Iluminação local MC-930 Tópicos em Computação Gráfica Luiz M. G. Gonçalves

Iluminação local Estudo de como os diferentes nmateriais refletem luz Optica –Geometrica (yes:-) –Ondas (not in this class) Como a BRDF f r encapsula as propriedades de reflectância de um material

Terms Flux – Power of light energy passing through a surface per unit time, measured in watts = joules/sec Irradiance (E) – Incoming power (flux) per unit area (W/m 2 ) Radiosity (B) – Outgoing power (flux) per unit area (W/m 2 )

Hemisphere Use a hemisphere over surface to measure incoming/outgoing flux Measured using the solid angle Unit is steradian (sr) = area of r 2 on sphere Area of sphere = 4 r 2 Number of steradians in a hemisphere = 2 r

Diminuindo (Foreshortening) Light arriving on a surface at an angle is distributed differently, d 1 =d 2 but dA 1 dA 2 dA 1 = dA 2 cos 2 Intensity (I) – Power (flux) per unit solid angle (W/sr) Irradiance is the foreshortened incident intensity E i = I i cos i d i d 1 d 2 d 1 d 2

The Reflectivity Measures the portion of incident irradiance (E i ) that is reflected as intensity (I r ) = dI r /dE i The reflected intensity is the forshortened incident intensity scaled by the reflectivity I r = I i cos i d i Ranges from 0 to 1 (conservation of energy)

Radiance Radiance (L) – Power per unit solid angle per unit foreshortened area (W/(sr m 2 )) Radiance is the intensity per area forshortened L = dI/(dA cos ) Or the irradiance per solid angle forshortened L = dE/(d cos )

The Bidirectional Reflectance Distribution Function (BRDF) Measures the portion of incident irradiance (E i ) that is reflected as radiance (L r ) f r = dL r /dE i Ranges from 0 to

Parameterizations 6-D BRDF f r ( i, i, r, r, u, v) –Incident direction i, i –Reflected direction r, r –Surface parameterization u,v 4-D BRDF f r ( i, i, r, r ) –Homogeneous material –Anisotropic, depends on incoming azimuth –e.g. hair, brushed metal, ornaments 3-D BRDF f r ( i, r, i – r ) –Isotropic, independent of incoming azimuth –e.g. Phong highlight 1-D BRDF f r ( i ) –Perfectly diffuse –e.g. Lambertian

BRDF Attributes Reciprocity f r ( i, i, r, r ) = f r ( r, r, i, i ) –Materials are not a one-way street –Incoming to outgoing pathway same as outgoing to incoming pathway Conservation of Energy –When integrated, must add to less than one –Materials must not add energy –Materials must absorb some amount of energy

Modeling BRDFs Mathematical derivation –Use laws of physics, geometry –Statistical model of idealized material Simulation –Model material directly –Render light reflected onto hemisphere Measurement –Reflect real light off of real material –Gonioreflectometer

Illumination via Reflectivity I r = k a a I a (N L) + k d d I d + k s s I s ) (N L) d Constants k d + k s = 1 Intensities –I a = average color of reflected light in scene –I d = color of material –I s = color of light source Reflectivities –Constant: a = 1/ (N L) –Lambertian: d = 1 –Phong: s = (V R) n / (N L)

Iluminação usando a BRDF Equação de reflectância radiância refletida é –a soma da radiância incidente sobre todo o hemisfério –diminuída –escalada pela função BRDF

Reflexão difusa d = (N L) Uniforme –Envia mesma quantidade de luz em todas as direções –Quantidade depende do ângulo de incidência Perfeita –toda luz incidente é refletida –não há absorção