Bidirectional reflectance distribution function

<p>The bidirectional reflectance distribution function (BRDF), symbol 
  
    
      
        
          f
          
            r
          
        
        (
        
          ω
          
            i
          
        
        ,
        
        
          ω
          
            r
          
        
        )
      
    
    {\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}
  
, is a function of four real variables that defines how light from a source is reflected off an <a href="/facts/Opacity_(optics)/l90q0sAV">opaque</a> surface. It is employed in the <a href="/facts/Optics/p0vq4S1T">optics</a> of real-world light, in <a href="/facts/Computer_graphics/lapBE8wv">computer graphics</a> algorithms, and in <a href="/facts/Computer_vision/Tl2Yyk66">computer vision</a> algorithms. The function takes an incoming light direction, 
  
    
      
        
          ω
          
            i
          
        
      
    
    {\displaystyle \omega _{\text{i}}}
  
, and outgoing direction, 
  
    
      
        
          ω
          
            r
          
        
      
    
    {\displaystyle \omega _{\text{r}}}
  
 (taken in a coordinate system where the <a href="/facts/Normal_(geometry)/jhtLIhcu">surface normal</a> 
  
    
      
        
          n
        
      
    
    {\displaystyle \mathbf {n} }
  
 lies along the <i>z</i>-axis), and returns the ratio of reflected <a href="/facts/Radiance/5kS1FhpD">radiance</a> exiting along 
  
    
      
        
          ω
          
            r
          
        
      
    
    {\displaystyle \omega _{\text{r}}}
  
 to the <a href="/facts/Irradiance/fgHwu7uh">irradiance</a> incident on the surface from direction 
  
    
      
        
          ω
          
            i
          
        
      
    
    {\displaystyle \omega _{\text{i}}}
  
. Each direction 
  
    
      
        ω
      
    
    {\displaystyle \omega }
  
 is itself <a href="/facts/Spherical_coordinate_system/5cVnNof3">parameterized by</a> <a href="/facts/Azimuth_angle/kEyt9nJ3">azimuth angle</a> 
  
    
      
        ϕ
      
    
    {\displaystyle \phi }
  
 and <a href="/facts/Zenith_angle/tcm21e6t">zenith angle</a> 
  
    
      
        θ
      
    
    {\displaystyle \theta }
  
, therefore the BRDF as a whole is a function of  4 variables. The BRDF has units sr−1, with <a href="/facts/Steradian/PRCqT4n1">steradians</a> (sr) being a unit of <a href="/facts/Solid_angle/se8IXufg">solid angle</a>.
</p>

Bidirectional reflectance distribution function open-in-new

Bidirectional reflectance distribution function