Classical ray-tracing techniques, which have produced the mostrealistic computer-generated images to date, are being

enhanced in this developmental system.

A Testbed for RealisticImage Synthesis

Roy A. Hall and Donald P. Greenberg

Cornell University

Our goal in realistic image synthesis is to generate animage that evokes from the visual perception system aresponse indistinguishable from that evoked by the ac-tual environment. This objective requires the ability tomodel the physical behavior of light, specifically withinthe visible range, as it is propagated through an environ-ment. Once the physical behavior is modeled, we mustthen display the result in such a manner that it is per-ceived correctly.We can describe the propagation of light through an

environment, using mathematical models of the physicallaws governing electromagnetic radiation. This descrip-tion of light propagation is independent of viewer posi-tion. In generating an image of the environment, we wishto "capture" the electromagnetic events, specificallylight energy, at an arbitrary image plane and display thisfor a viewer. For example, a camera is commonly used torecord the events at an image plane on film, which canthen be projected for viewing. In computer graphics, wecan bypass the camera, and even the physical environ-ment, and instead simulate the way light would reach animage plane from a modeled environment.

In the past, image generation schemes computed im-ages so that they could be sent directly to a displaydevice. The processes of light propagation, image cap-ture, and image display, as well as the perceptual con-siderations of the viewing environment, have traditional-ly been lumped into a single computational operation.However, image synthesis should be addressed as amultistep process because the problems and constraintsassociated with display resolution and color reproduc-

tion are independent of the methods used for the model-ing of light propagation and the determination of the in-tensity at the image plane.The initial step in the process is the modeling of the

physical environment, including object geometry, objectpositions and orientations, material characteristics andsurface finishes, and lighting attributes. Although themodel geometrically describes a physical environment, itis not necessary for the environment to actually exist.

The second step is the simulation of light propagationthrough the environment. The light energy incident on anysurface of the environment is described as a summation oflight coming directly from light-emitting sources and lightreflected from other surfaces in the environment. The in-direct light energy is often referred to as "global illumina-tion information." Once the global illumination informa-tion for the environment has been determined, it should bepossible to determine the intensity ofthe light leaving anysurface in the environment in any specified direction.The third step is to determine the intensity function at

the image plane (Figure 1). If an image plane could be in-strumented so that the spectral intensity moving throughthe plane toward a viewer could be sampled at any point,it would be possible to map the energy that reaches theeye through the image plane as a function of the locationon the plane (x,y) and the wavelength (X). We refer tothis mapping as the intensity function at the image plane.In a real scene, this function is continuous in both thespatial and intensity domains. In computer graphics, thecomputation of intensity at the image plane should

0272-1716/83/1100-OOOSO1.00 i 1983 IEEE10 IEEE CG&A

reduce to projecting small discrete areas on the imageplane into the environment and integrating the intensityof the visible objects within the projection of each dif-ferential area to determine the corresponding intensity.Prior to this computation, it is obviously necessary todefine the viewing conditions, including viewer position,view direction, and field of vision.The fourth step is the conversion of the discrete image

plane intensity information into a displayable form,culminating in the display of the image. This step can besubdivided into a number of operations, includingtransformation to the display pixel resolution, filteringto eliminate aliasing, adaptation to the color limitationsof the display device, and conversion to the appropriatered, green, and blue components. The distinction be-tween the intensity function generation process and thedisplay process is important; thus, we discuss displayoperations as a separate step in the total image genera-tion process.

This multistep process has been implemented in thesystem we describe in this article-a testbed system forthe generation and display of realistic images, developedin Cornell University's computer graphics program. Cur-rently, the system uses ray tracing for image generation,with a number of enhancements to previous ray-tracingschemes, but the flexibility of the system structure wouldallow the use of other rendering methods.

Historical overview

The methods applied to realistic image synthesis, aswell as the connotation of the term "realistic" in com-puter synthesized images, have changed greatly in thepast two decades. Many of these changes can be at-tributed to advances in hardware as well as in software.Increased computational speed of equipment and tech-nologies that allow both high spatial resolution and highcolor resolution have made possible the generation anddisplay of very sophisticated images.

