4! Computer Graphics, 26,2, July 1992

Sound Rendering

Tapio Takala* and James Hahn~

*Helsinki University of Technology02150 Espoo, Finland

tThe George Washington UniversityWashington, DC 20052

Abstract

We present a general methodology to produce synchronizedsoundtracks for animations. A sound world is modeled byassociating a characteristic sound for each object in a scene.These sounds can be generated from a behavioral orphysically-based simulation. Collision sounds can becomputed from vibrational response of elastic bodies to thecollision impulse. Alternatively, stereotypic recorded soundeffects can be associated with each interaction of objects.Sounds may also be generated procedurally, The soundworld is described with a sound event file, and is rendered intwo passes. First the propagation paths from 3D objects toeach microphone are analyzed and used to calculate soundtransformations according to the acoustic environment.These effects are convolutions, encoded into two essentialparameters, delay and attenuation of each sound. Time-ciependency of these two parameters is represented withkey frames, thus being completely independent of theoriginal 3D animation script. In the second pass the soundsassociated with objects are instantiated, modulated byinterpolated key parameters, and summed up to the finalsoundtrack. The advantage of a modular architecture is thatthe same methods can be used for all types of animations,keyframed, physically-based and behavioral. We also discussthe differences of sound and light, and the remarkablesimilarities in their rendering processes.

CR Categories and Subject Descriptors: 1.3.7[Computer Graphics]: Animation.

Additional keywords: audio, multimedia, soundtrack,physically-based modeling, virtual reality.

Permiwltm h} copy without fee all or part of this material !s grantedprovided that the copies orc not made or distributed for direcicommercial advantage, the ACM cupyrigh[ notice and the title nf thepublication and Its date appear, and nmice is gwen that copying is bypermission of the Association fur Computing Machinery. To COPYntherwise, or to republish, requires a fee and/or specific permission.

1 Introduction

In traditional hand-drawn animation, sound effects and theirsynchronization to the motion are of utmost importance.Often the whole story is first composed as a musical barsheet, on which the movements are designed based on keyevents [17]. Sounds are usually dubbed onto the action afterthe motions are generated but this is a tedious manualprocess and requires expertise to synchronize correctly. Incomputer animation, similar techniques have been used inkey-framing and rotoscoping. However, most of thecomputer animations produced have emphasized the motionitself and have added sound during post-production. Themajor reason is that there does not yet exist a generalframework for sound synchronization. This is especiallytrue in behavioral or physically-based motion control wherethe lack of absolute control have made the motion-to-soundsynchronization difficult. A notable exception from themainstream is the film “More Bells and Whistles” [9].There, both music and animation were designed as a singlescore, which served as a synchronizing controller for bothMIDI-driven music synthesizers and animated syntheticactors.

Video games and multimedia installations [22] havealso relied on synchronized sound. Sound as anotherdimension of interaction has been utilized in user interfacesto symbolize objects and to draw attention to alerts [6, 2].In scientific visualization, sound can be used to characterizeobjects’ attributes and to emphasize timing of events [10].Simulations of sound wave propagation have been done toanalyze room acoustics or dummy head models [21], andspecial hardware built to perform these effects in real time[5], but to our knowledge none of these has been combinedwith animated graphics except for visualizing the acousticalparameters [15].

1.1 The Nature of Sound

As waves, both light and sound behave similarly in manyways. Both propagate as wavefronts, spreading in alldirections according to the Huygens’ principle. They reflectand refract whenever there are discontinuities in the

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medium, and obstacle edges cause diffraction. However,their different propagation speeds and wavelengths causeessentialpracticaldifferences.Light travels instantaneouslywithout noticeabledelay, and its wave nature only appearswhen it interacts with structures of microscopic size. Onthe other hand, the speed of sound easily causes delaysperceived as echo or reverberation. There is considerablediffraction, too, because the wavelength is of humanproportions – the sound propagates around the edges ofobjects. For these reasons, sound propagation cannot beaccurately traced using simple ray optics.

The human sensory organs for light and sound aresensitive to different characteristics. The eye has goodspatial resolution, whereas the ear integrates signals fromall directions. Light is sensed as a color spectrum integratedover a period of time, and not as individual waveforms.Sound instead is perceived in time rather than as astationary spectrum in frequency domain.

