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