An evaluation of the quality of contemporary ray tracing methods on architectural materials

Predictive computer graphics can be used to visualize the appearance of an object or scene from a virtual design. A seminal experiment in that field was performed in 1984 to evaluate the perceptual quality of computer graphics images with a physical model of the scene. The original study was limited to ideally diffuse surfaces and simple geometry, with the greatest flaw being the artificially diffuse surface materials of a type rarely found in real scenes. Although subsequent work extended graphics algorithms to handle more complex environments and materials, comparisons of later results to a physical standard were scarce. This study attempts to recreate the original experiment in a more general setting using materials commonly found in real scenes. A physical scene was constructed using standard interior architectural materials, including carpet, a ceiling tile, and an incandescent light bulb, and photographed for use as a standard of comparison. A synthetic image of the same scene was rendered using Kajiya-style path tracing, a physically-based variant of the traditional ray casting algorithm, to simulate the effects of global illumination on micro-faceted geometry and directionally reflective materials lit by a hemispherical area light source. The resulting real and artificial images of the scene are presented together and subjectively analyzed to determine promising directions for further research on rendering common materials, and to comment on the legitimacy of ray tracing as a method for photorealistic image synthesis.

AN EVALUATION OF THE QUALITY OF COM TEMl'ORARY RAY TRACING METHODS ON ARCHITECTURAL MATERIALS By John E. Meier A Senior Honors Thesis Submitted to the Faculty of The University of Utah In Partial Fulfillment of the Requirements for the Honors Degree of Bachelor of Science In Computer Science Approved: Peter Shirley Martin Berzins Supervisor Director, School of Computing Peter Shirley M�/?�� '""S Department Honors Advisor Dean, Honors College May 2009 ABSTRACT ABSTRACT Predictive computer computer graphics can be used used to visualize the appearance object or Predictive appearance of of an object scene from experiment in that field was performed performed in 1984 to from a virtual design. A A seminal experiment evaluate the perceptual of computer computer graphics images with a physical model of of the perceptual quality of scene. The original study was limited to ideally diffuse surfaces and simple geometry, diffuse surfaces with the greatest diffuse surface surface materials of found of a type rarely found greatest flaw being the artificially artificially diffuse in real scenes. Although Although subsequent subsequent work work extended extended graphics algorithms to handle more complex environments comparisons of complex environments and materials, comparisons of later later results to a physical standard were scarce. This study attempts to recreate the original experiment experiment in a more general setting using materials materials commonly commonly found found in real scenes. A physical physical scene was constructed constructed standard interior architectural architectural materials, including including carpet, a ceiling ceiling tile, and an using standard incandescent light bulb, and photographed photographed for use as a standard of comparison. A incandescent standard of synthetic image of of the same scene was rendered rendered using Kajiya-style Kajiya-style path tracing, a physically-based variant variant of of the traditional traditional ray casting algorithm, to simulate the effects physically-based effects of of illumination on micro-faceted micro-faceted geometry geometry and directionaIly reflective materials lit by global illumination directionally reflective a hemispherical hemispherical area light source. The resulting real and artificial images of of the scene are presented together together and subjectively promising directions for presented subjectively analyzed analyzed to determine promising further research on rendering rendering common common materials, and to comment legitimacy of further comment on the legitimacy of method for photorealistic photorealistic image image synthesis. ray tracing as a method II ii TABLE OF CONTENTS CONTENTS ABSTRACT ABSTRACT 11 1. INTRODUCTION INTRODUCTION I. WORK 2. PREVIOUS PREV IOUS WORK 3 E T H O D S - PHYSICAL SCENE 3. M METHODS PHYSICAL SCENE 8 E T H O D S - SYNTHETIC SYNTHETIC SCENE SCENE 4. M METHODS 10 5. RESULTS 21 U T U R E WORK WORK 6. FFUTURE 27 7. REFERENCES REFERENCES 29 P P E N D IIX X A 8. A APPEND 32 iii III 1 1. INTRODUCTION INTRODUCTION photorealistic images has been been a driving force in the field of The generation generation of of photorealistic of computer graphics (CG) virtually computer virtually since the inception inception of of the field. Years of of intensive research significant advances towards solving the fundamental fundamental challenges challenges research have produced produced significant of of the problem: the generation generation and representation representation of of scene geometry, the accurate simulation of of light with different overcoming of of simulation of the interaction of different materials, and the overcoming limitations in processing processing speed, memory, and display display technology. A A variety variety of of techniques for generating synthetic images exist, including, notably, ray-tracing ray-tracing [17], radiosity [3], and z-buffer tradeoffs, z-buffer rasterization rasterization [1], among others. Each Each of of these methods makes tradeoffs, efficiency, as a result of the of physical accuracy versus computational computational efficiency, result of generally in terms of quality of of their respective approximations approximations to the true physical behavior behavior of of light light in a scene. out with the purpose characteristics of of a Research has also been carried carried out purpose of of defining defining the characteristics photorealistic image, and to determine how how best best to measure measure the extent extent to which which a CG image meets such criteria [4]. Methods include both evaluation of of perceptual both the evaluation satisfaction with of how satisfaction with such images as well as quantitative quantitative measurement measurement and analysis of accurately a simulation of of the behavior behavior of of light in an environment matches physical environment matches reality. [4] provides an excellent excellent overview overview of of the problem problem of of photorealistic photorealistic graphics, including of challenges, techniques, and strategies including discussion of strategies for evaluation. A series of of well-known experiments were performed University starting well-known experiments performed at Cornell University physically-based techniques techniques in 1984 to evaluate the quality of of images rendered rendered with with new, physically-based by comparing comparing the resulting synthetic simulations to photographs synthetic images or simulations photographs of of an identical physical scene or experimentally experimentally obtained obtained bidirectional function bidirectional reflectance reflectance distribution function 2 (BRDF) data for various materials ([2], [3], [5], [6], [9], [14]). The "Cornell Box" was a (BRDF) of these experiments; it consisted of a simple physical scene constructed physical constructed for use in most of consisted of box, open diffuse walls, a single diffuse, diffuse, ideally diffuse open in the front, with flat, monochromatic, ideally rectangular, area light source, and in some cases a few simple objects 1-a). objects (see Figure I-a). The physical physical dimensions, precisely precisely measured measured reflectance reflectance properties, and and calibrated photographs of the Cornell Box scene are publicly available, which which has made it a photographs of ( ,. relatively popular However, popular data set for the demonstration demonstration of of new rendering rendering algorithms. However, to the knowledge of subsequent work of the original Cornell Box of the author, subsequent work in the vein of experiments of synthetic images with a photographs photographs of of an identical experiments - direct comparison comparison of physical physical scene - has been been scarce. of the Cornell Box Box experiments to a more This study aims to apply the framework framework of realistic scene, and evaluate the results achievable using standard, contemporary contemporary ray tracing methods. The original Cornell Box Box was constructed constructed using a light source and surfaces with properties properties that can be approximated approximated easily by basic models in graphics surfaces clearly not a representative representative sample of of the lights and objects algorithms. However, this is clearly objects we see around us. The scene constructed constructed for this project project - the "Utah "Utah Box" - was purposefully designed to use common purposefully common architectural materials, such as carpet, ceiling tiles, and an incandescent incandescent light bulb (see Figure I-b). 