1.2 Sound Signals and Convolutions

Sound is a one-dimensional signal that can be represented asan intensity regularly sampled in time. Out of possiblerepresentations this appears to be the most general andsuitable for our purposes. The concepts of pitch and notelength are akin to traditional music but are unable todescribe speech or noise. A spectral distribution (Fouriertransform) with phase and amplitude of each component istheoretically complete, but is intuitively difficult for otherthan stationary waveforms, and is not at all suitable fortime-dependent effects like echo. Similar arguments applyto other integral representations, like Laplace transform forexample.

As an object generates sound in a three-dimensionalenvironment, it acts like a light source in image rendering.Its signal is propagated in all directions, reflected andrefracted by other objects and participating media, andfinally caught by a receiver. The received signal is anintegral of signals via multiple simultaneous paths fromthe emitter to the receiver. To compute this integral, eachpossible path can be independently traced through theenvironment, its effects on the sound signal calculated, andthe results composed as a convolution of the originalsound

m

received(t) = ~ w(t,%) oemitted(t – ~) dr

o

where w(t,~) is the amount of signal received through allpaths with delay z.

The convolution weighting function w(t,@ correspondsto the paths of different lengths causing different delays andattenuations for the same signal. Generally it is time-dependent, continuous and semi-infinite. For computationalpurposes it has to be discretized into a finite number ofsamples. The script format we are going to present is apossible way to do this, emphasizing the role of movingobjects as the cause of time-dependencies in convolution.

1.3 Outline of the Paper

In this paper we present a structured methodology forgeneration, representation, and synchronization of sounds incomputer animation. In section 2, we will outline theoverall system structure as a pipeline with sound signalsflowing through it. This is followed by a detaileddescription of each module of the system. First, (swtion 3)we describe how natural sounds may be generated byphysical phenomena and how characteristic sounds areattached to geometric objects in three-dimensional space(section 4). Next, we show how the modulation of signalsdue to their propagation in an environment can berepresented as convolutions (section 5). The finat process isthe rendering of key-framed sounds by resampling theoriginal signals (section 6). Examples of various effects arealso presented.

2 Sound Rendering Pipeline

Thebasic idea in our approach is that sounds are treated asone-dimensional data objects associated with geometricobjects of a three-dimensional world. Each sound is a time-dependent signal. Much like a graphical texture map, it islocated on a geometric object, but extends in time instead ofspatial dimensions. It may be bounded or semi-infinite. Inthe latter case it can be either a repeated waveform or afractal-like continuously changing noise pattern.

We call sound rendering the process of forming thecomposite soundtrack from component sound objects. Thisis due to its methodological similarity to image renderingand texture mapping and its close connections to the samegeometric data. To keep the process manageable, we havedivided it into a pipeline of processes, as shown by theoverall system architecture in figure 1. First process (I) isthe generation of the prototype sounds that are characteristicof each object and its interaction with others. These can beeitherbased on modal analysis of elastic body vibrations, orthey can be user-defined (recorded or synthesized). In thenext process (II), the prototype sounds are instantiated aridattached to moving three-dimensional objects, based on thesame physical or behavioral simulation that controlsmotion. Following that, (111)the modulatoq effects of thethree-dimensional environment are computed astransformations from sounds on the objects to sounds at amicrophone. These time-dependent sound transformationsare represented independently of the original object sounds,and are finally (IV) applied to the sounds in the last process.Thus just a reference of prototype sound goes throughprocesses 11and 111,and the samples are actually used onlyin process IV,

The sounds produced by objects may be endogenouslike barking, yelling or talking. Such prototypes can bedigitally recorded, analogous to using digitized photographicimages as textures. Alternatively they may be synthesizedby behavioral models, like the buzz of a bee determined bythe way it flies. Other, more physically-based soundsemanate from vibrations of bodies, caused by interactive

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Computer Graphics, 26, 2, July 1992

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Figure 1: Parallel pipelines for image and sound rendering.

forces between objects and their environment. Examples ofthese are collisions, friction, and turbulent air flow aroundan object. Spectral composition may be used for thesesounds, as has been used for textures [12].

