Virtual Light Field Groupvlfproject@cs.ucl.ac.ukUniversity College London

GR/R13685/01

Research funded by:

Propagating the VLF – Problems and Solutions I

Pankaj Khanna

p.khanna@cs.ucl.ac.uk

VLF Project

Introduction

Current state of the VLF– Area Emitters only– Specular and Diffuse planar polygons– Energy conserving (all equations balance)– Does all L(S|D)* paths– No diffuse texture maps

Easy to add though

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Implementing the VLF

Murphy’s Laws:– Nature always sides with the hidden flaw

The hidden flaw never stays hidden for long.

– Murphy’s Law of thermodynamics: Things get worse under pressure.

– If anything can go wrong, it will.– Every solution breeds new problems.– If anything simply cannot go wrong, it will anyway.– If everything seems to be going well, you have obviously

overlooked something

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Evolution of the VLF

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Outline of this section

Discretisation artefacts– Discretisation of directions

Accounting for variance Propagating with discretised directions

– Discretisation of surfaces Visibility issues Diffuse transfer of radiance

– Validity of transfer– Mechanism of transfer

Continued in Section II by Insu

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Discretisation of directions

What constitutes an “ideal” discretisation?– Unfortunately an ideal discretisation does not exist

Recursive subdivision of tetrahedron produces variance in solid-angle size and shape

– Results in non-uniform distribution– Aliasing and sampling problems

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Using discrete directions

Discrete directions have different significance depending on the nature of transport being performed

– Radiance to/from Diffuse surface A single direction (PSF) actually corresponds to the set of

directions contained in that direction’s solid-angle– Radiance to Specular surfaces

A specular surface has direction-dependent propagation and viewing attributes and can not be generalised over the solid angle

– Has error proportional to the number of discretised directions– SpecularDiffuse transfer can however be taken to be over the

solid-angle

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Normalising solid-angle area variance

Radiance sent along a PSF direction should be proportional to the area of the solid-angle associated to that discretised direction

– Normalise energy transfer per PSF direction by factor based on corresponding solid-angle

For Level 5, 2049 directions, SAMIN=0.0016, SAMAX=0.005

Energy conservation still required Normalisation= SAPSF/(SAPSF)

Without normalisation

Normalised Please note that illustrative images here and henceforth may have several inaccuracies as they were taken at various stages of the development of the VLF

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“Holes” due to discretised directions

Energy is only propagated along discretised directions (PSFs)

Error multiplies on successive iterations

Holes

Energy Source

PSF

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“Holes”

Problem is more severe with fewer directions and smaller emitters

513 directions 2049 directions

Ite

ratio

n 1

Ite

ratio

n 2

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Filling the holes

Discretised directions actually represent solid-angles for diffuse surfaces

Need to sample the solid angles during radiance transfer– How to sample?– How do we combine the samples?– Where do we put the sampled results?

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Filling holes with a jittered transfer

Send energy along original and a few additional sampled directions within the solid-angle

– Random or stratified sampling

Select samples over the solid-angle and rotate all directions by the corresponding angle to obtain a jittered set of discretised directions

– Use largest solid-angle & assume symmetry

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Jittered transfer

Jittered transfer is onlyonly used for transfer to diffuse surfaces

– Specular surfaces receive radiance only during Jitter 0 Combining samples from jittered transfer

– Use a Gaussian Kernel Small to prevent blurring out of details Need to manage filtering at edges of map Needs to be energy conserving

Results of transfer stored in Diffuse Maps as described earlier

– More details later…

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Constant time direction-lookup artefacts

Lookup involves referring to an OpenGL rasterised image

– Map needs to be of sufficiently high resolution to avoid aliasing

512x512 1024x1024 2048x2048

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Discretisation and the constant

IrradianceRadiance conversion requires division by

Discretisation of directions & points into patch areas lead is replaced by a constant obtained by summing

projected area of a cell along all PSF directions Level 3, 129 directions, discretised ‘’= 0.8291 Level 4, 513 directions, discretised ‘’= 5.2369 Level 5, 2049 directions, discretised ‘’= 20.9565

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Visibility

Visibility in tiles is at low resolution – need more detail for radiance transfer– Analytical computation– OpenGL visibility (P

buffers) Super-sampled exchange

(visibility) buffers

No super-sampling Super-sampled visibility

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Visibility for jittered transfer

Visibility (face-lists) stored in tiles is no longer valid

– Produces incorrect list of polygons to rasterise for visibility exchange buffer

More severe with fewer directions

3 possible options– Recomputing visibility by

OpenGL rasterisation is expensive but also most accurate

Visibility from Original PSF

Visibility from Nearest PSF

Recomputed Visibility (OpenGL)

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Transfer to Diffuse surfaces

Transfer of irradiance between 2 diffuse surfaces can be described by:– (CosACosB)/r2

In words this is:– (CosACosB) : product of projected areas : total projected area of source cell– r2 : term expressing angular spread with distance

rA B

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PS

F

PS

F

’Tile

Cell

Po

lyg

on

P2

Po

lyg

on

Q

Po

lyg

on

P1

Validity of diffuse transfer in the VLF

All parts of the previous equation are represented in the radiant transfer between two diffuse surfaces

– Actual projected areas are used in determining mapping of radiance– A constant equivalent to “” is obtained and used for the given

discretisation– The r2-term that represents the spread of the propagating solid-angle

with distance is explicitly represented in the VLF approach of propagation along discretised directions

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Transfer along a PSF Tile

Transfer of radiance from a sender to a receiver takes place in the PSF direction via a temporary radiance tile

– All senders push radiance into the temp tile– Temp tile pushes radiance into receiver

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han

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Bu

ffer

X(

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P)

PS

F

Sender Receiver

TemporaryRadiance Tile

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Mapping radiance

Radiance maps need to be sampled for each Tile-cell (per PSF)

The mapping is not one-to-one

PSF

Sender

Receiver

Temporary radiance tile

Tile

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Radiance sampling strategies

Point-sampling Sampling by determining cell overlaps

– DiscreteContinuousResampleDiscrete– Uses (slow) Liang-Barsky clipping

Currently the main bottleneck but high accuracy

Point-sampled Area-overlap

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Jittered diffuse transfer (an overview)

for (each Jitter) { if (Jitter>0) jitter the VLF for (each PSF, Tile) { if (Jitter>0) compute polygons in this tile for (each diffuse receiver R) { compute visibility exchange buffer for R for (each sender S) { Map radiance (URM) from sender S to temp radiance tile } // S Map temp radiance tile onto receiver’s DMN

} // R } // PSF, Tile} // Jitterdivide radiance in DMNs by NumJitters to normalise transferapply gaussian filter to diffuse DMNs and add to DMT

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Diffuse – bringing it all together