CSL 859: Advanced Computer Graphics

CSL 859: CSL 859: Advanced Advanced Computer Computer GraphicsGraphicsDept of Computer Sc. & Engg.Dept of Computer Sc. & Engg.

IIT DelhiIIT Delhi

Tracing RaysTracing Rays

Trace many more rays

Tracing RaysTracing Rays

Not just in the ideal specular directions

Tracing RaysTracing Rays

Could distribute rays based on surface property

Rendering EquationRendering Equation The total light leaving a point =The total light leaving a point =

Exitance from the point +Exitance from the point + Incoming light from other sources Incoming light from other sources

reflected at the pointreflected at the point

dLLL iooooeoo cos),,(),,,(),,(),,( xxx x

Light

leaving

Exitance Sum BRDF Incoming

light

Incoming light reflected at the point

Photorealistic LightingPhotorealistic Lighting Solve the equationSolve the equation

To compute light leaving x, need to find To compute light leaving x, need to find how much light reaches ithow much light reaches it

To find how much light reaches x, need to To find how much light reaches x, need to compute light leaves every other pointcompute light leaves every other point

Hard because BRDFs are high Hard because BRDFs are high dimensionaldimensional

But some light interaction in the scene is But some light interaction in the scene is diffuseddiffused

View angle independentView angle independent

Global IlluminationGlobal Illumination Traditional Raytracing only considers Traditional Raytracing only considers

specular reflectionsspecular reflections Does not account for (indirect) diffused Does not account for (indirect) diffused

reflections reaching eyereflections reaching eye Need to “trace” those rays alsoNeed to “trace” those rays also

Stochastic methodsStochastic methods Monte Carlo techniques to solve rendering Monte Carlo techniques to solve rendering

equationequation Separate diffused and specular reflectionSeparate diffused and specular reflection

RadiosityRadiosity

Radiosity AssumptionsRadiosity Assumptions All surfaces are perfectly diffuseAll surfaces are perfectly diffuse Illumination is Illumination is constantconstant over a over a patchpatch

Subdivide triangles into small patchesSubdivide triangles into small patches Problems at sharp illumination boundaries, Problems at sharp illumination boundaries,

e.g., shadowse.g., shadows Less space/time efficient solutionsLess space/time efficient solutions Discontinuity meshingDiscontinuity meshing

Can be pre-computedCan be pre-computed With view-dependent illumination With view-dependent illumination

computed and added latercomputed and added later

Radiosity ExampleRadiosity Example Extreme color Extreme color

bleeding herebleeding here Textures are post Textures are post

illuminationillumination Notice meshing Notice meshing

artifacts like the artifacts like the banding around the banding around the pictures on the wallpictures on the wall

From Alan Watt, “3D Computer Graphics”

Radiosity MeshingRadiosity Meshing Each patch is Each patch is

colored with its colored with its illuminationillumination

The previous The previous image was image was obtained by obtained by pushing color to pushing color to vertices and then vertices and then Gourand shadingGourand shading

From Alan Watt, “3D Computer Graphics”

Global IlluminationGlobal Illumination What’s wrong with factoring into What’s wrong with factoring into

Radiosity and Ray-tracing?Radiosity and Ray-tracing? Factor into direct illumination + Factor into direct illumination +

indirect illuminationindirect illumination Indirect illumination is the hard partIndirect illumination is the hard partBut:But: Indirect illumination has low varianceIndirect illumination has low variance

Can be sampled and interpolated (with Can be sampled and interpolated (with care)care)

Photon MappingPhoton Mapping

[Jensen]

Two-Pass AlgorithmTwo-Pass Algorithm Pass 1:Pass 1:

Photons are generated and tracedPhotons are generated and traced They are associated with surface points and They are associated with surface points and

storedstored Photon Map is createdPhoton Map is created View independent passView independent pass

Pass 2Pass 2 Photon map is a static and used toPhoton map is a static and used to

Compute estimates of the incoming flux and the Compute estimates of the incoming flux and the reflected radiance at any point in the scenereflected radiance at any point in the scene

Look up indirect illumination from Photon mapLook up indirect illumination from Photon map Or, Trace rays once and then look up illuminationOr, Trace rays once and then look up illumination

Photon TracingPhoton Tracing Indirect illumination on diffuse surfaces Trace photons from the light sources

