Radiosity _1_

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					Global Illumination (2)
    Radiosity (4)
                 Next
• We have the form factors
• How do we find the radiosity
  solution for the scene?
  – The "Full Matrix" Radiosity Algorithm
  – Gathering & Shooting
  – Progressive Radiosity
• Meshing
Classic Radiosity Algorithm


 Mesh Surfaces into Elements



   Compute Form Factors
     Between Elements



    Solve Linear System
      for Radiosities



      Reconstruct and
      Display Solution
Recall The Radiosity Equation


                     Bi  Ei  i  B j Fij
                                                    Form Factor of surface j
 Radiosity of surface i                             relative to surface i

 Emissivity of surface i         Radiosity of surface j


 Reflectivity of surface i
                                                            accounts for the
                                                            physical
                                                            relationship
                                                            between the two
                                               Surface j    surfaces
 will absorb a certain
 percentage of light
 energy which strikes
 the surface
                                   Surface i
Radiosity Matrix                                              Ei


                         n
Bi Ai  Ei Ai   i  F ji B j A j           Bi
                         j 1
Ai Fij  A j F ji
                     n
   Bi  Ei   i  Fij B j
                     j 1
              n
   Bi   i  Fij B j  Ei
              j 1


           1  1 F11  1 F12         1 F1n   B1   E1 
            F       1   2 F22      2 F2 n   B2   E2 
                2 21                                  
                                                   
                                                     
              n Fn1   n Fn 2     1   n Fnn   Bn   En 
                  Radiosity Matrix
• The "full matrix" radiosity solution calculates the form
  factors between each pair of surfaces in the
  environment, then forms a series of simultaneous linear
  equations.

      1  1 F11  1 F12         1 F1n   B1   E1 
       F       1   2 F22      2 F2 n   B2   E2 
           2 21                                  
                                              
                                                
         n Fn1   n Fn 2     1   n Fnn   Bn   En 

• This matrix equation is solved for the "B" values, which
  can be used as the final intensity (or color) value of
  each surface.
                 Radiosity Matrix
• This method produces a complete solution, at the
  substantial cost of
   – first calculating form factors between each pair of surfaces
   – and then the solution of the matrix equation.

• Each of these steps can be quite expensive if the
  number of surfaces is large: complex environments
  typically have upwards of ten thousand surfaces, and
  environments with one million surfaces are not
  uncommon.

• This leads to substantial costs not only in computation
  time but in storage.
                 Next
• We have the form factors
• How do we find the radiosity
  solution for the scene?
  – The "Full Matrix" Radiosity Algorithm
  – Gathering & Shooting
  – Progressive Radiosity
• Meshing
                Solve [F][B] = [E]
• Direct methods: O(n3)

   – Gaussian elimination
      • Goral, Torrance, Greenberg, Battaile, 1984

• Iterative methods: O(n2)

   Energy conservation
      ¨diagonally dominant ¨  iteration converges

   – Gauss-Seidel, Jacobi: Gathering
      • Nishita, Nakamae, 1985
      • Cohen, Greenberg, 1985

   – Southwell: Shooting
      • Cohen, Chen, Wallace, Greenberg, 1988
  Gathering
• In a sense, the light
  leaving patch i is
  determined by
  gathering in the light
  from the rest of the
  environment
                n
 Bi  Ei   i  B j Fij
                             Bi  Ei    i Fij B j
                                         n
               j 1
                                        j 1
Bi due to B j  i B j Fij
   Gathering

• Gathering light through
  a hemi-cube allows
  one patch radiosity to
  be updated.



                            Bi  Ei    i Fij B j
                                        n


                                       j 1
Gathering
Successive Approximation
    Shooting
• Shooting light through a
  single hemi-cube allows
  the whole environment's
  radiosity values to be
  updated simultaneously.



               For all j       B j  B j  Bi  j E ji 

                                              Fij Ai
                             where   F ji 
                                               Aj
Shooting
Progressive Radiosity
Classic Radiosity Algorithm


 Mesh Surfaces into Elements



   Compute Form Factors
     Between Elements



    Solve Linear System
      for Radiosities



      Reconstruct and
      Display Solution

				
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posted:9/29/2012
language:English
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