Early approaches to realistic image synthesis withraster displays primarily involved the visible surfacedetermination of polygons, not the determination oftheir color. Examples of such algorithms are those bySchumacker et al., l Newell et al., 2 Warnock,3 Watkins,4Weiler and Atherton,5 and Sechrest and Greenberg. 6 Acomprehensive review of this type of algorithm appears in"A Characterization of Ten Hidden-Surface Algorithms"by Sutherland et al. 7 In all of these efforts, emphasis wasplaced on the determination of the portion of the en-vironment that should be displayed, rather than on thelight reflection model and the realism that is generated bycolor and texture.Many of these algorithms used the reflection from a

Lambertian diffuse surface to determine the color of thedisplayed polygons. Warnock used a reflection modelthat included both an object color term and a specularterm. Gouraud8 proposed a method of color interpola-tion across polygonal approximations that wouldgenerate the appearance of smoothly curved surfaces.Phong9 proposed an alternate method that interpolatedsurface normals across each polyon and applied a reflec-

tion model for the determination of the color of each pix-el as a function of the direction of the surface normal.The Phong reflection model, an empirical approxima-

tion of observed data, has been particularly significant inthe evolution of realistic image synthesis methods. Itsformulation includes a diffuse term that provides surfacecolor and shading, and a specular term that providesrealistic highlights from direct light source reflections.The model is very easy to implement and is still widely inuse. Additionally, Phong recognized that to achieverealistic appearance, surface normals must be mapped toevery pixel before the application of the reflectionmodel.

Basing them upon the Torrance-Sparrow reflectionmodel, 10 Blinn11 12 suggested less empirical improve-ments of the Phong reflection model. His consideration ofthe specular component of the reflection led to the obser-vation that, for mirror-like surfaces, the magnitude of thespecular component is related to the intensity that reachesthe surface from the mirror direction. He also proposed anumber of methods for providing realistic textured ap-pearance, which greatly increased apparent scene com-plexity and, subsequently, increased scene realism.Cook and Torrance'3 proposed a reflection model

that describes the behavior of light in terms of energyequilibrium and electromagnetic wave theory, basedupon the Beckmann scattering model. 14 Application ofthis model results in a very realistic image appearance ofa wide variety of materials with varied surface finishes.Unfortunately, the model -requires spatial integration ofthe global illumination information to provide the inci-dent energy on a surface. None of the present methods ofimage synthesis can generate the information requiredfor application of this model to situations other than anisolated object suspended in space.

Perhaps the first use of global information in calculat-ing intensities for image generation was accomplished by

Figure 1. Intensity function at the image plane.

November 1983 11

mapping an environment onto a global hemisphere. 15Intensities were computed from a look-up table that pro-vided intensity information from any direction in the en-vironment. This method was adequate for describing thereflection of an environment distant from the object be-ing rendered, but could not provide information for theinteraction of two objects in close proximity.A more appropriate and general approach is ray trac-

ing. Ray tracing was suggested by Appel 16 and later usedby MAGI 17 to solve the hidden surface problem. In at-tempts to solve the global illumination problem, themethodology was extended by Kay 18 and by Whitted 19in his classic paper. Ray tracing is used to determine theglobal illumination information relevant to the imageplane.The results of ray tracing have been some of the most

realistic images to date. However, there are many scenesthat cannot be adequately modeled by ray tracing, andthere are several shortcomings to the methods that havebeen implemented. First, the reflection models are em-pirical and have not accounted for the theoreticalbehavior of light and the required energy equilibriumconditions. Second, the ray-tracing method providesonly point-sampled information, which, in addition tocausing aliasing problems, is not sufficient for the ap-plication of energy equilibrium models to light behavior.Third, the method combines the modeling of global il-lumination and the computation of the image plane in-tensity function into a single operation. Fourth, the

method of application of the reflection model hasresulted in a loss of spectral information at the imageplane. Thus, despite the impressive images, there are stillmany improvements to be made.

Implementation of a testbed system

Components of an image synthesis system must per-form the following tasks:

(1) environment modeling,(2) assignment of viewing parameters (setup opera-

tion),(3) simulation of light propagation through the en-

vironment,(4) calculation of the image plane intensity function

(image generation), and(5) display of the image plane intensity function (im-

age display).A testbed imaging system (diagrammed in broad

outline in Figure 2) was implemented in the Program ofComputer Graphics at Cornell University to performthese tasks. The main goal in the development of thisgraphics testbed was a flexible, modular system thatwould impose a minimum of constraints on futureresearch. The system separates the imaging process into aseries of functional processes that communicate throughthe use of files. The file structure has been designed toassure flexibility and the retention of all required image

ENVIRONMENT MODELING

lPLANARPOLYHEDRA l

I lOBJECTS OF IREVOLUTION I

I ENVIRONMENTI BUILDER

PARAMETRICl SURFACES

CANON ICALlllDESCRIPTIONS_l

I QUADRIClSURFACES MATERIAL

L__ _ LIBRARY

l LIGHTS TEXTURE I

I - | LIBRARY |

F__ __ _ _ _ ____

IMAGE GENERATION

I I

I II I

I

I SCAN-LINE I

I I

F'-

IMAGE DISPLAY

I IMAGE TDISPLAY

S R

I STOARAGEPARAMETERS) I I I I I

I RAYTRACE2 II

I ~~~ ~~~~~IiTDISPLAY I

I I I I

I I I I

L_ _1 L1Figure 2. Testbed image synthesis system of the Cornell Program of Computer Graphics.