In our system, we separate a sound and its associationto objects. The characteristic potential sound is representedas a sampled signal or procedure, whereas its instantiationis described in a sound script. The script describes when andhow a characteristic sound is actually generated, determinedby certain events in the animation, like physicallycalculated collisions. Attachment of prototype sounds toobjects located in space-time is comparable to the geometricmapping of textures to object’s surfaces.

For an animation, the sounds are recorded by virtualmicrophones usually attached to a virtual camera. A sound

may undergo various modulations during its course from ageometric object to the microphone, through the simulatedenvironment. It is attenuated due to the dispersion of energyin space, and is delayed by fhe traveling time along a soundpath. The emission of sound from an object may vary bydirection, and it maybe reflected, refracted or obscured byother objects, much as light waves are. The sound’sspectrum (sound color or timbre) may be modified in theseinteractions, as well as due to the participating medium.Finally, the intensity of a sound hemd by a microphonemay vary due to its directional sensitivity. These processescorrespond to the mapping of textures from geometricobjects to the image plane. This is why we use the termsobjec[ space and image space for the time-frames of soundsas well as for the corresponding geometric coordinatesystems.

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Since sound signals are additive, all the effectsdescribed above are computed in a resampling processindependently for each emitted sound, and summed up(mixed) to make a complete soundtrack. In stereo, this willbe done separately for each channel.

We have implemented an experimental sound rendereras a collection of software modules that can be pipelinedtogether. Our implementation is written in C language andcurrently runs on a Macintosh IIci. For this equipment thesound intensities are represented with only 8-bit sampleresolution, causing noticeable digitization noise. For higherquality sounds, we have used AIFF files with 16-bitresolution, from which the sounda are reproduced withSilicon Graphics Indigo. As an alternative, we have alsoconsidereda MIDI-basedinterface to a high-quality musicsynthesizer, with object sounds selected from its library andmodulated in real time. However, it has appeared ratherdifficult to find suitable MIDI-driven components toproduce all the effects needed.

v

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Figure 2: Vibration modes of a guitar string.

3 Sound Synthesis

Sound can be synthesized from physical principles in thesame way as physically-based motion control generatesmotion [1, 16]. However, this is a much more difficultproblem, because many material factors involved are poorlyknown. In this sense it is analogous to determining color ofa material based on its physical properties [8]. Someheuristics can be used to simplify the process for certainclasses of sounds.

3.1 Vibration of Bodies

Many sounds are generated when objects vibrak after beingstruck. The process is difficult to model for arbhm.ry objects

without using complex finite-element models [14]. Oneway to attack this problem is to calculate the naturalvibration modes of a body, and to approximate a complexvibration as a weighted sum of them [11]. Though notstrictly correct for transient vibrations, this approach can bedeveloped to give subjectively quite acceptable results.Crucial in it is the ability to calculate the appropriateweight for each mode, based on the body’s deformation at acollision. This is generally a complex problem. In thefollowing we demonstrate it with a simple example.

In thin bars or strings of musical instruments, thenatural harmonics are standing waves with displacementsalong the string given as dn(x) = wn sin(nnx). Thevibration modes are orthogonal, so assuming the initial restposition of the string as dJx), the weighting factor of eachmode is the integral

*1

Wn = I do(x) .dn(x) dx

o

For example, we assumed the initial displacement to betriangular, as when stretching a guitar string with a pick(figure 2). Then

do(x) = ~ for x SD, do(x) =% forx2D

and the weights will be

The sum of the weighted components is multiplied byan exponential decay function, with damping factorproportional to the frequency. This gives a waveformcorresponding to the displacement of string at the pointwhere it was struck, which can be used as a prototypecollision sound for the string. Each stroke of the string willthen generate an instance of that sound, with amplitudeproportional to the magnitude of the collision impulse.

3.2 Friction and Turbulence Noise

Sounds generated by two objects rubbing against each otheris a poorly understood process caused by microscopicsurface features of the materials of the two objects. We havechosen to represent the process as a combination of twofactors. First, the surface features cause both of the objectsto vibrate in the same way as a phonograph needle vibrateswhen dragged in the groove of a record disk. The waveformof the sound generated is similar to the shape of surfaceimperfections of the objects. The so-called I/f-noise [19,20] could be used to model this phenomenon for roughsurfaces. Another type of frictional noise we have simulatedis generated by an object which alternates between slidingand sticking on a surface. This kind of interaction happens,for example, between a violin string and the bow. Theresulting sound signal is approximated as a sawtoothwaveform. Variation in the coefficients of friction can be

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modeled by adding some randomness to the wavelength,introducing noise to the sound.

