Reflectance Models

Reflectance Models CS 319 Advanced Topics in Computer Graphics John C. Hart

N Local Illum. Context H (R) (S) S R • Surface point (x) and normal (N) • Light source (S, not L) • Vector from x to light “source” • Dir. incident radiance Li = L(S) comes from (like wind direction) • View vector (V) • Direction from x to “viewer” • Reflected radiance Lr = L(V) dir. • Reflection vector (R) R = 2(N S)N – S • Halfway vector (H) H = (V+S)/||V+S|| V x All vectors are unit length

Some Spec(tac)ular Hacks • Decompose BRDF  diffuse+specular Lr = (fd + fs(S,V)) LiN S • Phong: fs = ks max(V R,0)n / (N S) • Blinn: fs = ks max(N H,0)n / (N S) • Blinn n = 4 Phong n • Not based on anyphysical model • Not bidirectional Phong, n=11 Blinn, n=11 Blinn, n=11 Phong, n=11 Blinn, n=44 Blinn, n=44

Cook-Torrance Torrance-Sparrowmicrofacet model • Based on Torrance-Sparrow model • Physically plausible • Bidirectional, energy conserving • Models specular BRDF component • Fh(S,V) – Fresnel term • Dm(N,H) – Roughness term • G(N,S,V) – Geometry term • Denominator counteracts foreshortening but retains bidirectionality Fh(S,V)Dm(N,H)G(N,S,V)

Fresnel Effect sheen • % of light reflected increases as “halfway incidence angle” qh increases • Normal N of rough surface not well defined, so need H instead • S and V nearly constant across surface • Fresnel effect independent of N • Nearly constant across surface • Affects color of reflected light • Normal incidencesurface color • Tangent incidencelight color • Photographic trick: place brightlight behind subject to create a Fresnel outline of features/profile pigment H S qh qh V

Fresnel Term H S qh qh V • Fresnel term F controls portion of light reflected v. portion refracted (1 – F) • Physically accurate Fresnel function • Parameterized by index of refraction h • where c = S H and g2 =2 + c2 – 1 • Schlick’s hack Fs(S,V) = F0 + (1 – F0)(1 – S H)5 • Parameter h implicit in F0 • F0 = Specular reflectance at normalincidence (S H = 1) qt cos qh = S H = V H But how do we find  ? Fs(cos qr) F0 F(cos qr) qh

Roughness Term small mbig m • Statistical model of light reflectance • Roughness m = RMS of slope • Blinn’s hack Dm,c(N,H) = c exp(–a2 / m2) • Angle a = cos-1(NH)  [0,p/2] • Arbitrary scale c • Creates BRDF bulge at R • Beckman’s distribution function • Bulge in BRDF diffuses around R D/c m=½ m=1 m=2 a D m=½ m=2 m=1 a

Blinn v. Beckman S m=½ m=1 m=2 Blinn Beckman

Geometry Term • Shadowing • Incident light does not reach material Gs(N,S,V) = 2(NH)(NS)/(SH) • Masking • Reflected light does not reach viewer Gm(N,S,V) = 2(NH)(NV)/(VH) • Geometry term = shadow AND mask G(N,S,V) = min{Gs(N,S,V), Gm(N,S,V), 1} • Clamp to one to keep demoninators in check x S Gs Gm G

Cook-Torrance Demo All: h=2 SV=1 SV=.707 SV=0 SV= -.707 m=½ m=2 (brighter light)

Seeliger Skin • Model for diffuse reflectance from skin • Softer appearance than Lambertian • Used as a basis for subsurface scattering in volumetric skin models • See Hanrahan & Krueger S93 Lambert Seeliger

Hair • From Kajiya & Kay S88 • Anisotropic • Uses tangent vector T • Diffuse anisotropic fd = sin(T,S) • Specular anisotropic fs = ((TS) (TV) + sin(T,S) sin(T,V))n S S T sin(A,B) = sqrt(1-(AB)2) Chang, Jin &Yu, 2001

Hair Examples diffuse spec., n=1 spec., n=8 diff+spec

Fur • Goldman S97 • Scattering of light by fur • Dihedral angle between hair-light plane and hair-view plane • Opacity is an inverted Gaussian

Fur Examples scattering opacity fake fur

Reflectance Models