Document Sample

```					     Chapter11

안상진
• 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.
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
• Object space algorithm – independent
of viewer position
• Assumption – perfect diffuse reflections
– 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
E: emitted energy
j
n                  A: area
Bi  Ei  Ri  B j Fij             R: reflectivity
j 1                F: form factor

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.

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
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
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

• Approximation in the hemicube method
for determining the form factors
• Using bilinear interpolation as a
• 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
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

in progressive
refinement method
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

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 5 posted: 2/4/2012 language: pages: 36