1-b). In the next section previous efforts efforts at evaluating section of of the paper, previous evaluating the realism of of experimental framework framework that inspired our synthetic images are discussed, including including the experimental construction and measurement measurement of current work. In section 3, we then describe the construction current of the of obtaining obtaining a high quality digital representation representation of Utah Box Utah Box and the process of of the scene. 3 (b) (b) (a) Figure 1 Figure a) A photograph photograph of physical Cornell of the physical Cornell Box model. model.J b) A photograph photograph of physical Utah Box Box model. h) of the physical model. 1 In section 4, we present present the details of of modeling the virtual scene and the features ofthe of the render synthetic images of ray tracer used to render of the Utah Box. In the subsequent section, the resulting images are compared compared and the advantages and disadvantages of of our approach are evaluated. Finally, our contributions contributions and several directions for future future research are identified. identified. 2. PREVIOUS WORK WORK The original Cornell Box Box was constructed work in 1984 at Cornell constructed during work University [3] to demonstrate demonstrate a rendering algorithm capable of of simulating global illumination. The proposed proposed method, radiosity, was based on energy transfer transfer principles from thermodynamics, and involved simultaneously simultaneously solving a system of of linear equations equations radiant intensity exchange between surfaces for the radiant exchange between surfaces in an enclosed enclosed scene. Radiosity Photograph retrievedfrom retrieved from http://www.graphics.comell.edw'onlinelbox/measured.jpg, http://www.graphics.cornell.edu/online/box/measured.jpg, April April 2009. 2009. I1 Photograph 4 claimed claimed several advantages over other rendering algorithms of of the time in terms of of the accuracy of of the simulation, including proper conservation of of radiant energy in proper conservation physical accuracy the scene, the ability to use nearby area light sources rather than infinitely distant infinitely distant directional lights or point lights, and preclusion preclusion of of the need for an empirically and adjusted "ambient" term commonly commonly found found in other rendering algorithms to aesthetically adjusted imitate the effects effects of of global illumination. Limitations of included prohibitive computational Limitations of the early radiosity method method included computational complexity perform hidden complexity for finely detailed geometry, the inability to perform hidden surface surface removal, and importantly, the assumption assumption of of flat, ideally diffuse diffuse surfaces surfaces and emitters in the scene. These problems led directly to the choice of of simple geometry and diffuse diffuse materials in the first iteration of measuring the complete of the Cornell Box. A lack of of tools for accurately measuring complete spectral reflectance reflectance properties of of the materials in the physical physical scene prevented prevented the authors authors from performing performing a rigorous quantitative comparison comparison of of photographs of of the box to the CG CG image results, but the experiment provided useful useful guidelines for the construction experiment provided construction of of the physical scene and the proper environment environment in which to photograph photograph it. More importantly, importantly, motivated our current the study contributed the idea that motivated current work: Evaluation Evaluation of of CG image results using a physical standard. standard. In [10], Meyer Meyer et al. formalized formalized the evaluation evaluation framework framework for CG images both an in-depth cursorily introduced in the original Cornell Box study, including both cursorily introduced photorealistic CG image, as discussion of discussion of what is required to evaluate the fidelity of of a photorealistic well as a detailed specification physical experiment performed in consequence. specification for the physical experiment performed consequence. The authors defined defined a realistic image as consisting consisting of of two distinct components: A 5 of the behavior oflight of light in the scene, and a perceptually perceptually physically accurate simulation simulation of satisfying rendering and display of of the resulting data. Several popular popular rendering satisfying algorithms were evaluated evaluated from this standpoint. Traditional z-buffer z-buffer rasterization, which computes only direct interactions between geometry and between light sources and the scene geometry neglects surface-to-surface surface-to-surface inter-reflections inter-reflections in the environment, was claimed to be incapable of of producing producing truly realistic images; the necessity of of physically-groundless, physically-groundless, constant ambient ambient lighting to create the illusion of of true global illumination was deemed deemed constant extremely unsatisfying. unsatisfying. Similarly, it was noted that the standard ray tracing algorithm at the time, while comparatively comparatively a more physically based based method, also relied on a global ambient term to imitate true global illumination, and was only able to make use of of direct direct ambient paths from light source to image pixels. The authors therefore therefore supported supported radiosity as the only algorithm algorithm capable of of adequately approximating approximating the true behavior of light transport in behavior of the scene and decoupling decoupling the computation computation from from the actual rendering of of an image, therefore allowing separate experimental experimental verification of both stages. therefore verification of of the study performed of their proposed proposed experiment experiment performed both stages of The authors of Box scene, consisting using a second-generation second-generation Cornell Box consisting of of a box containing two blocks, with all surfaces reflectance properties. In order to make a surfaces exhibiting ideally diffuse diffuse reflectance quantitative comparison of the radiant intensities in the real scene with those of comparison of of the corresponding radiosity simulation, the physical scene had to be carefully carefully designed and corresponding exhaustively measured. Paints for the surfaces surfaces in the scene were chosen that behaved as exhaustively approximation of of ideal diffuse diffuse materials used in the simulation, simulation, closely as possible to the approximation and the spectral reflectance of each each paint paint were measured measured using a spectroret1ectance profiles profiles of 6 photometer. The light source for the scene was constructed constructed with specialized components components with specialized to maintain shown through a rectangular of maintain constant constant voltage, and the light was shown rectangular piece of flashed opal glass to approximate diffuse emitting surface flashed approximate the diffuse surface assumed assumed by the radiosity method. The distribution of of the spectral energy entering the scene was then measured. measured. All surfaces surfaces in the room room containing containing the Cornell Box Box were were covered covered with matte black black cloth to allow as little energy as possible reflected back of the box from box from possible to be reflected back into the open side side of the environment. Finally, a carefully carefully calibrated calibrated photometer photometer was used used to measure irradiation, which quantity of of radiant which is proportional proportional to the target quantity radiant intensity. These measurements for measurements were taken at 25 locations on a regular regular grid in the open face of of the box box for three arrangements arrangements of objects and colors corresponding of objects colors in the physical scene, and corresponding measurements authors simulated virtual environment. The authors measurements were then made in the simulated reported a satisfying of agreement satisfying level of agreement between between the predictions predictions of of their radiosity simulations and the actual photometric simulations photometric measurements. portion of of the experiment experiment required required producing visible CG CG image The perceptual portion producing a visible of from the radiosity radiosity simulation simulation