James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH 86 Conference Proceedings), volume 20, pages 143--150, August 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the full repertoire of light. Ray tracing [61] and radiosity [13, 38] feature nearly mutually exclusive models of light reflection: each valid in itself, but incomplete. Methods that combine ray tracing and radiosity typically neglect more complex modes of reflection [53] The rendering equation [19] and methods that incorporate complex surface reflection [4, 52] still neglect light scattering by participating media such as smoke. Methods that model participating media have thus far limited the forms of surface reflection [46, 47, 21] Finally, absent from all of the cited approaches are ....

....and physically similar effects [24] as well as subsurface scattering [15] But its usefulness extends beyond these applications. Because of the generality of the equation of transfer, it subsumes many of the equations used in global illumination and volume rendering. Just as the rendering equation [19] unifies an array of rendering techniques, the equation of transfer encompasses an even larger class. We now consider some of the special cases that it subsumes. 3.2.1 Vacuum Conditions If the space separating the surfaces is a vacuum, there can be no volume emission and no particle collisions ....

[Article contains additional citation context not shown here]

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

....mathematics (integral equations) and algorithms. In order to generate realistic images, global illumination models are required. These models account for the inter reflection of light between the elements of the scene. Kajiya showed in 1986 that they are derived from the rendering equation [15]. Having its origins in the Radiative Transfer field [28] Kajiya reformulated the equation to model (optical) physical phenomena of interest from the point of view of image synthesis. Thus, it does not consider for instance the phase of the light (diffraction is not studied, and the scattering is ....

James T. Kajiya. The Rendering Equation. In Computer Graphics (ACM SIGGRAPH '86 Proceedings),

....three photon maps are being used in the photon mapping algorithm. One for caustics, one for indirect illumination and one for participating media. In this paper we will only consider the indirect illumination. 2. BACKGROUND Photon mapping is one way to solve the rendering equation introduced in [Kajiya86]. The outgoing radiance L in the point x in the outgoing direction co can be described as a solution to the equation: Lo(X, 3) Le(x,3) x,3) Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are ....

James T. Kajiya, The rendering equation, SIGGRAPH 1986

.... systems describe surface reflection behavior using the bidirectional reflectance distribution function (BRDF) They then use it as a weighing function applied, along with an extra cosine term, to the illumination incident upon the surface to compute the final color using the rendering equation [Kajiya 86] This process can take into account light coming from all objects in the scene (indirect illumination) rather than only directly from light sources (direct illumination) In recent years, substantial research effort has been directed at incorporating both arbitrary BRDFs and indirect illu ....

James T. Kajiya. "The Rendering Equation." Proc. SIGGRAPH '86, Computer Graphics 20:4 (1986), 143-150.

....Unfortunately, in order to achieve reasonable performance, current global illumination systems typically trade freedom of viewer and scene motion for both scene complexity and physical accuracy; thus user interaction is severely limited or even prohibited. Currently, only Monte Carlo approaches [48] can handle a wide range of surface geometries, reflection models and lighting e#ects that occur in reality. However, it does not currently appear feasible to apply Monte Carlo methods to interactive context due to its notorious long converging time. To compromise, three methods are normally ....

....is not good at rendering caustics which are indirect (reflected or transmitted) illumination on the di#use surfaces. Due to the natural connection between caustics and reflection (or transmission) paths, some researchers have explored to simulate caustics based on ray tracing. Cook [27] Kajiya [48] used stochastic ray tracing methods to approximate caustics to low accuracy. Arvo [4] introduced a preprocessing step to compute caustics. The preprocessing step uses backward ray tracing (also known as light ray tracing, photon tracing) to emit photons towards the specular surfaces, photons get ....

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

.... is I(X, w) There are three popular methods for solving this integral equation, all explained in Siegel and Howell [8] The first is the Monte Carlo method, originally developed by physicists for neutron transport, and applied to rendering surface interreflection by Cook et al. 29] and Kajiya [30], and to volume applications by Rushmeier [31] Sample rays are traced from the eye through a pixel, and undergo random absorption or scattering, with probabilities based on the extinction coefficient t, the albedo a, and the phase function p. Those rays that end up at a light source or volume ....

James Kajiya, "The Rendering Equation," Computer Graphics Vol. 20 No. 4 (August 1986) pp. 143 - 150.

