# THE HEMI- CUBE A RADIOSITY SOLUT

Document Sample

```					     THE HEMI-CUBE
A RADIOSITY SOLUTION FOR
COMPLEX ENVIRONMENTS
Introduction
   This paper extends the use of the radiosity
environment
   Occluded surfaces are allow (hidden, shadow)
–   Efficient form-factor calculation
   Introduction of the hemi-cube
–   Efficient procedures to render an image
  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
–

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

Diffuse-diffuse
    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.