data, constructing constructing an apparatus for fair of the scene from comparison performing a survey of of human comparison of of the synthetic image with the real scene, and performing observers. The rendering step was performed performed by computing computing radiosity radiosity simulations over of the visual spectrum parameters matching matching those of evenly spaced spaced intervals of spectrum with input parameters of the camera would be used to view view the physical physical scene. A displayable displayable image was camera that would generated by applying a calibrated of the resulting energy calibrated transformation transformation of energy distributions distributions to generated the color specific monitor color space representable representable on the specific monitor hardware hardware being used. It was discovered that the because of its limited dynamic range, the monitor monitor would would not be able discovered because of 7 black panel was to correctly correctly display the light source directly in the scene, so an opaque black introduced at the top of of the box in both the real and virtual scenes to obscure obscure a direct introduced view view of of the light source from from outside the box. The viewing viewing environment environment for the experiment of a black black curtain curtain with holes for side-by-side side-by-side viewing screens, one experiment consisted consisted of of which displayed displayed an indirect view of the monitor of view of monitor displaying the CG image, while the other displayed view of of the physical physical scene. The rationale for using the displayed an indirect indirect view viewfinders of indirection viewfinders despite the additional level of indirection they introduced introduced was that the setup allowed comparison of clearly knowing which of the scenes without without the bias of which scene was allowed comparison of the real one. Enabling simultaneous comparison of both scenes also reduced Enabling simultaneous comparison of reduced the inaccuracy that inaccuracy that would be introduced introduced by requiring observers to remember remember one scene while viewing of viewing them in succession. Twenty observers participated participated in the experiment, ten of whom had significant significant knowledge of whom of computer computer graphics principles, and ten of of whom whom were unfamiliar unfamiliar with the field. The authors reported that when when asked to choose which which view was the real scene and which was artificial, nine of subjects selected of the twenty subjects future work incorrectly. Two directions for future work were called for by the study, including the use of of even more accurate physical measurements measurements for evaluation evaluation of of the fidelity fidelity of of the light transport transport simulations, and perceptual perceptual tests with different different modes of of viewing viewing and more complex environments and lighting models. This paper complex environments paper attempts to take the first steps in addressing the latter direction. other studies in the mid-1980's Box was featured featured in several other The Cornell Box complex scene geometry concerned with extending method to handle more complex concerned extending the radiosity method and visual effects. surface removal effects. In 1985, improvements improvements were made allowing hidden hidden surface 8 and soft soft shadows while maintaining the fidelity of of the global illumination illumination simulation simulation [2]. Box was rendered using the new algorithm, this time with two boxes in the The Cornell Box scene to showcase showcase the new effects. Although significantly added to the kinds Although the updates significantly of scenes the radiosity algorithm could simulate, the authors maintained maintained their assumption assumption of radiosity algorithm of ideal diffuse diffuse materials and relatively simple geometry, claiming that the majority of of majority of surfaces in real environments environments exhibit similar similar behavior. In 1986, the radiosity method was was surfaces further extended to allow materials with directional (i.e., non-diffuse) reflectance further non-diffuse) reflectance properties, while still maintaining of the algorithm algorithm [6]. maintaining the desirable global properties properties of The improvements demonstrated by rendering rendering an iteration iteration of of the Cornell Cornell Box, Box, improvements were again demonstrated this time with materials approximating approximating the Phong-specular perfect mirror reflectance reflectance Phong-specu1ar and perfect models. In 1987, the radiosity algorithm was augmented augmented to allow simulation of of light scattering and absorption absorption through a volume, or participating medium medium [14], however however the scattering authors returned to the assumption of of ideal diffuse diffuse surfaces. Although each of of these demonstrated the results of of their respective algorithms on an extended version of studies demonstrated the original original Cornell Box scene, no comparison comparison to a physical model incorporating the newly enabled effects or materials was provided. provided. enabled effects 3. M METHODS PHYSICAL SCENE E T H O D S - PHYSICAL SCENE The physical Utah Box Box model was constructed box with constructed as a five-sided five-sided box dimensions on the order of of two feet per side, open in the front front to allow the interior to be photographed without without obstruction. The dimensions of photographed of the various component component pieces were measured measured manually manually with a tape measure to the nearest sixteenth of of an inch. The 9 (a) (b) (c) (d) (eJ (e) Figure Figure 1 2 (f) a) A A view physical Utah Box model. view of of the the physical Utah Box model. molerial and light source. b) AA close-up close-up 0/ of the ceiling ceiling material and light source. c) A close-up close-up of of the the carpet carpet material. material. A close-up black Irim d) A close-up of of the reflective reflective black trim material. material. of the reflective reflective white trim material. material. e) A close-up close-up ofrhe white Irim f) room in which Utah Box photographed. J) The The room which the Utah Box was was photographed. materi als for fo r the interior surfaces were intentionally intentionall y chosen tectural materials chosen to represent represent archi architectural materi als typically typ ica lly found fo und in an indoor indoor office materials office environment environment (See Figures 2-a to 2-e). The The pa in(; the cei li ng consisted of in gle perfo rated wa lls were were painted w ith a matte walls with matte white paint; ceiling of a ssingle perforated ceilin til e with w ith a circu lar hole cut in the center to allow insertion insertion of of the lilight ght source: ceilingg tile circular source; the fl oor was covered patch ooff standard gray carpet. The strips along the bottom of floor covered in in a patch of the walls reflective, smooth smooth black electri electrical strips supporting the cei ceiling wall s were reflective, cal tape, while wh il e the stri ps supporting ling smooth white pa painted inted metal. The light source in the scene was a 3.5 inch tile were smooth incandescent escent light bulb bul b powered powered by a standard 120 volt vo lt outlet. The ddiameter, iameter. 60 watt incand such that approxi approximately lower hemisphere of the bulb extended bul b extended light was positioned posit ioned such mately the lower hemisphere of 10 through the hole in the ceiling tile. through Photographs with a tripod-mounted tripod-mounted Nikon Nikon D70 6.1 Photographs of of the Utah Box Box were taken with 6.1 mega-pixel single-lens reflex reflex digital camera. In order order to ensure as little light light pollution pollution as mega-pixel reflection of energy back of possible from from outside light light sources and reflection of energy back through through the open open face of from outside the scene, the box was photographed photographed in a small closed room the box from room that had been prepared covering the interior surfaces with matte black prepared by covering interior surfaces black cloth (See Figure 2- Photographs were saved saved in the raw N NEF image format format for for lossless storage and f). Photographs E F image conversion to formats useful comparison to computer conversion useful for comparison computer generated generated images of of the scene. 4. M METHODS SYNTHETIC SCENE E T H O D S - SYNTHETIC SCENE of rendering rendering a synthetic of the Utah Box Box into three We divide the process of synthetic image of subsections: the modeling of of the scene geometry, the choice of of material models for each surface, implemented to actually generate the final final surface, and the ray tracing architecture we implemented image. 