IEEE CG&A12

information. In the system's first generation, only ray-tracing routines have been implemented, although itcould use any type of visible surface or image generationalgorithm.We have attempted to use ray tracing to perform all

the required light propagation modeling during thecalculation of the intensity function, thus combining thethird and fourth operations of the steps listed above intoa single operation. Although this methodology fails toaddress some of the issues surrounding the modeling ofglobal illumination, it does have the capability to pro-duce very realistic images and can serve as an integralpart of a system that would allow exploration of alter-native methodologies.

Environment modeling. Individual objects areseparately created by means of a number of geometric in-put routines. Separate routines exist for the creation ofcomplex planar polyhedra, objects of revolution,parametric surfaces, canonical descriptions, and quadricsurfaces. Furthermore, any geometric modeling systemcan be used as an input routine to the imaging system,provided that the bounding surfaces are accurately de-fined and that attributes can be associated with eachdiscrete surface.A unique type of input routine is used for the modeling

of light sources. 20 In addition to standard geometric in-formation, the program allows the user to define spectralenergy distribution and directional intensity of the lightsource.The environment builder consists of a set of editing

routines that perform two basic functions. The first is thepositioning of created objects into a global environmentdescription. All the scaling, translation, and rotation op-tions are available to accurately place objects in relationto one another. The second function is the assignment ofattributes to the object surfaces. These include surfacefinish characteristics, such as roughness and root-mean-square slopes, and wavelength-dependent properties,such as material spectral reflection curves and texturepatterns.

Viewing and image parameters. A setup program pro-vides the additional information required for ray tracing,such as viewer position, image resolution, maximum

Figure 3. A ray traced through an environment.

depth of the intersection tree, cutoff threshold for the in-tersection tree, pixel subdivision criteria, spectral sam-pling criteria, and the reflection model type.

Ray tracing. A ray is traced from the eye through eachpixel into the environment. At each surface which isstruck by the ray, a reflected and/or refracted ray can bespawned (Figure 3). Each of these must be recursivelytraced to establish what surfaces they intersect. As theray is traced through the environment, an intersectiontree is constructed for each pixel (Figure 4). The final pix-el intensity is determined by traversing the tree and com-puting the intensity contribution of each branch accord-ing to the reflection model. 19The intensive computational operations in a ray-

tracing system are the intersection tree building and thetraversal of the tree for the intensity calculation. Testingfor shadows has been found to be very expensive com-putationally, particularly for environments that containcomplex lighting situations.The intersection tree consists of branches that repre-

sent the propagation of a ray through the environment,and of nodes that represent the intersection of rays withinterfaces in the environment (Figure 4). In the im-plementation used for this investigation, the intersectiontree is a binary tree implemented as a forward- andbackward-linked list. This implementation was chosenbecause the tree is generally neither full nor complete,and this scheme simplified the packing of used nodes intoa contiguous memory space. The backward link is not re-quired in the building of the tree or in the traversal of thetree for color computation, but it is often helpful in thedebugging process.

In this procedure, a dummy node is created as theparent node to the root node of the intersection tree. Thisdummy node can be thought of as representing the eye.The intersection location and direction cosines of thedummy node define the view vector for the sample point.The data block representing a node on the intersection

tree must contain sufficient information to fully describethe environment at that node. This includes informationsuch as the material at either side of the interface, the sur-face normal, the reflected vector, the refracted vector,and the distance from the previous node.

Figure 4. Intersection tree for a ray traced through the en-vironment.

