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11 The Radiosity method

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					     Chapter11
The Radiosity method




       안상진
    11 - The Radiosity method
• 11.1 Radiosity theory
• 11.2 Form factor determination
• 11.3 The Gauss-Siedel method
• 11.4 Seeing a partial solution-
  progressive refinement
• 11.5 Problems with the radiosity images
• 11.6 Artefacts in radiosity images
• 11.7 Meshing strategies
            Introduction
• Ray tracing – models one aspect of the
  light interaction
• Consider room with walls and ceiling
  painted with a matte material and
  carpeted.
• Radiosity(1984)- Render scenes is
  made up in their entirety of (perpect)
  diffuse surfaces(patches).
             Introduction
• Each patch reflects light received from
  every other patch in the environment
• The interaction between patches
  depends on their geometric
  relationship(distance and orientation)
• Cost vs Quality
• Deals with shadows well
• Object space algorithm – independent
  of viewer position
   11.1 Radiosity theory
• Assumption – perfect diffuse reflections
• Radiosity B
 – the energy per unit area leaving a surface
   patch per unit time
 - sum of the emitted and the reflected energy


    Bi dAi  Ei dAi  Ri  B j F ji dAi
                                          B: radiosity
                                          E: emitted energy
                             j
                       n                  A: area
       Bi  Ei  Ri  B j Fij             R: reflectivity
                      j 1                F: form factor
 11.1 Radiosity theory

 1  R1 F11  R1 F12     ...   R1 F1n   B1   E1 
 R F       1  R2 F22                   B  E 
                          ...  R2 F2 n   2   2 
      2 21
                                                 
     :           :       ...      :      :  : 
                                           
  Rn Fn1      Rn Fn 2   ... 1  Rn Fnn   Bn   E n 

• Solving this equation is the radiosity method
• R : known , wavelength-dependent
• F : the function of the geometry of the environment
• Any row of the form factors is 1.
11.1 Radiosity theory




           1           cos i cos j
     Fij 
           Ai   
                AiAj       r   2
                                       dA j dAi
    11.2 Form factor determination
                  cos i cos j                         1         cos i cos j
                                                             
      1
Fij                            dA j dAi   FdAiAj                              dA j
      Ai   AiAj       r   2
                                                        Ai   Aj       r   2




                   hemisphere                         hemicube
  11.2 Form factor determination
• Pixel form factor

                             cos  i cos  j
               FdAiAj                         A  AFq
                                   r   2

• form factor : sum of the pixel form factors
11.2 Form factor determination




    The state of a hemicube placed on the window
11.2 Form factor determination


                                             Form factor
                                             is calculated
                                             only once




                                             Bilinear
                                             interpolation




   Stages in a complete radiosity solution
11.3 The Gauss-Siedel method


 Jacobi iteration




Gauss-Siedel
method



                    Converge to (2,4,3)
   11.4 Seeing a partial solution-progressive refinement




• Progressive refinement enables a designer to
  see an early (but approximate) solution
• Cost factors: storage costs, calculation of the
  form factors.
• Progressive refinement & elemination of pre-
  calculation and storage of the form factors
         require reconstruction of radiosity Alg.
                            n
              Bi  Ei  Ri  B j Fij
                            j 1
11.4 Seeing a partial solution-progressive refinement

              n
Bi  Ei  Ri  B j Fij
              j 1
  11.4 Seeing a partial solution-progressive refinement




• Convergence optimizing
   – by sorting patches according to the
    amount of energy

• Progress from dark scene
    - adding ambient light
  11.5 Problems with the radiosity images



• Problems with the radiosity rendering
  -algorithm artefacts that appear in the
    image
  -The inability to deal with specular
    interaction
  -The inordinate time taken to render a
    scene of moderate complexity
    11.6 Artefacts in radiosity images


• Approximation in the hemicube method
  for determining the form factors
• Using bilinear interpolation as a
  reconstruction of the radiosity function
  from the constant radiosity solution
• Using a meshing or subdivision of the
  scene that is indefendent of the nature
  of the variations in the radiosity function
      11.6.1 Hemicube Artefacts




-aliasing
-inter-patch distance : at least five patch diameters.
-problem with insufficient subdivision of area light source
             11.6.1 Hemicube Artefacts




-The hemicube evaluates a form factor from a differential area
-Intervening patches may be missed
11.6.2
Reconstruction     Mach bands
artefacts


                 -Using Texture
                  mapping
                 -Subdivision
                  meshing
                  strategies
                 -Surface
                  interpolation
                  methods
11.6.3 Meshing Artefacts
11.6.3 Meshing Artefacts
            11.7 Meshing strategies




(1)A priori
      – by prediction
(2)A posterior
      - adaptive
meshing
          11.7.1 Adaptive or a posterior meshing
•Subdivision – if radiosity variation at the nodes or vertices exceeds some theshold
11.7.1 Adaptive or a posterior meshing
11.7.1 Adaptive or a posterior meshing
  11.7.1 Adaptive or a posterior meshing




• Adaptive subdivision
  in progressive
  refinement method
  can lead to
  unnessary subdivisions
11.7.2 A priori meshing
11.7.2 A priori meshing
11.7.2 A priori meshing
11.7.2 A priori meshing
            11.7.2 A priori meshing




D1 discontinuity                D2 discontinuity
11.7.2 A priori meshing
11.7.2 A priori meshing
11.7.2 A priori meshing
11.7.2 A priori meshing

				
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