# Nusselt Analog

## Transcription

Nusselt Analog
```CPSC 641 Computer Graphics:
Jinxiang Chai
Local Illumination
Ir = kaIa + Ii (kd (n.l) + ks(h.n)m )
ambient
diffuse
specular
Local Illumination
Ir = kaIa + Ii (kd (n.l) + ks(h.n)m )
ambient
diffuse
specular
Local Illumination
Ir = kaIa + Ii (kd (n.l) + ks(h.n)m )
ambient
diffuse
specular
if there are multiple lights there is a sum of the specular and
diffuse components for each light
Local Illumination
Ir = kaIa + Ii (kd (n.l) + ks(h.n)m )
ambient
diffuse
specular
if there are multiple lights there is a sum of the specular and
diffuse components for each light
What are limitations of local illumination?
Rendering: Illumination Computing
Direct (local) illumination

Light directly from light sources

Direct and Indirect Light
Rendering: Illumination Computing
Direct (local) illumination

Light directly from light sources

Indirect (global) illumination



Glossy interreflections (caustics)
Consolation Room
Challenge
To evaluate the reflection equation
the incoming radiance must be known
Lr ( x, r ) 
 f ( x,   )L ( x, )cos d
r
i
r
i
i
H2
the reflected radiance must be known
i
i
Only consider inter-reflections between diffuse
surfaces!
Diffuse Surface
Constant Surface Approximation
Energy Conservation Equation
Energy Conservation Equation
Form factor
Compute Form Factors
Compute Form Factors
Radiant energy reaching Ay from Ax
Radiant energy leaving Ax in all directions
Form Factor: Reciprocity
Linear System
Form Factors
Form Factor: How to compute?
Closed Form
- anlytical
Hemicube
Monte Carlo
Form Factor: Analytical
Form Factor: How to compute?
Closed Form
- anlytical
Hemicube
Monte Carlo
Form Factor: Nusselt Analog
Form Factor: Nusselt Analog
Why is it true?
Form Factor: Nusselt Analog
Form Factor: Nusselt Analog
How can we use this property?
Form Factor: Nusselt Analog
How can we use this property?
- Speed up form-factor evaluation
Form Factor: HemiCube
Delta Form Factor: Top Face
Top of hemicube
Delta Form Factors: Side Faces
Side of hemicube
The Hemicube in Action
Form Factor: HemiCube
Form Factors
How to Solve Linear System?
Matrix conversion
Iterative approaches
- Jacobian
- Gauss-Seidel
Matrix Conversion
Iterative Approaches
Jacobian
Successive Approximation
Le
K Le
Le
Le  K Le
K K Le
Le 
K 2 Le
K K K Le
Le 
K 3 Le
Gauss-Seidel
Gauss-Seidel (Cont.)
Rendering
The final Bi's can be used in place of intensities in a
standard renderer (Gouraud)
Radiosities are constant over the extent of a patch
A standard renderer requires vertex intensities (or
If the radiosities of surrounding patches are know,
vertex radiosities can be estimated using bilinear
interpolation
Vertex Intensity: Bilinear Interpolation
Theatre
Steel Mills
 Global illumination method: modeling diffuse interreflection
 Color bleeding: a red wall next to a white one casts a
reddish glow on the white wall near the corner
 Soft shadows – an “area” light source casts a soft
 No ambient term hack, so when you want to look at
parameters of the objects – just the intensities of the
lights!
 View independent: it assigns a brightness to every
surface