Paper by Alexander Keller Instant Radiosity Paper by Alexander Keller

What is Radiosity? Perfect Diffuse Interaction View-Independent Must be Followed By Projection Computation May have a post-process Ray Tracing enhancement

Process An array of emitting patches Diffuse-Diffuse Interaction between light patch and all receiving patches Mostly iterative procedure Applied to ENTIRE scene.

Output

Single Frame

Combined Solution

Advantages Needs only be calculated once Only if geometry changes is there a need to recalculate the form factors If lighting changes then only equation needs resolving Viewport changes do not need a form factor recalculation

Problems Basic Radiosity Solution is Slow Procedural Process Must cover entire scene

Instant Radiosity Solution Operates on the textured scene Produce photorealistic images without any finite kernel or solution discretization of underlying integral equation Rendering rates of a few seconds are obtained by Hardware, quasi-random walk, jittered low discrepancy sampling. Does NOT need to evaluate form factors or generate meshes

Algorithm Basics Photons are traced from the light source into the scene At the origin of the path of the photon, and where it hits a scene a point light is placed The scene is rendered several times for each light source Resulting image is composited in the accumulation buffer (hardware)

Algorithm Basics Generates a particle approximation of the diffuse radiant scene using Quasi-random walk based on quasi-Monte Carlo integration Hardware renders an image with shadows for each particle used as point light source Illumination is obtained by summing up the single images in an accumulation buffer and displaying the result

The Algorithm Calculate the average radiance passing through a pixel Add that to a discrete density of point light sources Evaluated for all pixels of the image matrix

In Mathematical Terms The Radiance of m to n is an approximation of Source Radiance * Avg Radiance from m to n + The Sum from 0 to M – 1 points of light of Reflectiveness(BRDF) * Radiance of light i * Kronecker delta function of The point on the surface – the position of light i

Pseudocode Variable Defs N – Number of Particles – average reflectivity w – attenuation L – radiance of a point y – point on the surface – aligned normal to y

Pseudocode 1st Level Loop Фn(i) – Base n Halton Sequence yo(Ф2(i), Ф3(i)) – Isometry from unit square to onto each light source Le(y) * supp Le – Sum of source radiance for y * support of the light sources

Pseudocode 2nd Level Loop - Shoot A ray into direction - Return the first point hit when shooting a ray from y into - Reflectivity of the diffuse surface texture /

GL Calls glRenderShadowedScene(LightPower,LightPosition) 2d image that doesn't 'see' that light is black, otherwise it is colored as usual (hard shadows) glAccum(GL_ACCUM, weight) 2d image that was rendered in previous step added to current accumulated buffer Repeated for different bright spots until N iterations are complete. Result is a soft shadowed scene that can be rendered very quickly in OpenGL

Result

Disadvantages View-dependency Rendering tens to hundreds of light sources each frame is too costly Somewhat more suitable for generating quick previews than interactive walkthroughs Not very precise Many point sources have to be rendered for accurate images Problematic! Accumulation buffer only has a limited precision!

Walkthroughs They are possible We could render each lit surface into a texture, and use these as light maps Very time consuming since for every texture a lot of images have to be composited Keep last N images from the last N paths in memory, while the system keeps rendering new images for new paths When an image is finished, the oldest image is replaced by the new one. Suited for extremely slow walkthroughs

Specular Effects Specular Effects Let the algorithm use a full BRDF in the hardware lighting pass, enabling specular highlights In The particle generation phase, random surfaces are tested to be specular or diffuse. Virtual Lights for specular object

Conclusions Provides quickly rendered images for the Global Illumination problem Low precision Inherent upper bounds issues with respect to hardware

OpenGL Implementation 2D Points and the Depth Buffer Shadow Maps Software Restraints Accumulation Buffer Hardware Issues Results

2D Points and the Depth Buffer

Applications Stored Z Values for an X,Y point Clamped [0, 1] Crude vector-object collision detection Special Cases Shadow Maps Hardware Restraints Software Restraints

Hardware Shadow Vs. Software Shadows

Accumulation Buffer Not Hardware Accelerated (Most Cases) Average execution time N = 300 ~265 seconds total ~270 for Software Render ~264 seconds in accumulator

Original Scene

Results: N=75

Results: N=150

Results: N=300