November 1983

EYEEYE

TRANSMITTED

L

13

The intersection procedure controls the searchthrough the objects in the environment to determinewhich object is first encountered by a ray. This routinecalculates intersections for all object and light source en-tities.The reflection model is applied during the traversal of

the intersection tree to generate an intensity for the cur-rent sample point. In this implementation of ray tracing,it was desirable to support a number of alternate reflec-tion models to allow easy modification and comparison.We accomplished this by establishing common callingconventions for all reflection models and loading the ap-propriate routine addresses into a branch table that wasused in the tree traversal procedure.The intersection tree is traversed from the bottom up

in the process of generating the intensity at the samplepoint on the image plane. The intensity information forthe children nodes of the node currently being evaluatedis retained, and the reflection model is applied togenerate the intensity at the current node. Once therecursive tree traversal procedure has been executed, theintensity for the sample point is contained in the rootnode data block.

In actuality, the testbed imaging system is structured asa set of programs, communicating through the use offiles. These programs utilize independent modules thatgroup logically related functions. Currently definedmodules include objects, light sources, materials, texturemaps, and a variety of reflection models. For example,each unique geometric entity is a separate object moduleand is controlled by its object manager. The objectmanager is responsible for maintaining its own internaldata structure, file input and output, intersectioncalculations of the object with an arbitrary ray, and anumber of other tasks specific to the object. Interfaceswith all object managers are procedurally defined, mak-ing it possible for the global testbed system to operatewithout specific knowledge of the details within each ob-ject manager.

This modular approach has flexibility advantages andoperating speed disadvantages. Because of the modulari-ty, an experimental object can easily be added anddebugged without affecting the operation of the entiresystem. Every object is handled identically by the ray-tracing simulation routines, which are performed with asmall body of code that is easily understood and main-tained. Thus, the testbed imaging system is not affectedby an alteration in the number of available object en-tities, provided the interactive menu control program hassufficient flexibility. But modularity results in a timepenalty because each request from the ray-tracingsimulation routines must be decoded through a modulemanager, no matter how simple the request. With ourconstantly changing research requirements in mind, wefelt that this speed trade-off was justified by the flexibili-ty and simplicity inherent in the system.

Image storage. For research comparisons, it was im-portant to store the data describing the image plane in-tensity function at a high spatial and spectral resolutionand to eliminate any constraints imposed by displaylimitations. The image information gathered by the ray

tracer is transformed from the spectrally sampled valuesused for computation into the CIEXYZ color space im-mediately before encoding and file writing. (CIEXYZ is acolorimetry system, based on three primaries, estab-lished in 1931 by the Commission Internationale del'Eclairage.) Three 16-bit-deep channels of any desiredspatial resolution are used to store the respective XYZ in-tensity values of the image in run-length encoded format.The CIEXYZ color space was chosen because it is

possible to represent all perceptible colors in the positiveoctant of the color space and because transformationfrom this format into any other color display space iseasily accomplished. The 16-bit-word-per-channelresolution was selected so that very high color resolutioncould be retained. These bounds are large enough toassure adequate color resolution when display processingis performed and they remove the constraints of thedisplay or recording color resolution from the intensityfunction calculations.

In preparing an image for display and/or recording, itis necessary to consider the limitations of the displayand/or recording device and adjust the image according-ly. These limitations include spatial resolution, spectralresolution, color gamut (in both displayable chromatici-ties and intensity range), and nonlinearities of the displayand/or recording device. The required corrections forsome of these limitations, such as gamma-correcting fornonlinearity, are straightforward. The required ad-justments for other limitations, such as the color gamutand dynamic range, involve the perception of thedisplayed and/or recorded image. These adjustmentscannot eliminate errors in the display, but may renderthem imperceptible.A matrix can be generated that will transform intensity

information from the CIEXYZ space into a color spacedescribed by three primary phosphors in the case ofmonitor display, or into a color space described byprimaries representing the composite behavior of themonitor, photographic filters, film sensitivity, and pro-jection media in the case of film recording. This matrixrequires knowledge of the chromaticities and maximumintensities of the three primaries. The generation of thistransformation matrix is detailed by Meyer,21 Meyerand Greenberg, 22 Neal,23 and Wintringham. 24

Results

The following describes some of the beneficial resultsof experimentation conducted to date. (Definitions ofterms used in the illumination model equations are listedin Table 1.)

Illumination model improvements. Historically, re-flection models have considered the illumination func-tion to be composed of two portions-light reflection asa result of direct illumination from light sources, andlight reflection and transmission as a result of the globalillumination from other parts of the environment.Perhaps th& first realistic images were modeled byPhong,9 whose model included diffuse and specularterms for the direct light sources and a constant globalambient term (Figure 5a):

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Figure 5. The Phong (a), Whitted (b), and Hall (c) illumination models, with specific light source models at left and

global Illumination modeis at right.

