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THE HEMI- CUBE A RADIOSITY SOLUT

VIEWS: 14 PAGES: 11

									     THE HEMI-CUBE
A RADIOSITY SOLUTION FOR
 COMPLEX ENVIRONMENTS
                     Introduction
   This paper extends the use of the radiosity
    –   Considering about radiosity in complex
        environment
           Occluded surfaces are allow (hidden, shadow)
    –   Efficient form-factor calculation
           Introduction of the hemi-cube
    –   Efficient procedures to render an image
               Reviewing Radiosity
  Radiant energy (flux) = energy flow per unit time across
  a surface (watts)
 Radiosity = flux per unit area radiated from a surface
    – Model lighting for diffusely reflecting surfaces only
    – Consist of self-emitted light and reflected light
   radiosity equation
    –

                    N
    B j  E j   j  B i Fij   for j  1, N
                    i 1


                                                        Diffuse-diffuse
                                                        (radiosity)
               Reviewing Radiosity
    environment is subdivided into n small patchs
    (elements), thus get a n radiosity equations of
    interactive light energy (after calculation form-factor)
                         Form-factor
    form factor : fraction of the energy leaving one surface which
    lands on another
   form factor geometry and term
                                  • from differential to differential
                                                 cos i cos j
                                      FdAi dAj 
                                                     r 2
                                  • from differential to Patch
                                                    cos ```` j
                                                           i cos
                                      FdAi Aj                     dAj
                                                 Aj      r  2


                                  • from Patch to Patch
                                                1           cos i cos j
                                      FAi Aj 
                                                Ai  Ai Aj r 2 dAj dAi
                            Form factor
   extent to occluded environments

               1           cos i cos j
    FAi Aj   
               Ai   Ai Aj r 2         HID dAj dAi

 geometric           analog (Nusselt analog)
    – The form-factor of a patch is equivalent to the fraction of the unit circle
      of hemisphere covered by the projection
                        Hemi-Cube
   Why introduce a hemi-cube?
    – Difficulty in creating equal sized elements on a sphere
   What is the hemi-cube?
    – An efficient algorithm to compute form-factor in complex
      environment
                                      Hemi-Cube
        approximation of form-factor
    1.    Start with a patch i (a surface)
    2.    Place a hemi-cube on its center
    3.    face of the hemi-cube are divided into “pixel”
    4.    Project all other patch onto this hemi-cube
    5.    Δform-factor has pre-computed values
          (because the contribution of each pixel is dependent on the pixel location and orientation // and stored in a
          lookup table)

    6.    Use z-buffer for each face – storing which patches remain
          visible
    7.    Summation all of pixel occupied by patch(j) for calculation of
          form-factor
                                                    R
                                                                     Fi j    Fq
    8.    Get a Fij form-factor
                                                                                  q 1
                 Delta form-factor
   Δform-factor on the top and side of Hemi-Cube
                        Render to image
   To render an image the discretized radiosity information is used to
    create a continuous shading across a given surface(or polygon)
    – Use a bilinear interpolation within each patch
   Bi radiosity values are constant over the extent of a patch.
    – patch radiosity  vertex radiosity
   How are they mapped to the vertex radiosities (intensities)?
    – Average the radiosities of patches that contribute to the vertex
    – Vertices on the edge of a surface are assigned values extrapolation
Vertex radiosity

								
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