Store them at diffuse surfaces Brighter light => More Photons

Photons of uniform flux Diffuse point light emits in uniformly distributed random

directions Directional light emits in its direction Square light source emits from random positions on the square

with directions limited to a hemisphere Photon emission should follow light’s emission

properties Controls origin and direction of each photon Cosine distribution (more photon’s emitted perpendicular to

light)

Photon OriginationPhoton Origination

Pphoton= Plight / nphoton

Photon DistributionPhoton Distribution Importance samplingImportance sampling

Multiple light sourcesMultiple light sources Projection mapProjection map

Project a bounding sphere for objectsProject a bounding sphere for objects Photons not wasted on backgroundPhotons not wasted on background

Photon InteractionsPhoton Interactions On intersection, a photon can beOn intersection, a photon can be

Reflected, transmitted, or absorbedReflected, transmitted, or absorbed Probabilistic method based on the Probabilistic method based on the

material propertiesmaterial properties Russian rouletteRussian roulette

Roll a dice and decide next step for the Roll a dice and decide next step for the photonphoton

Controls count not the power of the Controls count not the power of the reflected/transmitted photonreflected/transmitted photon

Photon Paths in Cornell Photon Paths in Cornell BoxBox

Chrome sphere (left) and Glass sphere (right)(a) Two diffuse reflections followed by absorption(b) Specular reflection followed by two diffuse reflections(c) Two specular transmissions followed by absorption

Monochromatic Photon Monochromatic Photon BehaviorBehavior

Consider monochromatic simulationConsider monochromatic simulation Reflective surface withReflective surface with

Diffuse reflection coefficient Diffuse reflection coefficient dd SSpecular reflection coefficient pecular reflection coefficient s s (with (with d d + + s <=s <= 11) )

Uniformly distributed random variableUniformly distributed random variable X X ϵϵ [0[0, , 1]1]

Sample X. IfSample X. If X X ϵϵ [0[0, d, d] =] => > diffuse reflectiondiffuse reflection X X ϵϵ ] ]d, s d, s + + dd] =] => > specular reflectionspecular reflection X X ϵϵ ] ]s s + + d, d, 1] =1] => > absorptionabsorption

““Chromatic” PhotonsChromatic” Photons Probability PProbability Pdd for diffuse reflection = for diffuse reflection =

MAX(dMAX(drrPPrr, d, dggPPgg, d, dbbPPbb) / MAX(P) / MAX(Prr, P, Pgg, P, Pbb)) where (dwhere (drr, d, dgg, d, dbb) are the diffuse reflection ) are the diffuse reflection

coefficientscoefficients (P(Prr, P, Pgg, P, Pbb) are the powers of the incident photons) are the powers of the incident photons

Probability PProbability Pss for specular reflection is for specular reflection is MAX(sMAX(srrPPrr, s, sggPPgg, s, sbbPPbb) / MAX(P) / MAX(Prr, P, Pgg, P, Pbb)) where (swhere (srr, s, sgg, s, sbb) are the specular reflection ) are the specular reflection

coefficientscoefficients Instead of MAX, probabilities can also be Instead of MAX, probabilities can also be

based on total powerbased on total power

Chromatic Photon Chromatic Photon BehaviorBehavior

Sample X. IfSample X. If X X ϵϵ [0, P [0, Pdd] => diffuse reflection] => diffuse reflection X X ϵϵ ]P ]Pdd, P, Pss + P + Pdd] => specular reflection] => specular reflection X X ϵϵ ]P ]Pss + P + Pdd, 1] => absorption, 1] => absorption

The power of the reflected photon must changeThe power of the reflected photon must change If specular reflection was chosen:If specular reflection was chosen:

PPrefl,rrefl,r = P = Pinc,rinc,r s srr/P/Pss PPrefl,grefl,g = P = Pinc,ginc,g s sgg/P/Pss PPrefl,brefl,b = P = Pinc,binc,b s sbb/P/Pss

where Pwhere Pincinc is the power of the incident photon is the power of the incident photon Similarly for diffused and absorbed photonsSimilarly for diffused and absorbed photons

Photon MapPhoton Map Photons are only stored where they hit Photons are only stored where they hit

non-specular surfacesnon-specular surfaces Global data structure: photon map storesGlobal data structure: photon map stores

PositionPosition Incoming photon powerIncoming photon power Incident directionIncident direction A flag for help with sorting and look-upA flag for help with sorting and look-up

For participative media, one might For participative media, one might construct a volume photon mapconstruct a volume photon map

ExampleExample

(a) Raytraced image (direct

illumination, specularreflection and

transmission)

(b) Photons in thephoton map.