November 1983 15

Table 1.

Definitions of terms In Illumination models.

=distance of reflected ray travel=distance of refracted ray travel=transmittance per unit length of material of reflected ray=transmittance per unit length of material of refracted ray=unit mirror-direction vector based on reflected ray=unit mirror-direction vector based on transmitted ray=intensity of sample point on the image plane=intensity of global ambient illumination=intensity of jth light source=Intensity of reflected ray=intensity of transmitted ray=light source index=material diffuse reflection coefficient=materlal specular reflection coefficient=material transmission coefficient=number of light sources=unit light source vector=exponent representing glossiness=unlt surface normal vector=unit reflection vector=Fresnel reflectance curve of material on wavelength basis-diffuse reflectance curve of material on wavelength basis=Fresnel transmissivity curve of material on wavelength basis=unit view vector

Figure 6. A ray-traced Image based on the Whitted Inter-face model (a); the same Image based on the Hall Im-proved Interface model (b).

I = kd (N.L) (object color)j=1

+ ks E nR.)Ij+I,

Whitted 19 improved the model by using a different in-terpretation of the direct specular term1I and additionalglobal illumination terms, given as the sum of the global,diffuse, global specular, and global transmitted terms(Figure 5b). The Whitted model is expressed as

I = kd (N.L) (object color)j=lI

J

diffuse fromlight sources

+ ks (N.H)1Ij + Ia + ksIr + ktI,.j=l

specular from global global globallight sources diffuse specular transmitted

We can further improve this model by including theFresnel relationships for the wavelength and angle-of-incidence dependence of the transmitted and reflectedlight, 13 the scattering of transmitted light from sources,and the attenuation of intensity of previous nodes as afunction of the filter properties of the material throughwhich the light passes (Figure 5c). 25The model for computing reflected intensity from

direct light sources is similar to that proposed by Blinn,but also includes an expression for scattered transmis-sion. Global illumination contributions other than lightsources are given as the sum of the diffuse, specular, andrefracted terms. The resulting model is expressed as

I= kd E (N.L) RdIjj_l1

diffuse fromlight sources

I

+ k, F, (N.H)nRfIjj=l

specular fromlight sources

+ ks E (N.H')TfIjj=1

transmitted fromlight sources

+ IaRd + ksRiIrFr dr + ks TfI,Ft dt

global global globaldiffuse specular transmitted

A comparison of ray-traced images based on the Whittedmodel with images based on the Hall improved interfacemodel is shown in Figure 6.

IEEE CG&A

drdtFrFtIf,Ra

Ii

IrIt

kdk,ktrn

RfRdTf7

16

Spectral sampling in color calculations. It is wellknown that the illumination, reflection, and transmis-sion characteristics of light sources, surfaces, or filtersare wavelength-dependent functions (Figure 7a). Thehuman eye is sensitive to these stimuli over the range ofvisible light, from roughly 380 to 800 nanometers. Eachof the three color receptors responds differently and can

be quantified by the typical tristimulus matching func-tions (Figure 7b). The total response received by thebrain is a result of multiplying the stimulus distributionby the tristimulus matching functions to obtain the tri-variant response functions (Figure 7c). The integrationof this response over all wavelengths leads to the threetristimulus values:

R= XErx7d X

G=jXExkxd X

B= xExbxd X

Historically, the computer graphics field has tacitlyrelied on the principles of tristimulus colorimetry but hasperformed calculations only on the red, green, and bluetristimulus color components. Since the illumination,reflection, and transmission curves are wavelength-dependent functions, this approach actually consists ofpoint sampling in the intensity domain and can lead tocolor aliasing artifacts. Furthermore, in ray-tracingschemes, since the computation of the image plane inten-sity function is the cumulative effect of the sequentialmultiplications of the wavelength-dependent functions,excessive color distortion can occur.

The testbed image synthesis system was designed toperform the color calculations at any spectral resolutionand can thus compute the correct resultant spectraldistribution on a continuous wavelength basis. The pro-cedures can also perform spectral sampling at arbitraryintervals, perform subsequent color calculations on thespectrally sampled values, and provide a means to trans-form the resulting sampled values into the CIEXYZcolor space prior to image storage and display. Unfor-tunately, when many sample points are used to approx-imate the wavelength-dependent functions, the pro-cedures are computationally expensive and more tract-able solutions are necessary.To illustrate the need to perform color calculations by

