Local Illumination. Outline. The Big Picture. Radiometry. Radiometry. Radiometry. hc λ Φ = Introduction Radiometry Reflectance Reflectance Models

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1 Loca Iumato Oute Itoucto Raomety Refectace Refectace Moe The Bg Pctue Raomety Eegy of a photo hc 34 8 e = h J c 3 10 m / λ λ Raat Eegy of photo Q = Raato fux (eectomagetc fux, aat fux) Ut: Watt Q Φ = t hc = 1 λ Raomety Raace aat fux pe ut o age pe ut pojecte aea Numbe of photo avg pe tme at a ma aea fom a patcua ecto Φ ω) = co A ω Watt Ut : mete teaa Raomety Iaace ffeeta fux fag oto ffeeta aea Φ Watt E = Ut : A mete Iaace ca be ee a a ety of the cet fux fag oto a uface. It ca be ao obtae by tegatg the aace ove the o age.

2 Lght Emo Oute Lght ouce: u, fe, ght bub etc. Coe a pot ght ouce that emt ght ufomy a ecto Φ co Φ L= Φ powe of the ght ouce E= Itoucto Raomety Refectace Refectace Moe tace to the ght ouce Suface Refecto & Refectace Refectace Refecto - the poce by whch eectomagetc fux cet o a uface eave the uface wthout a chage fequecy. Bectoa catteg-uface tbuto Fucto (BSSRDF) Refectace a facto of the cet fux that efecte Souce: Jee et.a 01 We o ot coe: abopto, tamo, fuoecece ffacto Suface Refectace Refectace Bectoa catteg-uface tbuto Fucto (BSSRDF) L (, φ, x, y ) S (, φ,, φ, x, y, x, y ) = Φ (, φ, x, y ) 1 Bectoa Refectace Dtbuto Fucto (BRDF) Ut : mete teaa f (, φ,, φ ) = L (, φ ) E (, φ ) Ut : L L φ 1 teaa φ Suface

3 Iotopc BRDF Aotopc BRDF Rotato aog uface oma oe ot chage efectace Suface wth togy oete mcogeomety eemet Exampe: f (,, φ φ ) = f (,, φ ) = L (, φ ) E (, φ ) L buhe meta, ha, fu, coth, vevet L φ Souce: Wet et.a 9 Popete of BRDF How to compute efecte aace? No-egatvty f (, φ,, φ ) 0 Cotuou veo L (ω ) = f (ω, ω )E (ω ) = Eegy Coevato Ω f (, φ,, φ )µ (, φ ) 1 fo a (, φ ) Ω = f (ω, ω ) L (ω ) co(ω ) ω ω = (, φ ) Ω Recpocty f (, φ,, φ ) = f (, φ,, φ ) Dcete veo pot ght ouce L (ω ) = f (ωj, ω )E j = j =1 Φ j j =1 j = f (ωj, ω ) co j Oute How o we obta BRDF? Itoucto Raomety Refectace Refectace Moe Meaue BRDF vaue ecty Aaytc Refectace Moe Souce: Geg Wa Phycay-bae moe bae o aw o phyc Empca moe a hoc fomua that wok 3

4 Iea Dffue Refectace Aume uface efect equay a ecto. A ea ffue uface, at the mcocopc eve, a vey ough uface. Exampe: chak, cay, ome pat Iea Dffue Refectace BRDF vaue cotat L ( ω ) = = f Ω = f E Ω E ( ω ) = f ( ω, ω ) E ( ω ) = B = Aco B Suface A Suface Iea Dffue Refectace Iea ffue efecto efect ght accog to Lambet' coe aw. Iea Dffue Refectace Sge Pot Lght Souce k : The ffue efecto coeffcet. : Suface oma. : Lght ecto. Φ ω ) = k ( ) Suface Iea Dffue Refectace Moe Deta If a ae facg away fom each othe, become egatve. Ug max( ( ),0 ) make ue that the eut zeo. Fom ow o, we mea max() whe we wte. Do ot foget to omaze you vecto fo the ot pouct! Iea Specua Refectace Refecto oy at mo age. Vew epeet Mcocopc uface eemet ae uuay oete the ame ecto a the uface tef. Exampe: mo, hghy pohe meta. Suface

5 Iea Specua Refectace Speca cae of Se Law The comg ay, the uface oma, a the efecte ay a e a commo pae. No-ea Refecto Se aw appe oy to ea mo efecto. Rea matea te to evate gfcaty fom ea mo efecto. They ae ot ea ffue uface ethe Suface = = = No-ea Refecto Smpe Empca Moe: We expect mot of the efecte ght to tave the ecto of the ea ay. Howeve, becaue of mcocopc uface vaato we mght expect ome of the ght to be efecte jut ghty offet fom the ea efecte ay. A we move fathe a fathe, the agua ee, fom the efecte ay we expect to ee e ght efecte. The Phog Moe How much ght efecte? Depe o the age betwee the ea efecto ecto a the vewe ecto α. Camea v α Suface The Phog Moe Paamete k : pecua efecto coeffcet q : pecua efecto expoet ω ) = k (coα) = k ( ) v q Φ The Phog Moe Effect of the q coeffcet Camea v α Suface

6 The Phog Moe B-Toace Vaato + = co = ( ) ω ) = k ( v ) = = k ( v (( ) )) Suface Ue the hafway vecto h betwee a v. + v h = + v ω ) = k (co β ) = k ( ) h h β Camea v Suface q Φ Phog Exampe The foowg phee utate pecua efecto a the ecto of the ght ouce a the coeffcet of he vae. The Phog Moe Sum of thee compoet: ffue efecto + pecua efecto + ambet. Phog B-Toace Suface Ambet Iumato Repeet the efecto of a ect umato. Th a tota hack! Avo the compexty of goba umato. Puttg t a togethe Phog Iumato Moe ω ) = ka + ( k ( ) + k ( v ) ) L (ω ) = k a

7 Fo Agmet 3 Vaato o Phog Iumato Moe q L ( ω ) = k La + ( k ( ) + k ( v ) ) L Ag coo Dffue coeffcet: k -e, k -gee, k -bue Specua coeffcet: k -e, k -gee, k -bue Specua expoet: q Phog Demo Fee Refecto Iceag pecuaty ea gazg age. Souce: Lafotue et a. 97 Off-pecua & Reto-efecto Off-pecua efecto Peak ot cetee at the efecto ecto Reto-efecto: Refecto the ecto of cet umato Exampe: Moo, oa makg The Phog Moe I t o-egatve? I t eegy-coevg? I t ecpoca? I t otopc?

8 Shae (Matea ca) Queto? Fucto execute whe ght teact wth a uface Cotucto: et hae paamete Iput: Icet aace Icet & efecte ght ecto uface taget (aotopc hae oy) Output: Refecte aace