1Acoustics Modeling forVirtual EnvironmentsThomas FunkhouserPrinceton UniversityThomas Thomas FunkhouserFunkhouserPrinceton UniversityPrinceton UniversityVirtual EnvironmentsSimulate experience of being in 3D modelSimulate experience of being in 3D modelSimulate experience of being in 3D model2Distributed Virtual EnvironmentsAllow interaction among networked usersAllow interaction among networked usersAllow interaction among networked usersAcoustic ModelingSpatialized sound facilitates ...• Sense of presence• Comprehension of space• Localization of auditory cues• Selectivity of audio signals (“cocktail party effect”)Spatialized Spatialized sound facilitates ...sound facilitates ...••Sense of presenceSense of presence••Comprehension of spaceComprehension of space••Localization of auditory cuesLocalization of auditory cues••Selectivity of audio signals (“cocktail party effect”)Selectivity of audio signals (“cocktail party effect”)Avery Fisher HallEvans & SutherlandId Software3Modeling EnvironmentsSimulate reverberations due to environmentSimulate reverberations due to environmentSimulate reverberations due to environmentInput Audio SignalsAcousticsModelingOutput Audio Signal(s)SourcesReceiverEnvironmentAuralizationGeometric Acoustic ModelingSpatialize sound by computingreverberation paths from source to receiverSpatialize Spatialize sound by computingsound by computingreverberation paths from source to receiverreverberation paths from source to receiver4Similarities to GraphicsBoth model wave propagationBoth model wave propagationBoth model wave propagationDifferences from Graphics ISound has longer wavelengths than light• Diffractions are significant• Specular reflections dominate diffuse reflections• Occlusions by small objects have little effectSound has longer wavelengths than lightSound has longer wavelengths than light••Diffractions Diffractions are significantare significant••Specular Specular reflections dominate diffuse reflectionsreflections dominate diffuse reflections••Occlusions by small objects have little effectOcclusions by small objects have little effectλ5Differences from Graphics IISound waves are coherent• Modeling phase is importantSound waves are coherentSound waves are coherent••Modeling phase is importantModeling phase is importantSSRRRigid Surfaceλ/4λ/2InterferenceInterferenceDifferences from Graphics IIISound travels more slowly than light• Reverberations are perceived over timeSound travels more slowly than lightSound travels more slowly than light••Reverberations are perceived over timeReverberations are perceived over timeAmplitudeTime DelayDirectSoundEarlyReflectionsLateReverberations6Overview of ApproachesRay tracingBoundary element methodsImage source methodsBeam tracingRay tracingRay tracingBoundary element methodsBoundary element methodsImage source methodsImage source methodsBeam tracingBeam tracingOverview of ApproachesRay tracingBoundary element methodsImage source methodsBeam tracingRay tracingRay tracingBoundary element methodsBoundary element methodsImage source methodsImage source methodsBeam tracingBeam tracing7Ray TracingTrace paths between source and receiverTrace paths between source and receiverTrace paths between source and receiverSourceReceiverRay Tracing Trade-offsAdvantagesAdvantages••Models all types of surfaces and scatteringModels all types of surfaces and scattering••Simple to implementSimple to implementIncoming raySampledreverberations8Ray Tracing Trade-offsDisadvantages• Subject to sampling errors (aliasing)• Depends on receiver positionDisadvantagesDisadvantages••Subject to sampling errors (Subject to sampling errors (aliasingaliasing))••Depends on receiver positionDepends on receiver positionOverview of ApproachesRay tracingBoundary element methodsImage source methodsBeam tracingRay tracingRay tracingBoundary element methodsBoundary element methodsImage source methodsImage source methodsBeam tracingBeam tracing9Boundary Element MethodsSolve wave equation over discretized surfacesSolve wave equation over Solve wave equation over discretized discretized surfacessurfacesRadiantEnergyExchangeRadiantEnergyExchangeBoundary Element Trade-offsAdvantages• Works well for low frequencies• Simple formulationAdvantagesAdvantages••Works well for low frequenciesWorks well for low frequencies••Simple formulationSimple formulationBi = Ei + ρi Σ Bj Fij10Boundary Element Trade-offsDisadvantages• Complex function stored with each element• Form factors must model diffractions & specularities• Elements must be much smaller than wavelengthDisadvantagesDisadvantages••Complex function stored with each elementComplex function stored with each element••Form factors must model Form factors must model diffractionsdiffractions & & specularitiesspecularities••Elements must be much smaller than wavelengthElements must be much smaller than wavelengthd2d1 |d1 - d2 | << λOverview of ApproachesRay tracingBoundary element methodsImage source methodsBeam tracingRay tracingRay tracingBoundary element methodsBoundary element methodsImage source methodsImage source methodsBeam tracingBeam tracing11Image Source MethodsConsider direct paths from “virtual sources”Consider direct paths from “virtual sources”Consider direct paths from “virtual sources”Image Source Trade-offsAdvantages• Simple for rectangular roomsAdvantagesAdvantages••Simple for rectangular roomsSimple for rectangular roomsVirtual Sources arranged in grid patternRS12Image Source Trade-offsDisadvantages• O(nr) visibility checks in arbitrary environments• Specular reflections onlyDisadvantagesDisadvantages••O(O(nnrr) visibility checks in arbitrary environments) visibility checks in arbitrary environments••SpecularSpecular reflections only reflections onlyOverview of ApproachesRay tracingBoundary element methodsImage source methodsBeam tracingRay tracingRay tracingBoundary element methodsBoundary element methodsImage source methodsImage source methodsBeam tracingBeam tracing13Beam TracingTrace beams (bundles of rays) from sourceTrace beams (bundles of rays) from sourceTrace beams (bundles of rays) from sourceBeam Tracing Trade-offsAdvantages• Takes advantage of spatial coherence• Predetermines visible virtual sourcesAdvantagesAdvantages••Takes advantage of spatial coherenceTakes advantage of spatial coherence••Predetermines visible virtual
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