Simplifying the Representation of Simplifying the Representation of Radiance from Multiple EmittersRadiance from Multiple Emitters

George DrettakisGeorge Drettakis

iMAGIS/IMAG-INRIAiMAGIS/IMAG-INRIAGrenoble, FRANCEGrenoble, FRANCE

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General MotivationGeneral Motivation

Sampling for multiple sourcesSampling for multiple sources– Unnecessary expensive meshingUnnecessary expensive meshing– too many elementstoo 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 WorkPrevious Work Shadow Meshing (Campbell & Fussell Shadow Meshing (Campbell & Fussell

90, 91, Chin & Feiner 90, 91)90, 91, Chin & Feiner 90, 91)– Extremal (umbral/penumbral, Extremal (umbral/penumbral,

penumbral/light) boundarypenumbral/light) boundary– Constant interpolantsConstant interpolants

Discontinuity Meshing (Lischinski et al. Discontinuity Meshing (Lischinski et al. 92, Heckbert 92)92, Heckbert 92)– Interior discontinuity surfaces (EV and EEE)Interior discontinuity surfaces (EV and EEE)– Higher order interpolantsHigher order interpolants

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(Previous Work cont. ) (Previous Work cont. ) Structured SamplingStructured Sampling Drettakis & Fiume 93: unoccluded Drettakis & Fiume 93: unoccluded

environmentsenvironments Drettakis & Fiume 94: discontinuity Drettakis & Fiume 94: discontinuity

meshingmeshing

IMAGE: Struct Mesh 1 src IMAGE: Backprojection (SIGRAPH)

IMPORTANT: Light mesh is accurate; allows simplification

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(Previous Work cont.) Structured (Previous Work cont.) Structured Sampling with ShadowsSampling with Shadows Penumbral groups; tensor products Penumbral groups; tensor products

(light), triangular (penumbra) (Drettakis (light), triangular (penumbra) (Drettakis 94)94)

IMAGE: Table 4 (SIGGRAPH)

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Extension to Multiple Sources and Two-Extension to Multiple Sources and Two-Pass MeshingPass Meshing

Simplification Criteria (two sources Simplification Criteria (two sources case)case)

First Implementation ResultsFirst Implementation Results Multiple Sources and ConclusionMultiple Sources and Conclusion

Organisation of Remaining TalkOrganisation of Remaining Talk

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Extension to Multiple SourcesExtension to Multiple Sources Multiple meshesMultiple meshes

– ray-tracing for image generationray-tracing for image generation Merge the multiple meshes Merge the multiple meshes

– light/light –> tensor product interpolantlight/light –> tensor product interpolant– penumbra/light –> triangular interpolantpenumbra/light –> triangular interpolant

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Two-pass MeshingTwo-pass Meshing Extremal boundary computationExtremal boundary computation

– include minimal EEE include minimal EEE – extremal boundary 4 times cheaper than extremal boundary 4 times cheaper than

complete meshcomplete mesh

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SimplificationSimplification Two-sources only case firstTwo-sources only case first Methodology: use structured light Methodology: use structured light

representationrepresentation– Light/Light: compare with simpler interpolantLight/Light: compare with simpler interpolant– Penumbra/Light: compare moderate quality Penumbra/Light: compare moderate quality

interpolant (triangular) to simpler (tensor interpolant (triangular) to simpler (tensor product)product)

– Penumbra/Penumbra: no simplificationPenumbra/Penumbra: no simplification Compare using Compare using LL22 error computation error computation

– All integral computations on polynomialsAll integral computations on polynomials

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Light-Light SimplificationLight-Light Simplification Simplified interpolant constructionSimplified interpolant construction

– 9-point biquadratic Lagrange interpolant9-point biquadratic Lagrange interpolant LL22-norm calculation-norm calculation

– difference of structured interpolant and difference of structured interpolant and simplified tensor productsimplified tensor product

– efficient computation (all quadratic efficient computation (all quadratic polynomials)polynomials)

Enforce Enforce CC00 continuitycontinuity

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Light-Light SimplificationLight-Light Simplification

Unsimplified mesh and image

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Light-Light Simplification ResultsLight-Light Simplification Results

Simplified mesh and image

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Light-Penumbra SimplificationLight-Penumbra Simplification First construct simplified meshFirst construct simplified mesh For each sourceFor each source

– extremal boundaryextremal boundary– structured sampling for lightstructured sampling for light

IMAGE: Src1 simplified mesh src2

complexity of triangles construction does not depend on scene

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Light-Penumbra SimplificationLight-Penumbra Simplification For each penumbral groupFor each penumbral group

– Create a mesh containing extremal Create a mesh containing extremal boundaryboundary

– Add light faces; calulate appropriate Add light faces; calulate appropriate radiance valuesradiance values

IMAGE MAXMINOUND IMAGE LIGHT ADDED

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Light-Penumbra Simplification Light-Penumbra Simplification (cont.)(cont.) Construct "moderate quality" Construct "moderate quality"

approximationapproximation Compute Compute LL22-norm-norm Perform full meshing only where neededPerform full meshing only where needed

IMAGE LIGHT TRIS IMAGE: Triangles ADDED

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Estimating Penumbral RadianceEstimating Penumbral Radiance For a point known to be in penumbraFor a point known to be in penumbra

– Find closest point on minimal and maximal Find closest point on minimal and maximal boundaryboundary

– Estimate derivativeEstimate derivative– Create interpolantsCreate interpolants– Evaluate interpolantEvaluate interpolant

Experimental verification pendingExperimental verification pending

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Light-Penumbra Implementation Light-Penumbra Implementation First implementationFirst implementation

– Construct full mesh; apply simplification Construct full mesh; apply simplification criteria a-posteriori. Promising first results.criteria a-posteriori. Promising first results.

IMAGE COMPLETE MESH IMAGE

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Light-Penumbra Results (1)Light-Penumbra Results (1)

IMAGE MESH (35%) 0.005 IMAGE

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Light-Penumbra Results (2)Light-Penumbra Results (2)

IMAGE MESH (40%) 0.001 IMAGE

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Multiple SourcesMultiple Sources Compute simplified mesh for each Compute simplified mesh for each

source source MM11, M, M22, ... M, ... Mnn

Merge to Merge to MM1,1,MM22, , create create MMmm

Subsequently merge each Subsequently merge each MMii into the into the mesh mesh MMm m

Perform complete meshing at the end Perform complete meshing at the end

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DiscussionDiscussion First results encouragingFirst results encouraging LL22-norm insufficient-norm insufficient

– specialised error norms need to be designedspecialised error norms need to be designed Gradation between "simplified" and Gradation between "simplified" and

"complete""complete" Results of complete implementation Results of complete implementation

required to determine savings in required to determine savings in computation timecomputation time

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FutureFuture Complete implementationComplete implementation

– partial meshingpartial meshing– simplifcationsimplifcation– complete meshing on demandcomplete meshing on demand

Application to complex environmentsApplication to complex environments Application to global illuminationApplication to global illumination

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AcknowledgementsAcknowledgements The author is an ERCIM fellow, currently The author is an ERCIM fellow, currently

hosted by INRIA in Grenoblehosted by INRIA in Grenoble Many ideas in this research originated Many ideas in this research originated

at the Dynamic Graphics Project (DGP) at the Dynamic Graphics Project (DGP) of the University of Toronto, Canadaof the University of Toronto, Canada

Software elements written by Software elements written by researchers at DGP have been used in researchers at DGP have been used in the implementationthe implementation