a spectral sampling methodology consistent with sam-

pling theory instead of by means of tristimulus colorspaces, we generated comparison images of a simple testenvironment. The environment consisted oftwo overlap-ping filters, illuminated by a standard D6500 lightsource. We generated a control image, using spectraldescriptions maintained at one-nanometer incrementsfrom 360 nm to 830 nm. Additional images were gen-erated, using the CIEXYZ color space, the RGB colorspace of the monitor, and a spectral sampling approachwith nine spectral sample values. It should be noted thatboth tristimulus methods yield significant color distor-tion, whereas the nine spectral samples closely approx-imate the correct intensity function (Figure 8). Althoughthe intensity calculation time increased, the total com-putation time for the nine-sample-point approach was

less than two percent greater than the tristimulus ap-

proach. The results indicate the need for increased spec-

tral resolution, and the search for correct and efficientsolutions is continuing.

Correct light source descriptions. Historically, theshading for most computer-generated images has beenbased on the assumption that lights are point sources

located at an infinite distance from the environment be-ing rendered. This assumption reduces image computa-tion because the light source vector direction is constant.Some of the illumination models previously discussed ex-

plicitly include the light vector; thus it is possible to placethe lights at finite positions and recalculate the light vec-tor for every illumination calculation. Nevertheless, thepoint source assumption leads to difficulties if the source

is within the viewable scenes.

400nm 700 nm-0 x n

TOTAL tRESPONSE B

Gt tG R

Figure 7. The response of a trivariant system to astimulus: (a) stimulus distribution function PAX; (b)tristimulus matching functions rA\ G bA; (c) trivariantresponse functions RA GA BA.

November 1983

(a) Px = EXor Px =EX TXor Px = Ex * REFL. x

17

Figure 8. Comparison of spectral sampling techniques:three samples In CIEXYZ color space (a); three samples InRGB color space (b); nine spectral samples (c). The RGBintensity graphs are shown for the same scan line in eachImage. The control Image, computed on a wavelengthbasis, appears on the left of each test Image.

Table 2.Comparative statistics for adaptive tree-depth control

In complex Image of mirrored room.

MAXIMUM TREE ADAPTIVE CONTROL AVERAGETREE IMAGE GENERATIONDEPTH DEPTH DEPTH TIME

1 NO 1.0 264 MIN.15 NO 14.89 3941 MIN.15 YES 1.71 480 MIN.

Luminaire data must include the geometric descrip-tions, positional information, and the spatial and spec-tral intensity information. The testbed image synthesissystem has incorporated this information. The geometryof the luminaire is completely defined as either a pointsource, surface of revolution, or a linear light sourcesuch as a fluorescent light fixture.20 The position andorientation of each fixture is defined in the environmentbuilder. Each light source also has two attributes asso-ciated with it. The spatial intensity information isdescribed by goniometric diagrams of revolution, such asFigure 9.26 For nonsymmetric light sources, the vectorintensity information can be interpolated between twogoniometric diagrams associated with each of the prin-cipal axes of the luminaire. This method for describingthe intensity distribution of a light source is typical in thelighting industry. Each light source also has a spectral in-tensity distribution, defined in the same manner as thematerial reflectance curves.With this information, it is possible to generate images

that not only contain the lights, but accurately simulatethe light distribution. The lights depicted in Figure 10and in the image shown on the cover were modeled assurfaces of revolution, with an intensity distributiondefined by a cosine function. This intensity function issimilar to that used for photographic light simulation,recently presented by Warn. 27 The intensity contribu-tion of the light source for each ray was determined byuse of the goniometric diagram of the source.

Adaptive tree-depth control. Ray tracing combines thevisible surface determination with a means for accumu-lating the global illumination information. Tradition-ally, an intersection tree for any sample point is con-structed to an arbitrary depth prespecified to assure thatrelevant reflections and refractions are captured in theimage. For most typical environments, however, the per-centage of the image that is comprised of reflective ortransparent surfaces is relatively low. Thus, there is con-siderable potential for computational savings if the cal-culations are carried out only when necessary.