4.1 Utah Box Geometry Geometry Models Models generate computer computer images of of the Utah Utah Box Box was The synthetic scene used to generate modeled to one-sixteenth matching the margin of of the manual modeled one-sixteenth of of an inch accuracy, matching of error error of measurements of the physical physical scene. The three walls and the strips along the floor and measuremen1s of ceiling were modeled diagonally opposed modeled as axis-aligned axis-aligned box box primitives primitives specified specified by diagonally corner consisted of of a single sphere primitive embedded embedded into corner positions. The light source consisted the ceiling such that exactly one hemisphere appeared inside the scene enclosure. hemisphere appeared 11 floor were modeled modeled as heightfields, heightfields, which which for the purpose of Both the ceiling and floor of experiment consisted of2500 resolution two-dimensional two-dimensional arrays of this experiment consisted of 2500 by 2500 resolution of double double representing the height height of of a continuous surface surface at precision floating floating point point height values representing regular, discrete sample points. The ceiling ceiling tile heightfield heightfield was generated generated by bilinear interpolation on the intensities of of a grayscale image of interpolation of a real ceiling tile, with with slight random perturbation of of each point surface roughness. The floor heightfield random perturbation point to give the surface floor heightfield randomly perturbing perturbing each sample point of heightfield by a small was generated generated by randomly sample point of a flat heightfield visualize heightfield heightfield primitives primitives is described described in the rendering amount. The method used to visualize subsection below. subsection 4.2 Utah Box Box Material Models The surfaces modeled as ideally diffuse surfaces of of the walls and ceiling tile were modeled diffuse that the energy energy reflected reflected by a surface point is reflectors. Conceptually, this means that surface point distributed uniformly over the unit hemisphere hemisphere based based at the hit point and pointing pointing in the distributed uniformly of the surface Gradated shading over such surfaces nearby light direction of surface normal. Gradated shading over surfaces for nearby sources occurs because because the energy energy reflected reflected is weighted weighted by the cosine of of the angle between the light source and surface Ideally diffuse diffuse shading between surface normal at the hit point. Ideally shading is dependent geometry and orientation, and the position position of of lights, and is dependent only on surface surface geometry invariant with respect respect to changing changing eye position. The lighting equation used to compute invariant equation used compute reflected energy from direct lighting for points on these surfaces [IS] was: the reflected surfaces [15] 2 Eo= ))·(NsoR)·(NL E = CmKt. CjKd * CCLA AL ·(l/(nD • (1 /(TTD )) . ( N - R ) . (No-R) --R) 2 0 L L s L where Eo reflected energy, C mis the RGB color where E is the reflected color of of the material, kkd is the diffuse diffuse 0 m d 12 reflection coefficient reflection coefficient of of the material, C L is the RGB color of of the light, AL A is the area of of the L L light surface, D is the distance from from the surface ~urface point to a sample point on the light ( N R ) is the cosine of of the angle between the surface surface normal and direction direction to a surface, (Ns-R) - s (N *-R) is the cosine of of the angle between the light sample point point on the light surface, and (NL--R) L surface normal from the light sample point to the hit point on the scene scene surface normal and direction from geometry. surfaces of of the white strips supporting the ceiling tile were modeled modeled with a The surfaces white Phong-specular Phong-specular reflective Phong-specular model behaves identically identically reflective material. The Phong-specular to the ideal diffuse diffuse model described above, but with the addition addition of of a specular reflective reflective term to simulate the direct reflection reflection of of light sources. The lighting equation used to compute the reflected reflected energy for points on these surfaces compute surfaces [15] was: Eo E = Ed E + [C [ Cs' .CL* C . ((N-H)"] N-H) ] a 0 d s L Eo is the final reflected reflected energy, E Ed is the ideal diffuse where E diffuse reflected reflected energy described described G d above, Cs C is the specular specular color of of the material, C L is the color of of the light, N is the surface surface s L half-vector, or vector normal at the hit point, H is the half-vector, vector from the surface surface point to the light parameter to control the size of incident ray direction, and a(1 is an input parameter minus the incident of specular specular highlights on the surface. surface. The surfaces surfaces of of the black strips along the floor were modeled with a perfectly perfectly reflected perfectly reflective surfaces is reflected reflective black black material. Energy incident to these surfaces perfectly around the surface surface normal at the hit point and shaded shaded recursively, with the result being reflective Fresnel coefficient reflective material. modulated by the reflective modulated coefficient and by the color color of of the reflective of directionally directionally reflective reflective materials varies as eye position changes. By nature, the color of 13 used to compute compute the reflected reflected energy for points on these surfaces The lighting equation used surfaces [15] was: E = C,.[(l-C )-(l-R-N) 0 m 5 + C ] m en is Eo is the final reflected reflected energy, C C, is the color color returned returned by the reflected reflected ray, C where E 0 r m the color of of the reflective reflective material, and R»N of the angle between R· N is the cosine of between the incident ray and surface surface normal. The carpet carpet in CG CG images of of the Utah Utah Box Box was modeled modeled as an ideally diffuse diffuse referenced from a textured meaning the color at each point point on the surface textured material, meaning surface was referenced of the actual patch patch of of carpet, and reflected reflected energy energy was color-corrected photograph photograph of color-corrected computed according according to the properties of diffuse material described computed of an ideally diffuse described above. A A of the carpet material would would have required required more advanced completely synthetic shading shading of completely advanced shading methods, and was beyond beyond the scope scope of of this project. Some possible techniques techniques for shading discussed in the further further work work section section at the end of doing so are discussed of this paper. Box Ray Tracer 4.3 Utah Box implemented to produce In this section, we describe the features of of the ray tracer implemented produce CG images of Box for this project, project, contrasting contrasting them with the characteristics characteristics of CG of the Utah Box of fundamental version version of the basic ray tracing algorithm. The fundamental of the algorithm algorithm [16] is presented in Listing 1. Standard presented Standard ray tracing methods augment augment this basic model in a number of ways to synthesize images more convincingly, and provide a variety of of ways number of deceptively simple tasks of of finding finding ray-object ray-object intersection points and to accomplish accomplish the deceptively computing the reflected computing reflected energy for various materials. 