
2292:
2286:
2282:
2279:
2277:
2274:
2272:
2269:
2267:
2264:
2262:
2259:
2257:
2254:
2252:
2249:
2247:
2244:
2242:
2239:
2238:
2234:
2228:
2225:
2221:
2217:
2214:
2208:
2202:
2200:
2196:
2195:
2194:
2188:
2185:
2181:
2177:
2174:
2171:
2170:
2169:
2162:
2160:
2156:
2154:
2149:
2146:
2138:
2133:
2130:
2127:
2124:
2121:
2118:
2115:
2112:
2109:
2106:
2103:
2100:
2097:
2094:
2091:
2088:
2085:
2082:
2079:
2076:
2073:
2070:
2067:
2066:
2063:Some examples
2062:
2046:
2034:
2022:
2013:
2007:
2003:
2000:
1996:
1993:
1990:
1986:
1985:
1984:
1982:
1978:
1974:
1966:
1964:
1962:
1958:
1953:
1951:
1947:
1943:
1939:
1935:
1931:
1927:
1923:
1919:
1915:
1907:
1891:
1888:
1879:
1875:
1865:
1860:
1857:
1844:
1839:
1830:
1817:
1807:
1802:
1793:
1781:
1758:
1753:
1744:
1731:
1727:
1715:
1710:
1701:
1688:
1679:
1675:
1661:
1658:
1646:
1641:
1632:
1619:
1610:
1609:
1608:
1602:
1600:
1577:
1572:
1563:
1558:
1555:
1543:
1516:
1512:
1503:
1482:
1479:
1467:
1462:
1453:
1448:
1439:
1434:
1425:
1412:
1403:
1378:
1373:
1364:
1359:
1350:
1345:
1336:
1323:
1314:
1310:
1306:
1301:
1278:
1273:
1257:
1248:
1243:
1225:
1217:
1213:
1208:
1206:
1202:
1198:
1194:
1189:
1144:
1135:
1130:
1121:
1108:
1099:
1091:
1089:
1066:
1053:
1018:
1005:
970:
957:
927:
922:
913:
900:
870:
857:
843:
842:differentials
838:
770:
748:
721:
712:
708:
692:
684:
680:
676:
672:
656:
647:
625:
610:
606:
603:
591:
578:
563:
550:
537:
521:
508:
488:
475:
462:
449:
444:
435:
422:
413:
407:
405:
403:
399:
383:
376:
360:
353:
352:azimuth angle
350:
334:
308:
299:
277:
268:
264:
239:
217:
190:
181:
177:
173:
169:
144:
139:
130:
117:
108:
104:
84:
58:
31:
21:
3163:3D rendering
3125:(1): 27–42.
3122:
3118:
3095:
3076:
3075:. Volume I:
3072:
3030:
3026:
3020:
3003:
2999:
2993:
2954:
2947:
2935:
2917:
2907:
2891:
2881:
2874:
2862:
2842:
2832:
2823:
2801:(2): 25–32.
2798:
2794:
2784:
2759:
2755:
2749:
2732:
2726:
2707:
2703:
2693:
2668:
2664:
2658:
2623:
2617:
2590:
2586:
2576:
2559:
2523:
2516:
2502:
2482:
2471:. Retrieved
2461:
2449:. Retrieved
2445:
2436:
2411:
2407:
2397:
2358:
2344:
2335:
2329:
2304:
2300:
2294:
2226:
2215:
2197:
2192:
2166:
2157:
2150:
2142:
2011:
1970:
1954:
1911:
1908:Applications
1611:positivity:
1606:
1495:except when
1313:luminescence
1302:
1211:
1209:
1204:
1192:
1190:
1097:
1095:
839:
793:. The index
711:surface area
710:
648:
414:
411:
375:zenith angle
262:
106:
102:
100:
3033:(4): 1–12.
2271:Reflectance
2139:Acquisition
1989:anisotropic
1942:solar cells
1914:radiometric
1309:iridescence
679:solid-angle
402:solid angle
3178:Radiometry
3157:Categories
3006:(5): 1–9.
2473:2007-09-05
2287:References
2266:Radiometry
2220:halftoning
2184:halftoning
2180:microfacet
2153:HDR images
2108:Ward model
1991:reflection
1305:wavelength
992:, whereas
707:irradiance
408:Definition
398:steradians
347:is itself
298:irradiance
109:), symbol
3047:0730-0301
2201:the BRDF:
2131:ABg model
1952:systems.
1932:for many
1889:≤
1880:ω
1866:θ
1861:
1845:ω
1831:ω
1812:Ω
1808:∫
1794:ω
1790:∀
1759:ω
1745:ω
1716:ω
1702:ω
1659:≥
1647:ω
1633:ω
1578:ω
1564:ω
1556:λ
1517:λ
1504:λ
1468:ω
1454:λ
1440:ω
1426:λ
1379:ω
1365:λ
1351:ω
1337:λ
1279:ω
1249:ω
1136:ω
1122:ω
1067:ω
1019:ω
971:ω
928:ω
914:ω
871:ω
749:ω
722:θ
677:per unit
626:ω
611:θ
607:
592:ω
564:ω
522:ω
489:ω
450:ω
436:ω
384:θ
361:ϕ
335:ω
309:ω
278:ω
218:ω
191:ω
145:ω
131:ω
59:ω
32:ω
2985:13932018
2925:Archived
2851:Archived
2815:18520447
2491:Archived
2451:March 9,
2428:40828010
2389:32127698
2235:See also
1936:such as
1676:obeying
1166:, where
767:and the
671:radiance
267:radiance
3127:Bibcode
3055:4960068
2776:2367943
2673:Bibcode
2650:8043767
2609:1439868
2529:Bibcode
2309:Bibcode
2199:Milling
2026:Diffuse
296:to the
3173:Optics
3106:
3083:
3053:
3045:
2983:
2973:
2912:Vienna
2813:
2774:
2648:
2638:
2607:
2547:
2426:
2387:
2377:
2241:Albedo
2050:Mirror
2038:Glossy
1967:Models
1961:albedo
1402:linear
1216:BSSRDF
713:, and
649:where
172:optics
168:opaque
3051:S2CID
2981:S2CID
2959:(PDF)
2837:1997.
2811:S2CID
2772:S2CID
2646:S2CID
2605:S2CID
2568:(PDF)
2424:S2CID
2385:S2CID
2363:(PDF)
2354:(PDF)
675:power
673:, or
3104:ISBN
3081:ISBN
3043:ISSN
2971:ISBN
2636:ISBN
2545:ISBN
2453:2017
2375:ISBN
2246:BSDF
1975:and
1920:for
1210:The
1191:The
1096:The
373:and
107:BRDF
101:The
3135:doi
3123:103
3035:doi
3008:doi
2963:doi
2897:doi
2803:doi
2764:doi
2737:doi
2712:doi
2681:doi
2628:doi
2595:doi
2537:doi
2416:doi
2367:doi
2317:doi
1858:cos
1311:or
1197:BTF
705:is
669:is
604:cos
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3029:.
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