.... used iterated kernels as well as the method of successive approximations to an alyze equation (63) and some of its simpler forms [28] Kajiya used the Neumann series of an operator equation similar to equation (62) to illustrate the effects of various approximations used in computer graphics [19]. The successive kernels, or terms of the expansion, correspond to rays that have undergone increasing numbers of reflections. This very natural physical interpretation is often referred to as successive orders of scattering in radiative transfer literature [24, 38] The method of discrete ....

James T. Kajiya. The rendering equation. Computer Craphics, 20(4):143 150, August 1986.

....in standard network environments. Memory coherent ray tracing by Pharr et al. [15] has also been able to efficiently render highly complex objects by exploiting coherence between rays. In addition to basic ray tracing their system also implements global illumination effects through path tracing [7]. We share the basic idea of splitting the scene into smaller voxels and using these for manual caching. However, our usage of the voxel structure is quite different, as Pharr et al. performs significantly more reordering and scheduling of computations. In their system intersection computations ....

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

....surface to surface interaction, called steps. The series of these steps composes the walk. In computer graphics the first Monte Carlo random walk algorithm called distributed ray tracing was proposed by Cook et al. CPC84] which spawned to a set of variations, including path tracing [Kaj86], light tracing [DLW93] Monte Carlo radiosity [Shi91] Neu95] PM95] and two pass methods which combine radiosity and ray tracing [WCG87] Random walks can be classified according to the direction they follow the light. A random walk can be initiated from the lightsources and be traced in the ....

James T. Kajiya. The rendering equation.

....surface to surface interactions, called steps. The series of these steps composes the walk. In computer graphics the first Monte Carlo random walk algorithm called distributed ray tracing was proposed by Cook et al. CPC84] which spawned to a set of variations, including path tracing [Kaj86], light tracing [DLW93] Monte Carlo radiosity [Shi91] Neu95] PM95] and two pass methods which combine radiosity and ray tracing [WCG87] Random walks can be classified according to the direction they follow the light. A random walk can be initiated from the lightsources and be traced in the ....

James T. Kajiya. The rendering equation. In Proceedings of SIGGRAPH '86, Computer Graphics, pages 143--150, 1986.

....patch. Whenever the path hits a source, the radiosity of the patch is updated. This method is in principle highly inefficient, due both to the fact that only the origin patch is updated and to the low probability of hitting a source. But if we come back to the integral equation (Rendering Equation [Kaj86]) whose discretisation (and specialization for diffuse surfaces) originates the Radiosity system, we see that we find the gathering method under the name of distributed ray tracing [CPC84] or also path tracing [Kaj86] The paths are only traced from the visible part of the scene (this would mean ....

....a source. But if we come back to the integral equation (Rendering Equation [Kaj86] whose discretisation (and specialization for diffuse surfaces) originates the Radiosity system, we see that we find the gathering method under the name of distributed ray tracing [CPC84] or also path tracing [Kaj86]. The paths are only traced from the visible part of the scene (this would mean in our case to trace them only from visible patches) and the low probability of hitting a source is dealt with by either splitting the ray into one ray directed at the source and another stochastic one, or instead the ....

James T. Kajiya. The rendering equation. In Computer Graphics (ACM SIGGRAPH '86 Proceedings), pages 143--150, August 1986.

....which is able to compute exact results for single pixels. The time to compute a high quality image is usually very long; therefore it is desirable to have already meaningful early images. With progressing computation the solution should improve and finally converge to the correct solution [Kajiy86]. The DCM incorporate such a progressive refinement as well by using a hierarchical block refinement technique. In the following, first the DCM algorithm will be described in more detail (Section 2) and then our improvements for this method will be given (Section 3) 2 The Directional Coherence ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

....Computers, 29(9) 836 840, Sept. 1980. 9] M. Ben Ari. Principles of Concurrent and Distributed Programming. AddisonWesley, Wokingham, England, 1990. 10] A. W. Burks. Programming and structural changes in parallel computers. In W. H andler, editor, Conpar, pages 1 24, Berlin, 1981. Springer. [11] N. Carriero and D. Gelernter. How to Write Parallel Programs. MIT Press, Cambridge, Massachusetts, 1990. 12] D. Chaiken, J. Kubiatowicz, and A. Agarwal. LimitLESS directories: A scalable cache coherence scheme. In Proceedings of the 4 th International Conference on Architectural Support for ....