Consider, for example, the image of a mirrored roomin Figure 1Oa. Although it appears to have vast reflectingareas, only a small percentage of the image actually con-sists of reflective surfaces. However, the specular reflec-tions are very important in generating the correct repre-sentation of the environment and must be traced to adepth of 15 reflections to recover sufficient image infor-mation. For comparison, Figure 10b shows the same im-age generated without reflection-that is, to a tree depthof one. Obviously, the resulting image is less than ade-quate.We can approximate the upper bound of the contribu-

tion of any node of the intersection tree to the final colorof the sample point, by considering the intensity of everynode on the tree to be maximum intensity. The first nodeon the tree will contribute 100 percent to the final colorof the sample point. The maximum contribution of thechildren nodes can be evaluated by setting I, and F, tounity for the reflected child and It and Ft to unity for thetransmitted child and then computing the respective con-

IEEE CG&A18

tributions. This process can be repeated for the childrenof any parent node in the tree. By multiplying the ap-proximate maximum contributions, we can compute themaximum cumulative contribution of the child node tothe sample point. Thus, by establishing a cutoff con-tribution threshold, we can adaptively control the depthof the tree during the ray-tracing process.The potential of this adaptive tree-depth control for

improving the computational efficiency in ray tracingwas tested on several environments. Statistics for thegeneration of the complex gallery environment ofFigures lOa and lOb are given in Table 2. Significantly,the average tree depth, even for this very reflective en-vironment, was 1.71, proving the efficiency of the ap-proach.

As we have shown here, Cornell University's testbedimage synthesis system has helped in the development ofa number of improvements of existing ray-tracing tech-niques. In summary, these include a hybrid reflectionmodel, a spectral-sampling method, the incorporation oflight sources, and adaptive tree-depth control. Never-theless, we point out again that many of the problems ofrealistic image generation through ray tracing have notbeen solved. The inherent point-sampling technique isprone to aliasing, the reflection models proposed do notinclude the correct energy formulations, and the com-putational expense is currently top high. The use of en-vironmental image coherence techniques would probablymake these approaches more tractable. It is our hope thatthe testbed imaging system will provide an appropriateenvironment for further exploration ofthese problems. R

Acknowledgments

Many people from the Program of Computer Graph-ics contributed to this research and the creation of thetestbed imaging system. Special thanks go to GaryMeyer, Ted Crane, Chan Verbeck, Rikk Carey, GaryHooper, Hank Weghorst, and Emil Ghinger. We hopethat this testbed environment will provide a foundationfor their continued research.We are also grateful to the National Science Founda-

tion, whose support was instrumental in the initiation ofthe laboratory and who directly supported this researchunder grant no. MCS-8203979, "Interactive ComputerGraphics Input and Display Techniques."

References

1. R. Schumacker, B. Brand, M. Gilliland, and W. Sharp,"Study for Applying Computer Generated Images toVisual Simulation," AFHRL-TR-69-14, US Air ForceHuman Resources Laboratory, 1969.

2. J. Newell, R. Newell, and T. Sancha, "A Solution to theHidden Surface Problem," Proc. ACM Nat'l Conf.,1972, pp. 443-450.

3. John E. Warnock, "A Hidden Surface Algorithm forComputer Generated Halftone Picture Representation,"tech. report 4-15, University of Utah, Salt Lake City, June1969.

Figure 9. Gonlometric diagram of luninalre showing In-tensity variations with vector direction.

Figure 10. Images of gallery with mirrored walls and locallight sources: adaptive tree depth (a); maximum treedepth =1 (b).

November 1983 19

4. G. S. Watkins, "A Real-Time Visible Surface Algorithm,"PhD dissertation and tech. report UTECH-CSC-70-101,University of Utah, Salt Lake City, June 1970.

5. Kevin Weiler and Peter Atherton, "Hidden SurfaceRemoval Using Polygon Area Sorting," ComputerGraphics (Proc. Siggraph '77), Vol. 11, No. 2, Summer1977, pp. 214-222.

6. Stuart Sechrest and Donald P. Greenberg, "A VisiblePolygon Reconstruction Algorithm," Computer Graphics(Proc. Siggraph '81), Vol. 15, No. 3, Aug. 1981, pp. 17-27.

7. I. E. Sutherland, R. F. Sproull, and R. A. Schumacker,"A Characterization of Ten Hidden-Surface Algorithms,"Computing Surveys, Vol. 6, No. 1, Mar. 1974, pp. 1-55.

8. Henri Gouraud, "Computer Display of Curved Surfaces,"PhD dissertation, University of Utah, Salt Lake City,1971.

9. Bui Tuong Phong, "Illumination for Computer-Gener-ated Images," PhD dissertation, University of Utah, SaltLake City, 1973.

10. Kenneth E. Torrance and Ephraim M. Sparrow, "Theoryfor Off-Specular Reflection from Roughened Surfaces,"J. Optical Society ofAmerica, Vol. 57, No. 9, Sept. 1967,pp. 1105-1114.

