cpsc 641 computer graphics: radiosity
DESCRIPTION
CPSC 641 Computer Graphics: Radiosity. Jinxiang Chai. Local Illumination. I r = k a I a + I i (k d (n.l) + k s (h.n) m ). ambient. diffuse. specular. Local Illumination. I r = k a I a + I i (k d (n.l) + k s (h.n) m ). ambient. diffuse. specular. Local Illumination. - PowerPoint PPT PresentationTRANSCRIPT
CPSC 641 Computer Graphics: Radiosity
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 )
if there are multiple lights there is a sum of the specular and diffuse components for each light
ambient diffuse specular
Local Illumination
Ir = kaIa + Ii (kd (n.l) + ks(h.n)m )
if there are multiple lights there is a sum of the specular and diffuse components for each light
ambient diffuse specular
What are limitations of local illumination?
Rendering: Illumination Computing
Direct (local) illumination
Light directly from light sources
No shadows
Direct and Indirect Light
Rendering: Illumination Computing
Direct (local) illumination
Light directly from light sources
No shadows
Indirect (global) illumination
Hard and soft shadows
Diffuse interreflections (radiosity)
Glossy interreflections (caustics)
Early Radiosity
Consolation Room
Challenge
To evaluate the reflection equation
the incoming radiance must be known
To evaluate the incoming radiance
the reflected radiance must be known
2
( , ) ( , ) ( , )cosr r r i r i i i i
H
L x f x L x d
Radiosity
Only consider inter-reflections between diffuse surfaces!
Radiosity: Key Idea #1
Diffuse Surface
Radiosity: Key Idea #2
Constant Surface Approximation
Radiosity Equation
Radiosity Equation
Radiosity Algorithm
Radiosity Algorithm
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
Radiosity Equation
Linear System
Radiosity Algorithm
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
Radiosity Algorithm
How to Solve Linear System?
Matrix conversion
Iterative approaches
- Jacobian
- Gauss-Seidel
Matrix Conversion
Iterative Approaches
Jacobian
Successive Approximation
eL
e eL K L eL
eK L eK K L eK K K L
2e eL K L 3
e eL K L
Gauss-Seidel
Gauss-Seidel (Cont.)
Radiosity Algorithm
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 radiosities)
If the radiosities of surrounding patches are know, vertex radiosities can be estimated using bilinear interpolation
Vertex Intensity: Bilinear Interpolation
Theatre
Steel Mills
Radiosity: Benefit
Global illumination method: modeling diffuse inter-reflection
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 shadow from a polygon
No ambient term hack, so when you want to look at your object in low light, you don’t have to adjust parameters of the objects – just the intensities of the lights!
View independent: it assigns a brightness to every surface
Radiosity: Limitation
Radiation is uniform in all directions
Radiosity is piecewise constant
– usual renderings make this assumption, but then interpolate cheaply to fake a nice-looking answer
– this introduces quantifiable errors
No surface is transparent or translucent
Reflectivity is independent of directions to source and destination