Objects that disturb the air by causing turbulence a~sogenerate sounds. Modeling the frequency components ofthis phenomenon is difficult and outside the scope of thispaper. We simply represent this as white noise modulatedby the velocity of the object through the air and by theamount of air that it disturbs (a purely geometric factorwith experimental values).

3.3 Other Procedural Sounds

Other subjectively interesting sounds can be genemted withprocedures that are not physically-based but model thebehavior of an object. For example, we have synthesizedthe sound of an ambulance siren as a single tone frequency-modulated by a slow sine wave (figures 4 and 7).

The insect-like sound for behaviorally animated bees(figure 9), was generated as a constant wave-form with anoisy but narrowly tuned wave-length. Each bee of a swarmhas a distinct base frequency that slowly drifts around apreselected mean frequency, either randomly or according tothe bee’s velocity.

4 Attaching Sounds to Objects

In hand-drawn animation, all important events, like thebounce of a hit in figure 3, are located at frame times.

In addition to the starting time, we can also specify the

sound’s amplitude any time along its duration. Betweenthese key values the amplitude can be interpolated (lowerpart of figure 3).

What we have described are sound [breads. These aresequences of key values extending over the sounds lifetimefor each sound event. They can be put in an interface file asa sound script, described in detail in section 6.

The key events of a script cart be either defined by theanimator, like in the example above, or automaticallycomputed by a behavioral or physically-based motioncontrol. For example, we have used the impulse after acollision calculated by a physically-based motion controlfor rigid bodies [7] to define the script (figure 8 shows aframe from the animation). For each object involved in acollision, a sound thread is started at the time of collisionwith an amplitude proportional to the impulse. With thismethod we can automatically produce accuratelysynchronized sound effects for complex situations thatwould be very difficult to achieve by other means.

Some sounds, like the turbulent wind noise, haveinfinite extent. They are represented in the script as threadsextending throughout the duration of an animation scene.

5 Sound PropagationIn the following, we overview various effects of the

These key frames can ‘k used to synchronize sound effects. acoustical environment and demonstrate how they can beFor example, we can mark the starting times of each incorporated into the system. The purpose is not to makerecorded sound effect and use a sequencer and mixer to put detailed modeling of acoustics, but to show that each effectthem all together. can be encoded as a transformation in the sound rendering

script.

Figure 3: Keyframedsoundthreadfor a hand-drawn animation.

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~omposition

I I I I I I I I [ I I-50 -40 -30 -20 -lo 0 10 20 30 40 50m

object spacesound

image spacesound

Figure 4: Key-framed values of amplitude and delay for a moving sound source,and the corresponding mapping of sound signal from object to image space.

5.1 Effects of Distance and Direction

The simplest acoustic effect is due to the dispersion ofsound waves into the environment. Assuming no otherattenuation, the intensity decays proportionally to thesquare of the distance travelled, and the signal is delayed bya time proportional to the same distance. Denoting soundvelocity by vS,we have for amplitude and delay

where d is the distance traveled, and A. is the sound

intensity at a certain reference distance ~. The effect of

delay should be taken into account if the scene dimensionsare of macroscopic magnitude, comparable to the soundspeed. A delay of less than 50 ms is already clearlynoticeable, corresponding to a distance of 15 m inatmosphere with a sound velocity of approximately 330m/s.

Figure 4 illustrates sound animation of an ambulancepassing a standing listener. The image space soundenvelope shows the amplitude variation due to the 1:5 ratioin minimum and maximum distance between source andreceiver of sound. Driving speed of 100 km/h gives anoticeable Doppler effect, with a deviation in pitch roughlycorresponding to two halftones up and down from the car’soriginal sound. When the car moves from the left field ofview to the right, it gives a stereophonic illusion ofmovement.

The emission of sound may be directional. However,usually some sound is emitted in all directions. Thereseldom are as abrupt edges in its directional distribution asthere are in directed light sources with flaps. Thus aspherical harmonics approximation [13] is appropriate.

