Simplifying the Representation of
Radiance from Multiple Emitters
George Drettakis
iMAGIS/IMAG-INRIA
Grenoble, FRANCE
General Motivation

Sampling for multiple sources
– Unnecessary expensive meshing
– too many elements
IMAGE: full mesh table (marked region)
IMAGE: rendered two image
Goal: reduce meshing cost; reduce number of interpolants
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Previous Work

Shadow Meshing (Campbell & Fussell 90,
91, Chin & Feiner 90, 91)
– Extremal (umbral/penumbral,
penumbral/light) boundary
– Constant interpolants

Discontinuity Meshing (Lischinski et al. 92,
Heckbert 92)
– Interior discontinuity surfaces (EV and EEE)
– Higher order interpolants
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(Previous Work cont. )
Structured Sampling


Drettakis & Fiume 93: unoccluded
environments
Drettakis & Fiume 94: discontinuity
meshing
IMAGE: Struct Mesh 1 src
IMAGE: Backprojection (SIGRAPH)
IMPORTANT: Light mesh is accurate; allows simplification
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(Previous Work cont.) Structured
Sampling with Shadows

Penumbral groups; tensor products (light),
triangular (penumbra) (Drettakis 94)
IMAGE: Table 4 (SIGGRAPH)
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Organisation of Remaining Talk
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
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
Extension to Multiple Sources and TwoPass Meshing
Simplification Criteria (two sources case)
First Implementation Results
Multiple Sources and Conclusion
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Extension to Multiple Sources

Multiple meshes
– ray-tracing for image generation

Merge the multiple meshes
– light/light –> tensor product interpolant
– penumbra/light –> triangular interpolant
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Two-pass Meshing

Extremal boundary computation
– include minimal EEE
– extremal boundary 4 times cheaper than
complete mesh
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Simplification


Two-sources only case first
Methodology: use structured light
representation
– Light/Light: compare with simpler interpolant
– Penumbra/Light: compare moderate quality
interpolant (triangular) to simpler (tensor
product)
– Penumbra/Penumbra: no simplification

Compare using L2 error computation
– All integral computations on polynomials
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Light-Light Simplification

Simplified interpolant construction
– 9-point biquadratic Lagrange interpolant

L2-norm calculation
– difference of structured interpolant and
simplified tensor product
– efficient computation (all quadratic
polynomials)

Enforce C0 continuity
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Light-Light Simplification
Unsimplified mesh and image
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Light-Light Simplification Results
Simplified mesh and image
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Light-Penumbra Simplification


First construct simplified mesh
For each source
– extremal boundary
– structured sampling for light
IMAGE: Src1 simplified mesh
src2
complexity of triangles construction does not depend on scene
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Light-Penumbra Simplification

For each penumbral group
– Create a mesh containing extremal boundary
– Add light faces; calulate appropriate
radiance values
IMAGE MAXMINOUND
IMAGE LIGHT ADDED
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Light-Penumbra Simplification
(cont.)



Construct "moderate quality"
approximation
Compute L2-norm
Perform full meshing only where needed
IMAGE LIGHT TRIS
IMAGE: Triangles ADDED
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Estimating Penumbral Radiance

For a point known to be in penumbra
– Find closest point on minimal and maximal
boundary
– Estimate derivative
– Create interpolants
– Evaluate interpolant

Experimental verification pending
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Light-Penumbra Implementation

First implementation
– Construct full mesh; apply simplification
criteria a-posteriori. Promising first results.
IMAGE COMPLETE MESH
IMAGE
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Light-Penumbra Results (1)
IMAGE MESH (35%) 0.005
IMAGE
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Light-Penumbra Results (2)
IMAGE MESH (40%) 0.001
IMAGE
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Multiple Sources



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Compute simplified mesh for each
source M1, M2, ... Mn
Merge to M1,M2, create Mm
Subsequently merge each Mi into the
mesh Mm
Perform complete meshing at the end
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Discussion


First results encouraging
L2-norm insufficient
– specialised error norms need to be designed


Gradation between "simplified" and
"complete"
Results of complete implementation
required to determine savings in
computation time
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Future

Complete implementation
– partial meshing
– simplifcation
– complete meshing on demand


Application to complex environments
Application to global illumination
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Acknowledgements



The author is an ERCIM fellow, currently
hosted by INRIA in Grenoble
Many ideas in this research originated at
the Dynamic Graphics Project (DGP) of
the University of Toronto, Canada
Software elements written by researchers
at DGP have been used in the
implementation
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