14 RayTrace(Objects, Lights, RayTrace(Objects, Lights, ViewPlane): ViewPlane): pixel in in ViewPlane: For each each pixel For ViewPlane: Cast ray from from pixel pixel center center perpendicular perpendicular to to ViewPlane. Cast aa ray ViewPlane. Search Objects Objects for the closest closest intersection, intersection, if Search for the if any. any. If an an intersection intersection occurred: If occurred: Sample each each light light in Lights for incident energy. Sample in Lights for incident energy. _____ Compute using the object material. '----_________c_o_mpu t e pixel pixel color col~~~u_si~~_~~~b j ec t~lT1a~ =~~~~~: ~ Listing 1: fundamental ray casting algorithm. Listing 1: The fundamental ray casting algorithm. projection of First, note that the algorithm above produces produces only an orthographic orthographic projection which all rays fired into the scene from the imaging plane are parallel. This the scene, in which perceptual effect of perspective, in which which the size of objects appears neglects the familiar familiar perceptual effect of of objects inversely proportional proportional to their distance from from the viewer. This is addressed addressed in our ray pinhole camera model [16]: An eye location, gaze direction, up direction, tracer using the pinhole camera model and horizontal horizontal field of of view angle are specified, specified, and rays are cast from from the eye point through viewing plane defined defined by the gaze direction, up vector, and viewing through pixels in the viewing angle. _ Another issue with the basic ray tracing model above is aliasing caused Another caused by taking sample of of the scene per pixel. The discrete nature of only one ray sample of the sampling sampling in the algorithm can cause cause severe visual artifacts artifacts and undesirable patterns in the resulting algorithm images when periodic periodic features features of specific frequencies frequencies are rendered, and causes smooth images of specific lines and surfaces surfaces to appear appear jagged, jagged, especially for low image resolutions and close-up close-up of scene geometry. The choice number and location of samples within each views of choice of of the number of samples domain of pixel is the problem problem domain of sampling, and filtering filtering deals with methods for reconstructing samples into a single value. Both Both sampling sampling and filtering reconstructing filtering are heavily 15 Figure 3 Figure aJ per pixel. a) 1I uniform uniform sample sample per pixel. b) 49 49 jittered jittered samples per pixel pixel with with a 2 pixel pixel wide wide tent samples per tent filter. filter. beyond the scope of paper, and we refer refer the interested researched topics that are well beyond of this paper, tracer provides provides support reader to [161 [ 16] for detail detailss in the context of of ray tracing. OUf Our ray tracer support for any perfect perfect sq uare number per pixel in either unifonn or jittered j ittered sampling square number of of samples per either uniform sampling imp lements both uniform un iform (box filter) filter) and triangle (tent filter) filter) reconstruction patterns, and implements reconstruction filters (See Figure 3). The abi li ty to accu rately and efficiently intersection points fo ability accurately efficiently compute ray-object ray-object intersection forr scene primitives is an extremely tracer, with a major major effect extremely important feature of of any ray tracer, effect on hmh ty and necessary rendering time. It is also another another topic refined refined by both image quali quality significant intersection algorithms used used to render significant research. We now briefly briefly describe the intersection the Utah Utah Box scene: ray-sphere, ray-sp here, ray-box, ray-box. and ray-height field intersection. ray-heightfield The ray-sphere intersection intersect ion algorithm we use [[15] 15] operates in two stages and takes of simple trigonometry advantage of tri gonometry and vector vector math. First, First, the distance from rrom the ray ray origin 16 of the sphere is compared to the center of compared with the radius of of the sphere to determine whether formed using the ray itself itself and a the ray originates inside. If If it does, a right triangle is formed vector equation that can be solved vector from from the ray origin to sphere center, giving a quadratic equation to determine the hit point. If of If the ray originates outside the sphere, checking the sign of the dot product product of of the ray direction and the vector vector from from the ray origin to the sphere center immediately of intersecting If the dot intersecting the object. If immediately indicates whether whether the ray has a chance of product is positive, we can again use a right triangle formed product formed using the two vectors to set up a quadratic equation, for which finding the smallest smallest real positive root gives the desired intersection point. intersection The key intuition behind behind the ray-box intersection intersection algorithm we use [18] is that the surfaces of intersected with with a ray as planes, producing producing intervals surfaces of a box can each be intersected consisting of of a first and second second intersection intersection point in each each dimension. Because Because we we deal consisting exclusively with axis-aligned axis-aligned box primitives, the special special cases that occur for rays parallel exclusively of the x, y, or z dimensions are trivial to verify. verify. Once the intersection intervals in to one of checked for overlap to each dimension have been computed, the intervals can be checked determine the possible intersection intersection points, with the lack of of an overlapping overlapping interval determine between any two of dimensions immediately immediately indicating indicating that that no intersection between of the three dimensions occurs. ray-heightfield intersection intersection algorithm algorithm [15] was the most performance of The performance of the ray-heightfield of the three intersection intersection techniques to the rendering of important important of of the Utah Box Box because of of heightfield primitives the comparatively comparatively enormous complexity complexity of of the ceiling and carpet carpet heightfield relative to the other objects intersection function objects in the scene. Our Our intersection function discretizes the 17 bounding-box volume volume of of a heightfield heightfield into regular cells during preprocessing, then bounding-box iteratively marches through iteratively through each grid cell along a given ray as efficiently efficiently as possible. In each cell, the height computed and height values at the entry and exit exit points for each each are computed compared minimum and maximum no overlap of of Ifno compared with the minimum maximum surface surface heights in that cell. If intervals occurs, intersection the two intervals intersection is impossible impossible and the ray can be marched marched to the next If there is a possible surface patch possible intersection, the surface patch within the cell is cell immediately. If functionally of the heightfield four functionally defined defined as the bilinear bilinear interpolation interpolation of heightfield values at the four corners of of the cell. The progress of of the ray through the cell is also parameterized, parameterized, and by comers equation is derived and can then be solved equating the two functions, a typical quadratic equation to find the intersection intersection point. often approximated Direct Direct lighting in a standard standard ray tracer is often approximated using some combination of infinitely distant directional directional lights or nearby point lights [16]. Infinitely combination of infinitely Infinitely distant specified as a single vector: the light direction. When When rays distant directional lights are specified strike scene geometry, they compute direct lighting from from directional directional lights by firing a ray in the negative direction of of the light and checking for occluding objects. Directional of the planar produce constant shading over planar surfaces, since the dot product product of lights produce constant shading over planar surface direction is constant. In addition, since a given directional surface normals and light direction directional light every time, each each point on scene geometry geometry falls is sampled in the same direction every exclusively giving hard-edged hard-edged shadows unless multiple lights exclusively into either either light or shadow, giving of soft-shadowing. approximation to a are used to fake the effects effects of soft-shadowing. Point Point lights provide an approximation point in the scene. When When rays strike scene geometry, nearby light source by occupying nearby occupying a point vector between between the light position position and the hit point the light direction direction is computed computed as the vector 18 on the geometry. This gives the desirable effect gradated shading over planar effect of of gradated planar surfaces, surfaces, but the hard shadow problem remains. sophisticated model of of a The Utah Box ray tracer implements the more sophisticated hemispherical Whenever the light in the Utah Box scene is queried, it hemispherical area light source. Whenever returns a random, uniform geometry point to If the ray from a geometry uniform sample on its hemisphere. If considered to be lit for that the light sample point is unobstructed, the scene point is considered problem of of generating noise in pixels containing points with sample. This model has the problem a partially obstructed view of of the light, as some samples will decide that the point as lit, while others will label it as shadowed. However, the principles of of Monte Carlo integration [16] [ 16] allow a good approximation of the correct value to be reconstructed by by integration using a sufficiently sufficiently large number of of