Similarly, the microphone’s dhwtional sensitivity canbe described with a spherical harmonic function. Arepresentation sufficient in practice is given by the formula

s(~) = c +(1 + Cosp)k

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Comouter GraDhics. 26, 2. Julv 1992

where p. is the angle between the microphone’s principalaxis and the incoming sound wave. Value k=O defines anomnidirectional shape, and k=l produces the typical cardioidsensitivity shape (figure 5). Lateral stereophonic hearing,due to differences in directional sensitivity of left and rightears, can be easily simulated with hvo microphones attachedto opposite directions on a camera. With the sensitivityparameter k= 1, the sum of left and right channels will beomnidirectional. Both sensitivities can be multiplied by afonvard directed shape function, if rear attenuation is desired.

s

/dlredbnor8ound

principaldlmtlonM ofmicrophone

— —. ..—.

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wFigure 5: Microphone sensitivity shape (with k=l, C=O).

visibility does not completely cut off a direct sound, butonly gives a smooth damping.

Based on these arguments and the fact that the purposeof sound in animation is rather illustrative than exactacoustical analysis, we use a heuristically simplified soundtracing model to calculate the effects of interfering objects.The basic idea is to find all major paths of sound from asource to the microphone. Each of them is represented as aseparate sound thread with delay and attenuationcorresponding to the path length and reflectivitycoefficients.

As in radiosity calculation, each reflecting surface isconsidered a secondary diffuse point source receiving energyproportional to its area and the cosine of the angle betweenits normal and sound source direction. To calculate theamount of re-radiated sound we use the same reflectionformula as is traditionally used for shading, consisting of adiffuse radiation in all directions, and a Phong-like specularterm. The ambient sound in an environment is not modeledas a separate term for each object, but as a globalbackground sound at each microphone.

Due to diffraction, the shadowing effect of objectsobscuring a sound path (the form factor) is moreapproximate than with radiosity. In this paper we do notattempt to make a detailed geometric analysis, but use arule of thumb. Attenuation is approximated with a formfactor proportional to the amount of occlusion.

The total modulation of sound intensity is now theproduct of all directional functions in addition to theattenuation by distance.

where c and u are the angles between the sound ray and theprincipal directions of sound source and microphone,respectively.

5.4 Sound Tracing in an AcousticEnvironment

A common effect in acoustic environments is reverberation.It is caused by reflective objects in the scene acting assecondary sound sources. Algorithmically, this meansmaking multiple instances of sound threads, with differentdelay and amplitude corresponding to each path through theenvironment. Generally this transformation would be aconvolution of the signal with a continuous weightingfunction. In practical calculations, the weighting function isdiscretized to a finite number of samples. Reverberation isthus modeled with multiple echoes. In our approach eachecho generates a separate thread for the sound renderer.

Because the sound wavelength is comparable to thegeometric features of the objects, reflections are usuallyvery diffuse. Specular reflection is soft, and refraction can inmost cases be neglected. Due to diffraction, sound wavescan propagate around a comer. Thus an obstacle occluding

Figure 6: Principle of sound rracing.

A frame from an animation to demonstrate these effectsis shown in figure 6. A standing car is producingcontinuous sound, which is received through two paths,directly and reflected by a wall. As the wall rotates, the echois strongest when it is in an ideal mirroring position, anddisappears when the tangent plane of the wall separates thecar and the listener. As another wall moves by, it obscuresvisibility of the car first and then the mirror, darnping eachsound for a period.

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6 Representation and Processing ofSound Scripts

The sound script defines how a prototype sound signal willbe instantiated, and how it is transformed by the acousticenvironment. This process will be best understood by ananalogy with the mapping of a texture from texture toimage space.

In a sound script all acoustic effects of the three-dimensional world are encoded in a geometry-fke form. Anadvantage of making this transformation a separate processis that all the complex effects can be precomputed andcombined in the same way as a sequence of geometrictransformations can be concatenated into a singletransformation matrix. Then each object sound can berendered and checked separately, before mixing (overlaying)all sounds together. Another benefit is that this part of thesound renderer can be used for any key-framed animation,without necessarily having a three-dimensional model.

In this section we first describe how a sound script isused to describe transformations of sounds from prototypesto the soundtrack. Then the resampling algorithmsinterpreting the script and performing the transformation foreach sound are discussed.

