Computer Graphics. - BRDFs & Texturing - Hendrik Lensch. Computer Graphics WS07/08 BRDFs and Texturing

Transcription

1 Cmputer Graphcs - BRDFs & Texturng - Hendrk Lensch Cmputer Graphcs WS07/08 BRDFs and Texturng

2 Overvew Last tme Radance Lght surces Renderng Equatn & Frmal Slutns Tday Bdrectnal Reflectance Dstrbutn Functn BRDF Reflectn mdels Prjectn nt sphercal bass functns Shadng Next lecture Varyng reflectn prpertes ver bject surface: texturng Cmputer Graphcs WS07/08 BRDFs and Texturng

3 Cmputer Graphcs WS07/08 BRDFs and Texturng Reflectn Equatn - Reflectance Reflectn equatn BRDF Rat f reflected radance t ncdent rradance Ω + = r ω d θ x L x f x L cs ω ω ω ω r x de x dl x f ω ω ω ω =

4 Bdrectnal Reflectance Dstrbutn Functn BRDF descrbes surface reflectn fr lght ncdent frm drectn θ φ bserved frm drectn θ ο φ ο Bdrectnal Depends n tw drectns and pstn 6-D functn Dstrbutn functn Can be nfnte Unt [1/sr] f r ω x ω = = dl x ω de x ω dl x ω dl x ω csθ dω Cmputer Graphcs WS07/08 BRDFs and Texturng

5 BRDF Prpertes Helmhltz recprcty prncple BRDF remans unchanged f ncdent and reflected drectns are nterchanged f r ω ω = fr ω ω Smth surface: strpc BRDF reflectvty ndependent f rtatn arund surface nrmal BRDF has nly 3 nstead f 4 drectnal degrees f freedm f r x θ θ ϕ ϕ Cmputer Graphcs WS07/08 BRDFs and Texturng

6 BRDF Prpertes Characterstcs BRDF unts [sr --1 ] Nt ntutve Range f values: Frm 0 absrptn t reflectn δ -functn Energy cnservatn law N self-emssn Pssble absrptn Ω f r ω x ω csθ dω 1 θ ϕ Reflectn nly at the pnt f entry x = x N subsurface scatterng Cmputer Graphcs WS07/08 BRDFs and Texturng

7 BRDF Measurement Gn-Reflectmeter BRDF measurement pnt lght surce pstn θϕ lght detectr pstn θ ϕ 4 drectnal degrees f freedm BRDF representatn m ncdent drectn samples θϕ n utgng drectn samples θ ϕ m*n reflectance values large!!! Stanfrd lght gantry Cmputer Graphcs WS07/08 BRDFs and Texturng

8 Reflectance Reflectance may vary wth Illumnatn angle Vewng angle Wavelength Plarzatn... Varatns due t Absrptn Surface mcr-gemetry Index f refractn / delectrc cnstant Scatterng Alumnum; λ=2.0μm Alumnum; λ=0.5μm Cmputer Graphcs WS07/08 BRDFs and Texturng Magnesum; λ=0.5μm

9 BRDF Mdelng Phenmenlgcal apprach Descrptn f vsual surface appearance Ideal specular reflectn Reflectn law Mrrr Glssy reflectn Drectnal dffuse Shny surfaces Ideal dffuse reflectn Lambert s law Matte surfaces Cmputer Graphcs WS07/08 BRDFs and Texturng

10 Reflectn Gemetry Drectn vectrs nrmalze: N: surface nrmal I: vectr t the lght surce V: vewpnt drectn vectr H: halfway vectr H= I + V / I + V RI: reflectn vectr RI= I -2I NN Tangental surface: lcal plane -I NN I N I RI -I NN RV Tp vew RV I N H RI V I H N V RI Cmputer Graphcs WS07/08 BRDFs and Texturng

11 Ideal Specular Reflectn Angle f reflectance equal t angle f ncdence Reflected vectr n a plane wth ncdent ray and surface nrmal vectr R+-I = 2 csθ N = -2I N N RI = I -2I N N I N R I θ θ ϕ ϕ θ = θ ϕ = ϕ Cmputer Graphcs WS07/08 BRDFs and Texturng

12 Cmputer Graphcs WS07/08 BRDFs and Texturng Mrrr BRDF Drac Delta functn δx δx : zer everywhere except at x=0 Unt ntegral ff ntegratn dman cntans zer zer therwse Specular reflectance ρ s Rat f reflected radance n specular drectn and ncmng radance Dmensnless quantty between 0 and 1 cs cs cs cs π ϕ θ θ ρ ω θ ϕ θ ω ω ω π ϕ ϕ δ θ θ θ δ θ ρ ω ω ± = = ± = Ω + s m r s m r L d L x f x L x f L N R θ θ s θ Φ θ Φ = θ ρ

13 Cmputer Graphcs WS07/08 BRDFs and Texturng Dffuse Reflectn Lght equally lkely t be reflected n any utput drectn ndependent f nput drectn Cnstant BRDF k d : dffuse ceffcent materal prperty [1/sr] E k d x L k d x L k x L k x f d d d d d r = = = = = Ω Ω ω θ ω ω θ ω ω ω ω cs cs cnst N I L = cnst