samples per per pixel. A significant photorealism in standard significant obstacle to photorealism standard ray tracers is their negligence negligence of disguised by reliance on a global of the effects effects of of global illumination, which is often often disguised reflection between non-emitting surfaces ambient ambient lighting term to approximate reflection surfaces [4]. This is usually implemented implemented by simply simply adding a small amount amount of of constant constant light energy to every scene point, regardless of of the actual lighting lighting in the environment. Although Although the visually appealing, there is no physical basis for the result in standalone images is often often visually effect. ambient lighting is unable to capture realistic behaviors like effect. In addition, simple ambient color between neighboring neighboring surfaces color bleeding between surfaces or reflections reflections of of light sources in nonemitting emitting surfaces. surfaces. known as path tracing was developed An extension of of ray tracing known developed to address this of computing computing the color at a weakness [7]. Path tracing operates by abandoning the idea of 19 hit point point based based only on direct sampling of of lights from from the hit location. Instead, huge numbers of of rays are fired into the scene and reflected surface reflected recursively recursively based on the surface material material models encountered encountered until they either either hit a light source - providing providing energy energy - or reach specified recursion reach some specified recursion depth or light attenuation attenuation threshold and are discarded. energy from of modulated by the material properties of Since the energy from the lights in a scene is modulated surface hit on the way way to the camera, the effects each surface effects of of global illumination illumination are properly accounted exponential growth growth in the number of rays cast at each number of accounted for. In order order to avoid exponential recursive step, Monte Monte Carlo integration integration principles [16] must must be applied applied in practice. For although exact surface with of the energy energy incident incident to a point on a surface example, although exact computation computation of ideal diffuse over the entire hemisphere diffuse reflectance reflectance properties would require integration integration over of the integral can be approximated of many approximated as the sum of at the hit point, the value value of individual from the hemisphere individual reflected reflected ray samples chosen chosen randomly randomly from hemisphere at the point. As in the case of of area lighting described earlier, the error of this approximation error of approximation establishes itself of samples per resulting images, which which must be offset offset by large numbers of itself as noise in resulting pixel to reduce the variance. of path path tracing [16] in which wh ich energy energy at a Our ray tracer tracer implements imp lements a variant variant of given geometry geometry point sampling light sources directly for direct computed by by sampling direct lighting point is computed standard ray casting casting algorithm), and by recursively recursively computing computing the indirect (as in the standard lighting contribution contribution using Monte Monte Carlo path tracing. We avoid counting energy emitted from the light source twice by ignoring rays that hit the light source at a depth greater from than zero. This strategy illumination effects effects of of pure path strategy allows us to achieve the global iHumination tracing while at the same time reducing variance same variance in the resulting image for the same 20 (a) (b) Figure 4 Figure 0) Pure path path tracing. 10,000 samples per pixel pixel (10 - 12 hours). a) Pure tracing, 10,000 samples per (-10 hours). b) Path Path tracing with direct per pixel pixel (7.5 hours). tracing with direct light light sampling, sampling, 4,900 4,900 samples samples per (-7.5 hours). of sampl samples This greatlyy reduces the number of of sam samples number of es per pixel. pixel . Th is in turn tum greatl pl es per pixel and rendering time needed for visually sati satisfying sfying results (See Figure 4). software used for this research was initially provi provided The ray tracing software thi s research ded by Dr. Steven Parker as a skeleton program for a graduate ray tracing course in the Graph Graphics and Steven ics and Visualization of Utah School of of Computin Computing. author Visuali zat ion Track at the University of g. The author implemented much of of the functionality of the application as part of of the required required functionality of coursework, including a first attempt at Kajiya-style Kajiya-style [7] global illumi illumination effects for nation effects fo r an coursework, componentt of of independently chosen final project for the course. The global illumination componen subsequentlyy refined implement the ray tracer was subsequentl refi ned and rewritten to more faithfully fa ithfully implement Kajiya-style of the images in th this source is paper. The full source Kajiya-style path tracing for the rendering of of the ray tracer, specification file for the final image, and uncompressed uncompressed code of tracer. the scene specification disc, image results and input data are contained on the attached di sc, and described briefly briefly in Appendix A. Appendix A. 21 21 (a) (b) Figure 5 Figure oj synthetic image image of oj the the Utah a) The The synthetic Utah Box. Box. b) The reference reference photograph photograph of of the the Utah Utah Box. Box. 5. RESULTS The reference af the physical phys ical Utah Utah Box and final CG image of the reference photograph photograph of s ide~by -s ide in Figure Figure 5. S. The The synthetic image was rendered rendered at virtual scene are presented presented side-by-side 1,400 resol uti on, with with just just over over 25,600 25 ,600 box-filtered box-filtered samples per per pixel. It 1,400 by 1,000 1,000 pixel resolution, was generated piecewise on fou r machines machin es simultaneously simultaneous ly in a total total of of approximately approximatel y 150 I SO on four reader, further fu rther details regarding regarding the settings settings used hours of of CPU time. For the interested reader, to re nder the synthetic image are available avai labl e in the scene definition defin ition file fil e on the attached render appendix di sc, along with the full fu ll source code of ray tracer. disc, of the ray A [though formal forma l quantitative verification verification experiments perfonned in in [[10] 10] and Although experiments as performed described in the previous works section section above above were were beyond beyond the scope and resources resources of ve evaluation evaluation of of the results in the manner manner ooff the orig inal this study, we feel that a subjecti subjective original Cornell Box study [4] is worthwhile worthwhile both bOlh as an an indicator indicator of of the image quality achievable with standard contemporary contemporary ray tracing trac ing techniques, and a nd as a guide to promising further directions for fu rther research. 22 The global illumination illumination effects effects in our results are consistent consistent with those of of the original Cornell Box Box experiments: The patterns of of intensity in the scene caused by indirect of light between satisfyingly indirect inter-reflection inter-reflection of between non-emitting non-emitting surfaces surfaces are satisfyingly reproduced reproduced in the CG CG image, but the overall brightness brightness of of the scene scene is dimmer dimmer in the of the physical model. This is most reference photograph photograph of synthetic image than in the reference easily observed of each each interior interior surface surface of of the box, with with the observed around around the boundaries boundaries of difference being especially nearest the difference especially pronounced pronounced at the edges of of the interior interior surfaces surfaces nearest careful preparation camera. This suggests suggests that that despite the careful preparation of of the room room in order order to reduce light of escaped escaped light back light pollution pollution when when photographing photographing the physical scene, reflection reflection of into the box of the areas of of the scene box may have played played a role in increasing the brightness brightness of along the open face of of of the box. The virtual scene was guaranteed guaranteed to be free of of the ray illumination from light that had escaped escaped the open face by the implementation implementation of tracer, which immediately out of of the open face of of the immediately discarded rays once they bounced bounced out box. In addition, without