Instant Radiosity

Alexander KellerUniversity Kaiserslautern

Present by Li-Fong Lin

Outline

• Global Illumination

• Quai-Monte Carlo Integration

• Algorithm

• Extensions

• Reasults

Global Illumination

• Radiance equation :

• Shorthand :

• In the radiosity setting, restricted to only diffuse reflection :

Global Illumination

• Detector functional Ψ: the sum of orthonormal base vectors of a finite vector space.

• Directly select the function below in this paper

Global Illumination

• In realistic applications : ||Tfr|| < 1, less than 100% of the incident radiance is reflected.

• So the Neumann series converges and can be used to solve the integral equation.

Quasi-Monte Carlo Integration

• Replace the random numbers used in standard Monte Carlo with low-discrepancy points.

• Much smoother convergence at a slightly superior rate.

• Halton sequence is used in this paper.

van der Corput sequence

Algorithm

• Approximate the radiance L in the radiosity setting by a discrete density of M point light sources.

• The particle approximation yields the very fast rendering algorithm:

Li

PiPi

Pi

y

L(y)

Algorithm

• Only small deviation from mean reflectivity in realistic scene models.

• We can use fractional absorption and avoid Russian Roulette absorption.

• ρN particles will survive after one reflection.

Algorithm

• The Quasi-Random Walk– Evaluate TmnLe using N point lights, TmnTfdLe by using

ρN point lights, and so on.

– Finally the quasi-Monte Carlo integration is performed by accumulating all images with the weight 1/N

Pseudo-Code

Extensions

• Jittered Low Discrepancy Sampling

Extensions

• Specular Effects– By a random decision each surface is tested to be specular or

diffuse according to its BRDF.– Mirror the origin ray by the specular surface.

• Realtime Walkthroughs– In an animated environment, trace fixed length paths.– Keeping the last N images of the last N paths, the oldest image is

replaced by the new one each time .– Render the global diffuse illumination (only direct illumination)

into textures, then can be displayed interactively.

Results

Results

Results