14 Lambertan Dffuse Reflectn Radsty B Dffuse Reflectance = L x csθ dω = L Ω Ω ω csθ dω = π L B ρ = = π E d k d Lambert s Csne Law B = ρ E d = ρ E d csθ Fr each lght surce L rd = k d L csθ = k d L I N I N L rd θ Cmputer Graphcs WS07/08 BRDFs and Texturng

15 Lambertan Objects Self-Lumnus sphercal Lambertan Lght Surce Eye-lght llumnated Sphercal Lambertan Reflectr Φ 0 L 0 dω Φ 1 L 0 csϕ dω ϕ dω dω Cmputer Graphcs WS07/08 BRDFs and Texturng

16 Lambertan Objects II The Sun The Mn Absrptn n phtsphere Path length thrugh phtsphere lnger frm the Sun s rm Surface cvered wth fne dust Dust n TV vsble best frm slanted vewng angle Nether the Sun nr the Mn are Lambertan Cmputer Graphcs WS07/08 BRDFs and Texturng

17 Dffuse Reflectn Theretcal explanatn Multple scatterng Expermental realzatn Pressed magnesum xde pwder Almst never vald at hgh angles f ncdence Pant manufacturers attempt t create deal dffuse pants Cmputer Graphcs WS07/08 BRDFs and Texturng

18 Glssy Reflectn Cmputer Graphcs WS07/08 BRDFs and Texturng

19 Glssy Reflectn Due t surface rughness Emprcal mdels Phng Blnn-Phng Physcal mdels Blnn Ck & Trrance Cmputer Graphcs WS07/08 BRDFs and Texturng

20 Phng Reflectn Mdel Csne pwer lbe f r ω x ω s k R I V e = k L rs = L k s cs ke θ RV Dt prduct & pwer Nt energy cnservng/recprcal Plastc-lke appearance I N θ HN H RI θ RV I RV N RI V H V Cmputer Graphcs WS07/08 BRDFs and Texturng

21 Phng Expnent k e f r ω x ω Determnes sze f hghlght s k R I V e = k Cmputer Graphcs WS07/08 BRDFs and Texturng

22 Blnn-Phng Reflectn Mdel Blnn-Phng reflectn mdel f r ω x ω = k s k H N e L rs = L k s cs ke θ HN θ RV θ HN Lght surce vewer far away I R cnstant: H cnstant θ HN less expensve t cmpute I N θ HN H RI θ RV I RV N RI V H V Cmputer Graphcs WS07/08 BRDFs and Texturng

23 Cmputer Graphcs WS07/08 BRDFs and Texturng Phng Illumnatn Mdel Extended lght surces: l pnt lght surces Clr f specular reflectn equal t lght surce Heurstc mdel Cntradcts physcs Purely lcal llumnatn Only drect lght frm the lght surces N further reflectn n ther surfaces Cnstant ambent term Often: lght surces & vewer assumed t be far away Blnn L Phng L r r + + = + + = l k l l l s l l d a a l k l l l s l l d a a e e N H L k N I L k L k V I R L k N I L k L k

24 Mcrfacet Mdel Istrpc mcrfacet cllectn Mcrfacets assumed as perfectly smth reflectrs BRDF Dstrbutn f mcrfacets Often prbablstc dstrbutn f rentatn r V-grve assumptn Planar reflectn prpertes Self-maskng shadwng Cmputer Graphcs WS07/08 BRDFs and Texturng

25 Ward Reflectn Mdel BRDF f r = ρ π d + ρ s I 1 N V N 2 2 exp tan H N / σ 2 4πσ σ standard devatn RMS f surface slpe Smple expansn t anstrpc mdel σ x σ y Emprcal nt physcs-based Inspred by ntn f reflectng mcrfacets Cnvncng results Gd match t measured data N vewer V H θ I surface mcrfacet Cmputer Graphcs WS07/08 BRDFs and Texturng

26 Physcs-nspred BRDFs Ntn f reflectng mcrfacet Specular reflectvty f the frm f r = D G F λ θ π N V λ D : statstcal mcrfacet dstrbutn G : gemetrc attenuatn self-shadwng F : Fresnel term wavelength angle dependency f reflectn alng mrrr drectn N V : flarng effect at lw angle f ncdence Ck-Trrance mdel F : wavelength- and angle-dependent reflectn Metal surfaces Cmputer Graphcs WS07/08 BRDFs and Texturng

27 Ck-Trrance Reflectn Mdel Ck-Trrance reflectance mdel s based n the mcrfacet mdel. The BRDF s defned as the sum f a dffuse and specular cmpnents: f r = kdρd + ksρs; kd + ks 1 where k s and k d are the specular and dffuse ceffcents. Dervatn f the specular cmpnent ρ s s based n a physcally derved theretcal reflectance mdel Cmputer Graphcs WS07/08 BRDFs and Texturng