6.1 Representing Sound Transformationsby Key-Framing

For describing a sound signal we have two independentcoordinates, time and intensity, each of which can betransformed. For intensity, only scaling (amplitudemodulation) is usually acceptable, since any non-linearity isperceived as distortion. Simple translation in time defineswhen a sound begins or how much it is delayed, whereasmodifying the time scale causes change in pitch (frequencymodulation). An arbitrary monotonic mapping – excludingreversal of time, which would be rather unnatural – can beapproximated by interpolating specified key values of soundattenuation and delay (corresponding to the amplitude andphase angle of stationaq signals),

Our script format for sound transformations consists ofthreads of values for attenuation and delay, one thread foreach instantiated object sound. Each line of a script filecontains the following information:

- keyword (start, in-between key, or end of a thread)

- ID (number) of a thread

- time stamp of the key

- attenuation and delay (for each stereo channel).

The file may be sorted by thread ID and or time s?amp,depending on the resampling algorithm that calculates thesoundtrack.

Key values may be specified at any points of time. Inbetween the values are interpolated. Since the ear’sresolution of intensity is not very high, we have found that

linear interpolation is usually sufficient for amplitudevalues. However, the ear is very sensitive to abrupt changesin pitch. Thus, in order to keep the delay’s rate of change(pitch level) continuous, either higher order interpolation ordense spacing of keys is needed. For simplicity, we haveused the latter solution, specifying keys at each frame of ananimation.

6.2 Resampling Algorithm

Just as in texture mapping, a sound transformation can becomputed with an algorithm doing resampling either insound object space or sound image space.

With an object space algorithm, each sample of aprototype sound is multiplied by the correspondinginterpolated amplitude, and is written to a sound imagebuffer translated in time according to the correspondinginterpolated delay (figure 4). A major problem with thisapproach is that gaps may be left in image space if thesignal is expanded

An image space algorithm determines the value foreach image buffer position by sampling in object space at apoint determined by the inverse transformation. The inversemapping cannot be directly computed in our case, becausethe mapping of time (the delay) is defined in object space.We solve this problem by mapping the key positions fromobject space to image space, and interpolating the mappingparameters linearly. The interpolated delay gives the inversemapping for each sample.

The same aliasing problems arise in soundtransformations and sampling, just as they do in texturemapping, and could be solved similarly [4].

7 ConclusionsSound rendering is a novel approach allowing the motion todefine the sound, as opposed to the traditional way ofstarting with a soundtrack. This allows all types of motioncontrol schemes to synchronize sound. With a physically-based motion control the sound events can be automaticallyproduced, even if the objects’ prototype sounds are notphysically defined. With keyframed motion, the soundparameters can be keyframed as well. If the motion is three-dimensional, physically-based simulation of soundpropagation can determine many acoustical parameters in anatural way.

In this work we have defined a modular sonic extensionof the image rendering pipeline. Analogies have been drawnbetween sound and texture. Both are transformed fromobject to image space using similar algorithms with similaraliasing problems. We have simulated acoustical effects bysound tracing, analogous to forward ray-tracing andradiosity. With this analogy, the sound transformationscorrespond to shaders in a shade tree during its traversalfrom a source to a camera [3, 18]. We have applied thetechnique to generate sounds for a complex animation usingkey framing, behavioral, and physically-based motioncontrols that illustrates its generality and flexibility.

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One area we are currently working on is more rigorousphysically-based modeling of sound-causing phenomena andsound propagation in acoustical environments. In this paperwe have only given hints on how to approach the problemheuristically.

8 AcknowledgementsThis work has been made possible in part by HelsinkiUniversity of Technology, who provided support for TapioTakala’s sabbatical to the George Washington University.

This work was also partly supported by funding fromNASA (NCC 5-43) and NRL (NAVY NOO014-91-K-203).

We would like to thank the students in the ComputerGraphics and User Interface Group at George WashingtonUniversity for their assistance. Special thanks go to LarryGritz, Daria Bergen, and Rudy Darken for providing theimage from “Graphic Violence”.

We would also like to thank the reviewers for theirenthusiastic comments and many useful suggestions.

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SIGGRAPH ‘92 Chicago, July 26-31, 1992

Figures 7: Frame from a key-framed animation. Figure 8: Frame from a physically based animation.

Figure 9: Frame from a behavioral animation.