....of radiosity [7, 5] has been the foundation on which current global illumination methods are based. Neither of the two methods satisfy the needs in global illumination. Ray tracing only simulates ideal specular reflection while radiosity only handles ideal di#use reflection. In 1986 Kajiya [11] introduced the path tracing method which is an extension of the ray tracing method with Monte Carlo techniques. Path tracing is still today the most general global illumination solution. It can simulate global illumination in arbitrarilly complex models both with respect to geometry and ....

[Article contains additional citation context not shown here]

James T. Kajiya, The Rendering Equation. Computer Graphics 20 (4), 143-149, 1986

....would be more densely distributed and a sparse sampling would be tolerable in the periphery. 2 A combination of existing techniques can be combined to build a renderer that handles diffuse as well as specular lighting and computes the sample values independently by tracing independent rays [3]. A Monte Carlo method can be used for stochasticly sampling rays to approximate the surface reflectance function. A sufficient number of independent rays are cast nonuniformly to avoid aliasing artifacts [5] 3.2 Display Sample size and distribution, based on a user s eyepoint, can address only ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, Aug 1986.

....operation of calculating a lighting solution for an environment benefits greatly from our new technique, which can be applied to animation as well as motion blurred still images such as shown above. 3 Global illumination algorithms work by solving the rendering equation proposed by Kajiya [Kaji86]: 1.1) where L Out is the radiance leaving a surface, L E is the radiance emitted radiance by the surface, L In is the radiance of an incoming light ray arriving at the surface from light sources and other surfaces (e.g. reflector R) f r is the bidirectional reflection distribution ....

James T. Kajiya. The Rendering Equation. In SIGGRAPH 86 Conference Proceedings, volume 20, pages 143-150, August 1986. 88

....architecture. The implementation of the framework is covered in Section 4 which also demonstrates the construction of various rendering algorithms. Conclusions and future work are presented in Section 5. 2 Previous Work Many mathematical models are used in image synthesis, the rendering equation [Kajiy86] being one example. These mathematical models are solved by a variety of techniques. By simplifying these, easier and faster methods of solution may be found. For instance the radiosity equation [Cohen88] is a simplified form of the rendering equation that can be solved using finite element ....

....that provides this. What follows are some example setups using the scripting language that illustrate some typical uses of the framework. Each configuration is presented with a diagram showing the communication links between the components that make up the method. 4. 1 Path Tracer The path tracer [Kajiy86, Dutre94] is constructed from a few basic components as shown in Figure 5. Direct Lighting is achieved using an IFunction interface which evaluates rays from the light to the point in question. This is then called from inside the path evaluator. Each box represents a component which can be substituted at ....

James T. Kajiya. The rendering equation. Computer Graphics (SIGGRAPH '86 Proceedings), 20(4):143--150, August 1986. Held in Dallas, Texas.

....quantities we are interested in. In contrast, the FEM has unknowns in the interior as well. For an excellent survey of boundary integral equation issues we refer the reader to [2] We remark that boundary integral equations also arise in global illumination in the form of the Rendering Equation [17], where it is derived from the physics of radiative energy transport. Therefore many of the same issues arise in solving such integral equations. There are also important di#erences; equation 2 is a vector integral equation instead of a scalar equation, and far from being a Fredholm integral ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH 86 Conference Proceedings), volume 20, pages 143--150, August 1986.

....in each domain. In Section 6 we terminate the proof of the main result. Section 7 describes the experimental results obtained by our method in computing FFs, for which exact reference values are available. 2 Background Rendering equation. The rendering integral equation was introduced by Kajiya [15] to model the equilibrium of radiant energy exchange in a scene under a variety of local shading models including diffuse, glossy and specular reflectance within a a non partecipating medium. Extended description of such equations can be found in books such as [7, 4, 28] Using notation in [28] we ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

....and hence we need to recompute the luminance dependent threshold during the indirect illumination computation. Fortunately, evaluation of this component of the threshold model is cheap. 5. 2 An adaptive global illumination algorithm We applied our framework to speed up a path tracing algorithm [15]. Path tracing is a type of stochastic ray tracing that traces random paths through the scene to compute the illumination value for each pixel on the image plane. The variance for computing indirect illumination is generally much higher than for computing direct illumination, so a large number of ....

James T. Kajiya. The Rendering Equation. In Computer Graphics (SIGGRAPH 86 Proceedings), volume 20, pages 143--150, Dallas, Texas, August 1986.