sophisticated equipment reflectance without sophisticated equipment with which which to measure measure the reflectance of the materials in the physical scene and radiant properties of radiant intensity intensity of of the light source, it was not possible to guarantee that the settings used to render the synthetic image in this study conservation of of light energy. study would would produce produce perfectly perfectly physically physically accurate conservation next address the quality with which which the effects of directionally We next effects of directionally reflective reflective materials in the physical physical reference reference scene were synthesized Both the synthesized in the CG CG image. Both specular reflection of of the of the ceiling ceiling tile and the reflection specular highlight highlight in the metal strip at the front front of carpet of the box are appropriately carpet in the black black trim on the sides of appropriately observable observable in the CG image (See Figure 6). The shape and of the reflection reflection in the black black trim, and intensity of 23 '." -' - - . ., ~ ... .' , (a) (b) (c) (d) Figure 6 Figure The specular while trim specular highlight highlight in tile the white trim in (a) the synlhelic synthetic image. image, and and (b) the physical reference. reflection of the physical reference. The reflection of carpel carpet in the black black trim trim in in fic image physical reference. (e) fhe ,~ynlhe (c) the synthetic image and and (d) the physical reference. espec especially, iall y. appears to closel closelyy mimi mimicc the behavior behavior in the physical physical scene, neg neglecting lecting the difference in co color resulting of the synthetic carpet. The The difference lor resul ti ng from the incorrect appearance ofthe specular hi ghlight in the white trim at the front front of the cei lin g til is fy ing highlight ceiling tilee is a sat satisfying on of th e effect [he physical ty of reproducti reproduction of the effect in the physical scene, but the fideli fidelity of the shape of of the refl ecti on in the black trim. Thi y reflect ion is not quite as good as that of reflection of the reflection Thiss is likel likely tile Phong-specular fo r the material caused in large pan part by the use of the Phong-specular mode modell for material of of the 24 24 (h) "(b) (a) Figure Figure 7 Ceiling tile geometry detail in (a) the synthetic synthetic image, Ceiling tile geometry detail image, and (b) the the physical reference. and physical reference. surface, approximates the specular reflective reflective behavior behavior as an intuitively surface, which approximates intuitively derived derived empirical Perspective discrepancies between the pinhole camera camera model used used in the empirical term. Perspective si mulation and the actual physical [ens gita l camera used to photograph photograph the scene simulation lens in the di digital scene lth ough sufficient particular scene, a scene featuring may have also contributed. A Although sufficient for this particular featuring specularly reflective prominently would require require a sticated reflective geometry geometry more prominently a more more sophi sophisticated For example, the Phong Phong specular perhaps be replaced by a model. For specular term could perhaps modification of BRDF implemented tracer with one that modification of the perfect perfect diffuse diffuse BRDF implemented in our ray tracer wou ld samp le reflection reflection rays more heavily in a given hemisphere at the hit would sample given portion o off the hemisphere normal , rather rather than choosing choosing a point based on on the incident ray direction direction and surface normal, reflection direction uniformly uniformly at random. reflection The appearance of micro-geometry of ling tile ti le is a of fine deta detailil in the micro-geometry of the cei ceiling promising result of of this study (See Figure 7). Because forr Because we chose to create geometry fo the ce ceiling characteristics of the physical analog but not as a direct il ing tile with w ith the physical physical characteristi cs of 25 '- ." . :':.. (a) (a) (b) (b) Figure 8 Figure light source source in The problem 0at1 the The tone tone mapping mapping problem the light (a) the physical reference. the synthetic synthetic image. image, and and (b) the physical reference. copy of identica l rendering was not possible, possible, nor was it the goal. OUf of it, an identical Our aim was to physical scene, generate an object object that looked convincingly similar similar to the tile in the physical scene, in the manner that two neighboring nei ghboring ce ilin g tiles ti les in a real office ight appear same manner ceiling office hallway hallway m might appear more or less identical. While the ceiling ceil in g tile in the final synthetic image we arrived at in mistaken for a sib li ng of reference, its geometry this study may not quite be mistaken sibling of the physical reference, geometry was quickly and eas ily generated us ing a simple aalgorithm lgorithm as a proof proof of of concept, nd sti ll easily generated using concept, aand still manages to realistically reali sticall y convey the essence of of the physical texture in the real tile without resorti ng to compromises that if if the resorting compromises like texture mapping mapping or bump mapping. We feel that refined and executed using us in g an orthograph ic image of generation aalgorithm lgorithm was slightly refined orthographic of ling tile ti le in the model rather than a gene ric image, image. a close match to the the physical cei ceiling generic ld be achieved. actual pixels in the photograph cou could achieved. A weakness of the light in the scene, which weakness in the final results is the appearance of appears as a solid white region in both the CG image and in the photograph of the photograph of appears 26 problem of physical scene (See Figure 8). This is the well known problem of tone mapping; current monitor of representing the full visible scale of of intensity, so regions monitor hardware is incapable of that fall outside the displayable brightness range in any digital image must be clamped to the maximum rendered using a more sophisticated sophisticated technique to improve the maximum value, or rendered perceptual of the displayed displayed image. High Dynamic Dynamic Range (HDR) imaging [13] is perceptual quality of of images of of the same scene taken at one such technique which operates on a series of different shutter speeds, combining them to display as much visible detail as possible in different neighboring regions of of significantly significantly different different overall intensity. Although application Although the application of D R imaging was considered for this project, it does not provide a physically accurate accurate of H HDR solution to the tone mapping problem, and therefore therefore was not viable for this study. Even solution during the extremely extremely thorough perceptual experiment performed perceptual verification verification experiment performed in [10], the tone mapping problem was avoided by simply obscuring obscuring the direct view of of the light mapping problem comparison testing source in both the CG and physical scenes with a black black panel during comparison with human observers. We proceed proceed in similar fashion, ignoring the issue of of tone mapping mapping in this study. wee conclude that the use of From our results w of ray tracing to visualize scenes with the physical physical fidelity required required for design applications is a feasible goal. Our experiment experiment using the Cornell Box Box framework framework for evaluating the physical accuracy of of a rendering established ray tracing techniques and produced algorithm used primarily primarily standard, established satisfying results; this suggests that implementation implementation of of more advanced ray tracing satisfying methods and development development of of new, physically-based components such as physically-based ray tracing components BRDF's could make simulation simulation for design a viable application. application. improved material BRDF's 27 6. FUTURE FUTURE WORK WORK During the course of of this research, we identified identified several directions for further further of the synthesized synthesized image of of the Utah Box that was not study. First, the only component component of completely artificial artificial was the carpet. As we noted above, this was beyond of the completely beyond the scope of considered. current project, project, though this is not to say that possible methods were not considered. Potential avenues we identified convincing carpet carpet include: Generating Generating Potential identified for rendering convincing micro-geometry (for (for example, a heightfield) heightfield) from