Images courtesy of Henrik Wann Jensen

Participative MediaParticipative Media Photons can be emitted from volumes (and Photons can be emitted from volumes (and

surfaces and points) surfaces and points) Probability of being Probability of being scatteredscattered or or absorpedabsorped in the in the

medium depends onmedium depends on Density of the mediumDensity of the medium Distance the photon travels through the mediumDistance the photon travels through the medium

The denser the medium, the shorter the average distance The denser the medium, the shorter the average distance before a photon interaction happens.before a photon interaction happens.

Photons are stored at the positions where a Photons are stored at the positions where a scattering event happensscattering event happens Exception photons directly from the light sourceException photons directly from the light source Direct illumination is evaluated using ray tracingDirect illumination is evaluated using ray tracing Not necessary, but this separation improves efficiencyNot necessary, but this separation improves efficiency

Participative MediumParticipative Medium

Glass sphere in fog illuminated by directional light

Images courtesy of Henrik Wann Jensen

Three Photon MapsThree Photon Maps Caustic photon map

Photons that have been through at least one specular reflection before hitting a diffuse surface: LS+D.

Global photon map Approximate representation of the global

illumination solution Scene for all diffuse surfaces

Volume photon map Indirect illumination of a participating medium

Rendering PassRendering Pass To find radiance at a pointTo find radiance at a point

Find the nearest photonsFind the nearest photons Use balanced K-d treeUse balanced K-d tree

Heap-like, store in an arrayHeap-like, store in an array Element i has its left child at 2i+1 and right Element i has its left child at 2i+1 and right

at 2i+2at 2i+2 Root at 0Root at 0

Radiance EstimateRadiance Estimate

Find a sphere around x containing n photons.Use these n photons to estimate the radiance.

n

ppoooor x

rL

12 ,,),,,(1),,(

xx

Photon p has power ΔΦp

Estimate FilteringEstimate Filtering Averaging samples creates blurAveraging samples creates blur

Good for radiosity, they are smoothGood for radiosity, they are smooth Not so good for caustics, they have sharp Not so good for caustics, they have sharp

boundariesboundaries Use weigted averagingUse weigted averaging Use differential filtersUse differential filters

Detect edges from the samplesDetect edges from the samples ““Zero” weights for samples outside edges Zero” weights for samples outside edges

RenderingRendering

Perform a single step of secondary illumination

ExamplesExamples

Raytraced Cornell boxSharp shadows

Raytraced Cornell boxSoft shadows

Images courtesy of Henrik Wann Jensen

Caustic Photon MapCaustic Photon Map

Photon map has 50000 photons and the estimate uses60 photons Images courtesy of Henrik Wann Jensen

Global Illumination with Global Illumination with Photon MapPhoton Map

200000 photons in the global photon map. 100 photons used in the estimate.

Images courtesy of Henrik Wann Jensen

Photon NeighborhoodPhoton Neighborhood

Global photon map radiance estimates visualized directly using 500 photons

Sphere EstimateSphere Estimate Disk EstimateDisk Estimate

Images courtesy of Henrik Wann Jensen

Cornell Box with WaterCornell Box with Water

Displacement-mapped water surface (20,000 tris). 500,000 photons in both the caustics and the global photon maps, and 100 photons in the radiance estimate. Images courtesy of Henrik Wann Jensen

Cognac Glass and Cognac Glass and CausticCaustic

Glass made with 12000 triangles. 200,000 photons in the map. The radiance estimates with 40 photons.Images courtesy of Henrik Wann Jensen

Caustic through Prism Caustic through Prism DispersionDispersion

Only three separate wavelengths have been sampled. 500, 000 photons in the caustics and 80 photons in the radiance estimate.

Images courtesy of Henrik Wann Jensen

Diana, the HuntressDiana, the Huntress

Light behind translucent marble. (200,000 photons)