28 Ck-Trrance Specular Term ρ s Fλ DG = π N V N I N vewer V H θ I surface mcrfacet D : Dstrbutn functn f mcrfacet rentatns G : Gemetrcal attenuatn factr represents self-maskng and shadwng effects f mcrfacets F λ : Fresnel term F cmputed by Fresnel equatn λ 1+ V N relates ncdent lght t reflected lght fr each planar mcrfacet N V : Prprtnal t vsble surface area N I : Prprtnal t llumnated surface area λ Cmputer Graphcs WS07/08 BRDFs and Texturng

29 Mcrfacet Dstrbutn Functns Istrpc Dstrbutns D ω D α α = N H α : angle t average nrmal f surface Characterzed by half-angle β 1 D β = 2 Blnn Trrance-Sparrw D α = cs α D α = e ln 2 lncs β 2 α β 2 vewer surface V N H θ I mcrfacet Beckmann m : average slpe f the mcrfacets Used by Ck-Trrance D 1 m [ tanα / ] α = e 2 4m 2 cs 4 α Cmputer Graphcs WS07/08 BRDFs and Texturng

30 Beckman Mcrfacet Dstrbutn Functn m=0.2 m=0.6 Cmputer Graphcs WS07/08 BRDFs and Texturng

31 Gemetrc Attenuatn Factr V-shaped grves Fully llumnated and vsble G =1 Partal maskng f reflected lght G 2 N H N = V H V Partal shadwng f ncdent lght G = 2 N H N V H I G = mn 1 2 N H N V H V 2 N H N V H I Cmputer Graphcs WS07/08 BRDFs and Texturng

32 Cmparsn Phng vs. Trrance Cmputer Graphcs WS07/08 BRDFs and Texturng

33 Cmputer Graphcs WS07/08 BRDFs and Texturng Texturng

34 Smple Illumnatn N llumnatn Cnstant clrs Parallel lght Dffuse reflectn Cmputer Graphcs WS07/08 BRDFs and Texturng

35 Standard Illumnatn Parallel lght Specular reflectn Multple lcal lght surces Dfferent BRDFs Object prpertes cnstant ver surface Cmputer Graphcs WS07/08 BRDFs and Texturng

36 Texturng Lcally varyng bject characterstcs 2D Image Textures Shadws Bump-Mappng Reflectn textures Cmputer Graphcs WS07/08 BRDFs and Texturng

37 Texture-mdulated Quanttes Mdulatn f bject surface prpertes Reflectance Clr RGB dffuse reflectn ceffcent kd Specular reflectn ceffcent ks Opacty α Nrmal vectr NP= NP+ t N r N= N+dN Bump mappng r Nrmal mappng Gemetry P= P + dp Dsplacement mappng Dstant llumnatn Envrnment mappng Reflectn mappng Cmputer Graphcs WS07/08 BRDFs and Texturng

38 Texture Mappng Transfrmatns Texture Space 2-D Object Space 3-D Image Space 2-D Texture-Surface Transfrmatn Vewng/Prjectn Transfrmatn The texture s mapped nt a surface n 3-D bject space whch s then mapped t the screen by the vewng prjectn. These tw mappngs are cmpsed t fnd the verall 2-D texture space t 2-D mage space mappng and the ntermedate 3-D space s ften frgtten. Ths smplfcatn suggests texture mappng s clse tes wth mage warpng and gemetrc dstrtn. Texture space uv Object space x y z Screen space xy Cmputer Graphcs WS07/08 BRDFs and Texturng

39 2D Texturng 2D texture mapped nt bject Object prjected nt 2D screen 2D 2D: warpng peratn Unfrm samplng? Hle-fllng/blendng? Cmputer Graphcs WS07/08 BRDFs and Texturng

40 Texture Mappng n a Ray Tracer apprxmatn: ray hts surface surface lcatn crrespnds t crdnate nsde a texture Cmputer Graphcs WS07/08 BRDFs and Texturng

41 Texture Mappng n a Ray Tracer apprxmatn: ray hts surface surface lcatn crrespnds t crdnate nsde a texture Cmputer Graphcs WS07/08 BRDFs and Texturng

42 Interplatn 1D c3 c2 c0 c1 Hw t nterplate the clr f the pxel? Cmputer Graphcs WS07/08 BRDFs and Texturng

43 Interplatn 1D c3 c0 1-s s c2 c1 Hw t nterplate the clr f the pxel? Cmputer Graphcs WS07/08 BRDFs and Texturng

44 Interplatn 2D c3 c0 1-s s c2 c1 Hw t nterplate the clr f the pxel? Cmputer Graphcs WS07/08 BRDFs and Texturng

45 Interplatn 2D c3 c0 s t 1-t 1-s c2 c1 Hw t nterplate the clr f the pxel? 1D: 0 = 1-tc0 + tc1 1 = 1-tc3 + tc2 2D: c = 1-s 0 + s 1 Cmputer Graphcs WS07/08 BRDFs and Texturng