from a procedural texture such as Perlin micro-geometry noise [11]; designing a BRDF BRDF that behaves similarly to carpet by returning different different colors depending depending on which of the "grain" of of the carpet carpet a ray is incident to; which side of implementing seemed to be the most implementing a volumetric texture [8], or hypertexture [12], which seemed promising methods, but whose integration into the ray tracer w promising wee wrote to render the Utah Box would have been non-trivial. A logical continuation of A of this research would be more rigorous quantitative quantitative evaluation evaluation of of the results in the vein of of the experiment experiment detailed in [10], in terms of of both accuracy of noted in the accuracy of the physical simulation simulation and quality of of the perceptual perceptual results. As noted the discussion discussion above, verification verification of of the fidelity fidelity of of the light transport simulation simulation would require a significant measurement equipment. An significant array of of sophisticated sophisticated laboratory measurement work with the goal of informal performed early in the course of informal research project project was performed of this work of finding finding simple, inexpensive ways to approximate approximate useful useful physical quantities like spectral spectral reflectance curves for sample materials, and showed showed some potential. However, analysis analysis reflectance of that performed difficult to achieve. The The performed in [10] would would be difficult even approaching the level of perceptual comparison comparison study is a much more practical next step, and could be performed performed perceptual 28 of this project project or future future iterations with a reasonable amount of using the results of of additional effort effort and resources, including the involvement involvement of of a perceptual perceptual psychologist. A final direction for further further work, which we inherit from from the original Cornell Box studies, is the undertaking current state, our undertaking of of more interesting interesting scenes. In its current our rendering software is capable of infinite number, if if of handling handling several other other geometric geometric primitives - an infinite software triangle meshes considered - and a variety of material models including transparency, meshes are considered variety of translucency, procedural effects procedural noise texture, and glossy reflection. Introducing these effects experiment would of obtaining physical objects objects with such into the experiment would merely be a matter matter of characteristics to add add to the physical characteristics physical scene. project, we have performed performed a novel experiment experiment using the Cornell Cornell Box With this project, framework for evaluating evaluating the photorealistic photorealistic quality quality of framework of CG images using a different different method and more complex complex reference reference scene. The physical scene was rendering method constructed using typical interior interior architectural architectural materials with micro-faceted micro-faceted geometry geometry and constructed both diffuse diffuse and and directionally directionally reflective reflective surface surface materials. Synthetic images of both of the scene were generated generated using the path path tracing generalization of the standard were generalization of standard ray tracing algorithm virtual scenes were subjectively to simulate global illumination. The physical physical and virtual subjectively compared to present present an initial demonstration demonstration of compared of the ability of of ray tracing to render physically realistic geometry geometry and lighting effects. physically effects. 29 7. REFERENCES REFERENCES [I] [1] Catmull, E. (1978). A hidden-surface hidden-surface algorithm with anti-aliasing. ACM ACM SIGGRAPHComputer SIGGRAPH Computer Graphics, Graphics, 12 (3),6-11. (3), 6-11. [2] P. 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APPENDIX APPENDIX A of The following following is a brief brief guide to the attached attached disc containing containing the source code of the Utah Box Box ray tracer, the virtual scene specification specification for the final image, and the uncompressed uncompressed image result and input data used for for the render. of the applications written written for this study is just just under The total code length of under 6500 lines. The ray tracer tracer and support support utilities used to produce the images in this study were written successfully compiled Windows written in C++ and have been been successfully compiled and executed on Microsoft Microsoft Windows G N U g++ (using Microsoft Microsoft Visual Visual Studio), as well as Mac OS X and Linux (using the GNU of all image of the rendering software software and rendering of image results compiler). Development Development of seen in this paper paper was performed performed using the latter two operating operating systems. of the Utah Box ray tracer tracer is contained folder on the The source of contained in the "ubrayl" "ubray/" folder attached disc. The entry point point of of the application contained in the file "ubray.cc". attached application is contained Utility classes (such as Vector, Point, Color, etc.) and abstract base classes (such (such as Utility found in files with names Scene, Image, Primitive, Material, Light, Camera, etc.) are found without underscores. Extensions Extensions of of the abstract abstract bases are found found in files with names without beginning with an abbreviation abbreviation of of the base they extend, followed underscore and beginning followed by an underscore specific extension (i.e., the Lambertian Lambertian material material extension of the Material the name of of the specific extension of abstract base class is found found in "Mat_ Lambertian.h" and "Mat_ Lambertian.cc"). abstract "Mat_Lambertian.h" "Mat_Lambertian.cc"). ofthe generate heightfields heightfields from The source of the application application used to generate from grayscale grayscale RGB RGB _ hfl" folder of the images is contained contained in the "ubray "ubray_hf/" folder on the attached disc. The entry point of application application is contained contained in "genheightfield.cc". "genheightfield.ee". The final rendering of the synthetic synthetic scene for this study required approximately rendering of required approximately 33 150 hours of CPU time, and was therefore therefore rendered rendered piecewise piecewise on four of CPU four servers simultaneously and reconstructed of the application simultaneously reconstructed into a single image. The The source of application used to recombine contained in the "ubray "ubray_combine/" recombine the image image segments is contained _combine!" folder folder on the attached disc. The entry point of the application attached point of application is contained contained in "combine.cc". The scene specification specification file file used used to render render the final image of of the virtual Utah Box scene is contained contained on the attached attached disc as "ubray _ scene/UB_ scene.scn". It describes the "ubray_scene/UB_scene.scn". output resolution, ray depth attenuation settings, sampling output depth and attenuation sampling and filtering filtering settings, camera orientation, lighting camera lighting setup, material models, and primitive geometry geometry used used to produce SCN specification specification file format format produce the final image. Detailed Detailed options available in the SCN used "ubray/Parser.cc" in used by by the Utah Utah Box Box ray tracer tracer can be found found by examining examining the file "ubraylParser.cc" the ray tracer source code on the attached attached disc. The input data used to render the final CG image for this study as well as the fullThe fullsize image result and physical physical reference reference image can be found jmage/" folder found in the "ubray "ubray_image/" folder binary heightfield heightfield data used by the The file "ceiling.hr' on the attached disc. The "ceiling.hf' contains the binary tracer to render render the ceiling tile in the virtual scene. The file "carpet.hr' ray tracer "carpet.hf' contains the heightfield data used used to render render the carpet. The file binary heightfield file "carpet.ppm" "carpet.ppm" contains the when computing computing the color color of of carpet carpet pixels in the Utah Box texture image referenced referenced when full-size version version of of the final Utah Utah Box image. The file file "UB_final.png" "UB_final.png" contains the full-size and the file "UB--'photo.ner' contains the raw photograph image (1400 by 1000 pixels), and file "UB_photo.nef' of the physical physical reference reference scene. of