Reflection Model (BRDF/BTF/BSSRDF)

Reflection Model

Bidirectioanl Reflectance Distribution Function (BRDF)

Lambertian Refrection Model
Phong Refrection Model
Blinn-Phong Reflection Model
Cook-Torrance Refrection Model
Oren-Nayer Reflection Model
Torrance-Sparrow Model
Bidirectional Texture Function (BTF)

Bidirectional Subsurface Reflectance Distribution Function (BSSRDF)

BRDF

$$
f(\theta_i, \phi_i, \theta_r, \phi_r)=\frac{L(\theta_r, \phi_r)}{E(\theta_i, \phi_i)}
$$

$f(\theta_i, \phi_i, \theta_r, \phi_r)$ is BRDF which showing reflectance from incoming direction $\theta_i, \phi_i)$ to outgoing direction $\theta_r, \phi_r)$.

$L(\theta_r, \phi_r)$ is the radiance in the outgoing direction $\theta_r, \phi_r)$.

$E(\theta_i, \phi_i)$ is the irradiance from the incident direction $(\theta_i, \phi_i)$.

BSSRDF

Outgoing radiance equation:
$$
dL_o (x_o , \vec{\omega_o})=S(x_i, \vec{\omega_i} ; x_o, \vec{\omega_o})d\mathbf{\Phi_i}(x_i, \vec{\omega_i})
$$

Integrating the incident radiance over incoming direction and area:
$$
dL_o (x_o , \vec{\omega_o})=
\int_{A} \int_{2\pi}
S(x_i, \vec{\omega_i} ; x_o, \vec{\omega_o})L_i(x_i, \vec{\omega_i})
\, \, d\omega_i dA(x_i)
$$
where $A$ is the area and $2\pi$ is the incident light flux from hemisphere.