Light

Intensity calculation = wavelength I( ) = wavelength intensity of light reaching eye I( ) = I diff ( ) + I spec ( ) + I refl ( ) + I trans ( ) + I amb ( ). I diff ( ) = diffuse component of I( ) I spec ( ) = specular component of I( ) I refl ( ) = reflected light component of I( ) I trans ( ) = transmitted light component of I( ) I amb ( ) = ambient component of I( )

Diffuse reflection I diff ( ) = diffuse component of I( ). I diff ( ) = k diff  j S j I Lj ( ) F diff ( ) (N L j ). k diff = diffuse reflectance coefficient; S j = light j shadow coefficient (0 = shadow; 1= no shadow); I Lj ( ) = intensity of light j; F diff ( ) = diffuse reflection curve (object color); N = surface normal; L j = light direction for light j.

Specular reflection I spec ( ) = specular component of I( ). I spec ( ) = k spec  j S j I Lj ( ) F spec ( ) (N H j ) f. k spec = specular reflectance coefficient; S j = light j shadow coefficient (0 = shadow; 1= no shadow); I Lj ( ) = intensity of light j; F spec ( ) = specular reflection curve (white); f = specular exponent; N = surface normal; H j = vector halfway between viewing direction and light. H j = where V and L j are the viewing and light directions.

Ambient light I amb ( ) = ambient component of I( ). I amb ( ) = k amb E a ( ) F amb ( ). k amb = ambient coefficient; E a ( ) = ambient light intensity of environment; F amb ( ) = ambient reflection curve (usually F amb ( ) = F diff ( )).

Reflection from other surfaces I refl ( ) = reflected light component of I( ). I refl ( ) = k spec I(R*, ) F spec ( ) A(|R*|). k spec = specular reflectance coefficient; I(R*, ) = intensity of wavelength in reflection ray R*; F spec ( ) = 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 I trans ( ) = transmitted light component of I( ). I trans ( ) = k trans I(T*, ) F spec ( ) A(|T*|). k trans = transparency coefficient (0 = opaque; 1 = transparent); I(T*, ) = intensity of wavelength in transmitted ray T*; F spec ( ) = 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 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) + ((  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: 1.33; Fused quartz: 1.46.

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

Fresnel term F(,  ) = Fresnel term. where: c = cos(  ) = L j  H j ; g 2 =  2 + c 2 – 1;  = index of refraction at wavelength. When  = 0:

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