11. James F. Blinn, "Models of Light Reflection for Com-puter Synthesized Pictures," Computer Graphics (Proc.Siggraph '77), Vol. 11, No. 2, Summer 1977, pp. 192-198.

12. James F. Blinn, "Computer Display of Curved Surfaces,"PhD dissertation, University of Utah, Salt Lake City,1978.

13. Robert L. Cook and Kenneth E. Torrance, "A ReflectionModel for Computer Graphics," ACM Trans. Graphics,Vol. 1, No. 1, 1982, pp. 7-24.

.-, I

CAD SoftwareDevelopment

Impell Corporation is an $80 million company sup-plying engineering services and sottware to theelectric power industry. We have Initiated a newventure in computer aided design systems for ap-pilcatlon to architect engineering and construc-tion projects. Mini-computer experience Isdesirable for Programmers, Analysts and SystemsDesigners In the following areas:

* Computer Aided Design and Graphics Systems* Computer Aided Design and EngineeringDatabase Systems

* Engineering and Constructlon ManagementApplications

Impell offers an outstanding compensationpackage, and a stimulating environment whichfosters rapid growth for high achievers, If you wantto work on our exciting new products, contact LeeRees at (415) 5444512 or submit your resume inconfidence to Impell Corporation, 220Montgomery Street, San Francisco, CA 94104.

IMVPEU.COiC01ORATIONL lV *

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14. Peter Beckmann and Andre Spizzichino, The Scattering ofElectromagenetic Waves from Rough Surfaces, Mac-Millan, New York, 1963, pp. 1-33, 70-98.

15. James F. Blinn and M. E. Newell, "Texture and Reflec-tion in Computer Generated Images," Comm. ACM, Vol.19, No. 10, 1976, pp. 542-547.

16. A. Appel, "The Notion of Quantitative Invisibility andthe Machine Rendering of Solids," Proc. ACM Nat'lConf., 1967, pp. 387-393.

17. R. A. Goldstein and R. Nagel, "3-D Visual Simulation,"Simulation, Jan. 1971, pp. 25-31.

18. Douglas Scott Kay, "A Transparency Refraction and RayTracing for Computer Synthesized Images," master'sthesis, Cornell University, 1979.

19. Turner Whitted, "An Improved Illumination Model forShaded Display," Comm. ACM, Vol. 23, No. 6, June1980, pp. 343-349.

20. Channing P. Verbeck, Untitled, unpublished master'sthesis, Cornell University, 1984.

21. Gary W. Meyer, "Colorimetry and Computer Graphics,"Cornell University, Program of Computer GraphicsReport 83-1, Apr. 1983.

22. Gary W. Meyer and Donald P. Greenberg, "PerceptualColor Spaces for Computer Graphics," Computer Graph-ics (Proc. Siggraph '80), Vol. 14, No. 3, Aug. 1980,pp. 254-261.

23. C. B. Neal, "Television Colorimetry for ReceiverEngineers," IEEE Trans. Broadcast Television andReceiver, Aug. 1973, pp. 63-73.

24. W. T. Wintringham, "Color Television and Colorimetry,"Proc. IRE, Oct. 1951, pp. 1135-1172.

25. Roy A. Hall, "A Methodology for Realistic ImageSyntehsis," master's thesis, Cornell University, 1983.

26. R. Christopher Odgers, "An Interactive Computer AidedSystem for Artificial Lighting Design," thesis, CornellUniversity, 1978.

27. David R. Warn, "Lighting Controls for Synthetic Images,"Computer Graphics (Proc. Siggraph '83), Vol. 17, No. 3,July 1983, pp. 13-21.

jtMRoy Hall develops image generation soft-ware at Robert Abel & Associates. His cur-rent focus is increased image realism with-in the constraints of a film production en-vironment.

Hall received bachelor's degrees in civilengineering and architecture from Rensse-laer Polytechnic Institute in 1976. For thenext several years, he was a structuralengineer for Birdair Structures, where he

was introduced to computer graphics. He received an MS incomputer graphics from Cornell University in 1983.

Donald P. Greenberg is director of theProgram of Computer Graphics and theComputer-Aided Design Instructional Fa-cility at Cornell University. He presentlyteaches in the departments of ComputerScience and Architecture. Researchingand teaching in the field of computergraphics since 1966, Greenberg's special-ties include hidden-surface algorithms,geometric modeling, color science, and

synthetic image generation.Greenberg received his PhD in structural engineering from

Cornell University. He is a member of the IEEE and the ACMand has published more than fifty articles related to computergraphics and computer-aided design.

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