....center would be more densely distributed and a sparse sampling would be tolerable in the periphery. A combination of existing techniques can be combined to build a renderer that handles diffuse as well as specular lighting and computes the sample values independently by tracing independent rays [17]. A Monte Carlo method can be used for stochasticly sampling rays to approximate the surface reflectance function. A sufficient number of independentrays are cast nonuniformly to avoid aliasing artifacts [29] The display: Sample size and distribution, based on a user s eyepoint, can address only ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay,editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, Aug 1986.

....water body. Figure 6 shows fresh water lake Crater Lake a lake in volcanic caldera. Figure 7 shows the same scene with different atmospheric conditions. Whitecaps can be seen during the stormy and rainy conditions. The water surface mesh and water type was input to a Monte Carlo path tracer [8] with a sky model similar to that used by Preetham et al. 17] that appropriately controls illumination based on time date place. We model clouds procedurally using an approach similar to [2] instead of points we use a turbulence function to control the placement of the clouds. Glare effects ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

....through the IAggregate interface. Thus the framework provides similar features and functionality to Arvo and Kirk s Ray tracing Kernel [14] 4. 2 A More Interesting Example A far more interesting example of using the framework occurs when implementing a method for solving the rendering equation[11] via a ray based method. The two most common ray based approaches are # distribution ray tracing # path tracing These two contrasting approaches can easily be represented in the framework. The first approach is implemented as a modified recursive descent distribution raytracer[25] In the ....

....creation of these methods relatively easy. We now have a rendering package, which can be configured to use a multitude of different rendering techniques. The following methods have been implemented with the framework # classical ray tracer [25] # distribution ray tracer[3] # eye path tracer [11] # light path tracer [21] # bi directional path tracer [17] # photon map[9, 7, 8] # irradiance maps [6] A progressive refinement radioisty implementation is currently being developed. What follows are some example pictures that use a variety of the rendering methods implemented with the ....

[Article contains additional citation context not shown here]

James T. Kajiya. The rendering equation. In Computer Graphics, volume 20, pages 143--150. ACM Press, 1986.

....is relatively short. But the lack of effects like soft shadows, caustics, and indirect illumination has lead to the introduction of a more sophisticated, physically based model that describe the interaction of light with surfaces. The most widely used example was introduced by Kajiya in 1986 [26], who adopted an already known model from heat transfer theory [5] It is an integral equation, called the rendering equation that describes the light leaving from a point on a surface as an integral of the light arriving at this location scaled by some function. This function is responsible for ....

....important in computer graphics. It means that instead of using hacks ( If it looks good enough, it is good enough , 1] a physically based model is used that is responsible for a particular effect in the real world. This section provides some motivation for such a model, the rendering equation [26]. 1.1. The Rendering Equation 4 The rendering equation describes the intensity of outgoing light 1 at a point on the surface, as the sum of the self emission of the surface (if it is a light source) plus the incoming light weighted by the reflectance properties of the surface: L(s; L e ....

[Article contains additional citation context not shown here]

James T. Kajiya. The rendering equation. Computer Graphics (SIGGRAPH '86 Proceedings), 20(4):143--150, August 1986.

....into a simple sum of weighted incoming radiances. To our knowledge, this decomposition was first used by Cleary et al. 2] to reduce storage and communication demands in a parallel ray tracing system. 5. 1 Computation Decomposition We can take advantage of the structure of the rendering equation[14] to decompose the rendering computation into parts that can be scheduled independently. When we sample the rendering equation to computing outgoing radiance at a pointx in the direction #r , the result is: Lo#x# #r # # Le#x# #r # # 1 N X N fr #x# # i # #r # L i #x# # i # cos # i # (1) where ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

....two functions M#x;t# and N#x;t# with values over IR 3 giving us the 4 position and outgoing normal of point x in space at time t. We should also be given the diffuse reflectance r#x# of each point x, and the exitance E#x; t# at point x at time t. Under those assumptions, the rendering equation [12] becomes : 8X =#x;t#2#S#T# B#X#=E#X# Z Y=#y;t 0 #2#S#T# B#Y #K#X ;Y #dY (1) where # K is a function defined over #S #T# 2 by K##x; t#; #y; t 0 ## = r#x#k#x;y; t#V #x;y; t#d#t; t 0 # (2) # d#t;t 0 # is equal to 1 when t = t 0 and 0 otherwise. # k is the kernel function defined as ....

