Radiosity

Jiří Bittner

Radiosity Methods MPG 15.10- Assumptions

- Basic principle

- Radiosity equation

- Iterative methods

- Meshing

- Instant radiosity

Outline

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Globall Illumination Computation

Assumption: Diffuse surfaces

Energy transport- Balance of emitted and absorbed energy

- Origin in heat transfer simulation

Radiosity - Overview

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Example

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Illumination computed for planar patches- Finite element method

View independent solution- Long preprocessing (1x)

- Fast viewing (Nx)

Good soft shadows, bad sharp shadows

Cannot simulate specular reflection/refraction

Basic Properties

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Directionally independent radiance

Diffuse emitor- Equal radiance in all directions

Reflection on a diffuse patch

B (x) = rd(x) *E (x)

B … radiosity [W/m2]

E … irradiance [W/m2]

rd ... reflectivity

View independent solution

Assumption #1: Diffuse emission and reflection

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Scene subdivision to patches

Piecewise constant approximation

of radiosity

Assumption #2: Constant radiosity on patches

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Radiosity Equation

N

j

ijjiiei FBBB1

, r

Bi

B1

B2

Bj

Be,i, ρi

radiosity Bi

self emmision Be,i (Ei)reflectivity ρi

form factor Fij

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Form factor Fij

- Portion of energy from Ai reaching Aj

Form Factor

i jA

ij

A

jiji

i

ij dAdAr

xxv

AF

2

coscos),(1

jijiji FAFA

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Leads to system of N equations with unknowns Bi

Radiosity Equation

Bi

B1

B2

BN

Be,i, ρi ij

N

j

jiiei FBBB

1

, r

ji

N

j

jjiieiii FBABABA

1

, r Power formulation

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Linear system: N equations with N uknowns (radiosities) Bi … (uknown)

Be,i …(known)

ri … (known)

Fij … form factors• Have to be computed, known when solving the system

Solving Radiosity Equation

N

j

ijjiiei FBBB1

, r

1 − 𝜌1𝐹1→1 −𝜌1𝐹1→2 … −𝜌1𝐹1→𝑛−𝜌2𝐹2→1 1 − 𝜌2𝐹2→2 … −𝜌2𝐹2→𝑛

… … … …−𝜌𝑛𝐹𝑛→1 1 − 𝜌𝑛𝐹𝑛→2 … 1 − 𝜌𝑛𝐹𝑛→𝑛

𝐵1𝐵2…𝐵𝑛

=

𝐵𝑒,1𝐵𝑒,2…𝐵𝑒,𝑛

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Part of energy emmited by patch i to patch j

or

How patch i sees patch j (Nusselt analogy)

Configuration Factor Fij

Aj

A’j

dAiFij

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Hemicube instead of Hemisphere

Configuration factors from patch projections- Cell weights (δ factors)

- z-buffer

Computing Fij using Hemicube

Aj

Aioccluder

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Classical Computation Scheme

Computing

configuration factors

Subdivision to patches

Radiosity solution(system of equations)

Scene with planar polygonsand area light sources

Change or self emmision (E)

Change of patch reflectivity (ρ)

Change of viewpoint

Rendering

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replaced by explicitly iterative methods

Progressive radiosity- Southwell iteration: shooting energy from brightest patches

Hierarchical radiosity- Patches in a hierarchy

- Energy transfer between hierarchy nodes

Stochastic radiosity (Monte-Carlo)- Using rays to stochastically distribute energy

- Diffuse ray reflection

- Register #hits per patch

Iterative Methods

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(Cohen & Wallace)

Meshing

Reference solution Uniform subdivision

finecoarse

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Adaptive Subdivision

solution adaptive subdivision

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Subdivision along illumination discontinuities

Discontinuity Meshing

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Discontinuity Meshing - Example

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Radiosity determines patch color at patch center

For Gouraud shading values at vertices needed

Radiosity and Shading

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B1

B2

B3

B4

B1

B2

B4

B1

(B1+B2)/2

(B1+B2 +B3)/3

Use many virtual point lights (VPLs)

No explicit meshing needed

1. Create VPLs- Shoot photons

- Random walk

2. Render- For each VPL

- Render with shadows

Instant Radiosty

Images courtesy of M. Hasan 21

Radiosity - DEMO

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Radiosity Methods MPG 15.10- Assumptions

- Basic principle

- Radiosity equation

- Iterative methods

- Meshing

- Instant radiosity

Outline

23

Questions?