Light Intensity calculation wavelength I wavelength intensity of

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Light

Intensity calculation = wavelength I( ) = wavelength intensity of light reaching eye I(

Intensity calculation = wavelength I( ) = wavelength intensity of light reaching eye I( ) = Idiff( ) + Ispec( ) + Irefl( ) + Itrans( ) + Iamb( ). Idiff( ) = diffuse component of I( ) Ispec( ) = specular component of I( ) Irefl( ) = reflected light component of I( ) Itrans( ) = transmitted light component of I( ) Iamb( ) = ambient component of I( )

Diffuse reflection Idiff( ) = diffuse component of I( ). Idiff( ) = kdiff

Diffuse reflection Idiff( ) = diffuse component of I( ). Idiff( ) = kdiff j Sj ILj( ) Fdiff( ) (N • Lj). kdiff = diffuse reflectance coefficient; Sj = light j shadow coefficient (0 = shadow; 1= no shadow); ILj( ) = intensity of light j; Fdiff( ) = diffuse reflection curve (object color); N = surface normal; Lj = light direction for light j.

Specular reflection Ispec( ) = specular component of I( ). Ispec( ) = kspec

Specular reflection Ispec( ) = specular component of I( ). Ispec( ) = kspec j Sj ILj( ) Fspec( ) (N • Hj)f. kspec = specular reflectance coefficient; Sj = light j shadow coefficient (0 = shadow; 1= no shadow); ILj( ) = intensity of light j; Fspec( ) = specular reflection curve (white); f = specular exponent; N = surface normal; Hj = vector halfway between viewing direction and light. Hj = where V and Lj are the viewing and light directions.

Ambient light Iamb( ) = ambient component of I( ). Iamb( ) = kamb

Ambient light Iamb( ) = ambient component of I( ). Iamb( ) = kamb Ea( ) Famb( ). kamb = ambient coefficient; Ea( ) = ambient light intensity of environment; Famb( ) = ambient reflection curve (usually Famb( ) = Fdiff( )).

Reflection from other surfaces Irefl( ) = reflected light component of I( ). Irefl(

Reflection from other surfaces Irefl( ) = reflected light component of I( ). Irefl( ) = kspec I(R*, ) Fspec( ) A(|R*|). kspec = specular reflectance coefficient; I(R*, ) = intensity of wavelength in reflection ray R*; Fspec( ) = specular reflection curve (usually white); A(|R*|) = distance attenuation of reflection ray R*; R* = reflection ray; |R*| = length of reflection ray R*; R = reflection direction. R = –V + 2 (N • V) N where N and V are the normal and view directions.

Transmitted light Itrans( ) = transmitted light component of I( ). Itrans( ) =

Transmitted light Itrans( ) = transmitted light component of I( ). Itrans( ) = ktrans I(T*, ) Fspec( ) A(|T*|). ktrans = transparency coefficient (0 = opaque; 1 = transparent); I(T*, ) = intensity of wavelength in transmitted ray T*; Fspec( ) = specular reflection curve (usually white); A(|T*|) = distance attenuation of transmitted ray T*; T* = transmitted ray; |T*| = length of reflection ray T*; T = transmitted ray direction. T = ( 1/ 2)(–V) + (( 1/ 2)cos( 1) – cos( 2)) N.

Snell’s Law N = normal direction; V = view direction; T = transmitted ray

Snell’s Law N = normal direction; V = view direction; T = transmitted ray direction; 1 = refraction index for material 1 (V and N point to material 1); 2 = refraction index for material 2 (T points to material 2); 1 = angle of incidence (cos( 1) = N V); 2 = angle of refraction (cos( 2) = (–N) T). Snell’s law:

Transmitted ray direction T = transmitted ray direction. T = ( 1/ 2)(–V) +

Transmitted ray direction T = transmitted ray direction. T = ( 1/ 2)(–V) + (( 1/ 2)cos( 1) – cos( 2)) N = ( 1/ 2)(–V) + (( 1/ 2)(N V) – cos( 2)) N. where: N = normal direction; V = view direction; 1 = refraction index for material 1 (V and N point to material 1); 2 = refraction index for material 2 (T points to material 2); 1 = angle of incidence; 2 = angle of refraction. cos( 2) =

Refraction Index Vacuum: 1; Glass (crown): 1. 52; Glass (dense flint): 1. 66; Water:

Refraction Index Vacuum: 1; Glass (crown): 1. 52; Glass (dense flint): 1. 66; Water: 1. 33; Fused quartz: 1. 46.

Cook-Torrance lighting model Ispec( ) = specular component of I( ). Ispec( ) =

Cook-Torrance lighting model Ispec( ) = specular component of I( ). Ispec( ) = F( , ) = Fresnel term; = half of angle between V and Lj = angle between Hj and Lj; D(m, ) = density of microfacets in direction Hj; = angle between Hj and N; m = surface roughness (between 0 and 1); G(N, V, Lj) = masking and shadowing term; V = viewing direction; Lj = light direction for light j; N = surface normal; Hj = vector halfway between V and Lj.

Fresnel term F( , ) = Fresnel term. where: c = cos( ) =

Fresnel term F( , ) = Fresnel term. where: c = cos( ) = Lj Hj; g 2 = 2 + c 2 – 1; = index of refraction at wavelength . When = 0:

Density and masking terms D(m, ) = density of microfacets in direction Hj. m

Density and masking terms D(m, ) = density of microfacets in direction Hj. m = surface roughness (between 0 and 1. ) G(N, V, Lj) = masking and shadowing term.