James T. Kajiya. The Rendering Equation. In Computer Graphics (ACM SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986. 13

.... is the reflected radiance (watts steradian meter in SI units) rrr 2 iii L(q,f) is the incident radiance f (q ,f ;q ,f ) is the bidirectional reflectance transmittance distribution function (steradian ) iirr 1 The radiance equation is essentially Kajiya s rendering equation [Kajiya86] with the notion of energy transfer between 3To reduce the variance between samples and speed convergence of Monte Carlo integration, light sources are accounted for separately using an adaptive sampling scheme [Ward91] As in most ray tracing algorithms, specular contributions are computed ....

....slowly over surfaces in most scenes, it is more efficient to perform the calculation only occasionally, caching the computed values for local interpolation. This caching of irradiance samples is a significant optimization of more brute force Monte Carlo ray tracing algorithms such as Kajiya s [Kajiya86]. In the meshless caching scheme described in [Ward88b] the location of the computed indirect irradiance values is determined by the proximity and curvature of the surfaces, and does not fall on a regular grid, so a weighted sum is used in place of a more standard bilinear interpolation. ....

James T. Kajiya, "The Rendering Equation," Computer Graphics, Vol. 20, No. 4, August 1986.

....two functions M#x; t# and N#x; t# with values over IR 3 giving us the position and outgoing normal of point x in space at time t. We should also be given the diffuse reflectance ##x# of each point x, and the exitance E#x; t# at point x at time t. Under those assumptions, the rendering equation [12] becomes : 8X =#x; t# 2 #S#T # B#X#=E#X# Z Y=#y;t 0 #2#S#T# B#Y #K#X;Y #dY (1) where 4 # K is a function defined over #S # T # 2 by K##x; t#; #y; t 0 ## = ##x#k#x; y; t#V #x; y; t###t; t 0 # (2) # ##t; t 0 # is equal to 1 when t = t 0 and 0 otherwise. # k is the kernel function ....

James T. Kajiya. The Rendering Equation. In Computer Graphics (ACM SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

....Unfortunately, in order to achieve reasonable performance, current global illumination systems typically trade freedom of viewer and scene motion for both scene complexity and physical accuracy; thus user interaction is severely limited or even prohibited. Currently, only Monte Carlo approaches [48] can handle a wide range of surface geometries, reflection models and lighting e#ects that occur in reality. However, it does not currently appear feasible to apply Monte Carlo methods to interactive context due to its notorious long converging time. To compromise, three methods are normally ....

....is not good at rendering caustics which are indirect (reflected or transmitted) illumination on the di#use surfaces. Due to the natural connection between caustics and reflection (or transmission) paths, some researchers have explored to simulate caustics based on ray tracing. Cook [27] Kajiya [48] used stochastic ray tracing methods to approximate caustics to low accuracy. Arvo [4] introduced a preprocessing step to compute caustics. The preprocessing step uses backward ray tracing (also known as light ray tracing, photon tracing) to emit photons towards the specular surfaces, photons get ....

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

....and reflectances of any point in the scene in any direction to the same quantities for all other positions and directions in the scene. Solving these equations at the surface sample points for each pixel will provide accurate intensities, so the final image will show all effects modeled. Kajiya [Kaj86] and Heckbert [Hec91] have worked to unify these results into a form suitable for use in computer graphics. The following presentation is adapted from their work. To generate an image, we must compute the intensity of light at each wavelength of interest for each pixel. The intensity leaving a ....

....and it is 0 for all points which are not on light sources. 23 Most existing soft shadow algorithms model an area source as a finite collection of point sources. Point shadow algorithms are then applied for each sample point. This has been done with the depth buffer [HA90] ray tracing [CPC84] Kaj86] and shadow volumes [BB84] Unless care is taken, inaccuracies in the approximation of the illumination of an area light source may result and aliasing may occur. Amanatides [Ama84] developed an analytic approach for circular or spherical light sources. This works by constructing a cone of ....

[Article contains additional citation context not shown here]

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

....a high frame rate. We describe methods to generate soft shadows, approximate one bounce indirect lighting, and specular reflection and refraction effects. 1 Introduction and previous work Research in photorealistic rendering has concentrated on numerically solving the rendering equation[9]. Ray tracers[22] use Monte Carlo methods while radiosity systems[6] use finite element methods. These give accurate solutions but are computationally expensive. Classic radiosity methods typically converge faster to a solution to the rendering equation than ray tracers but cannot account for ....

....expensive. Classic radiosity methods typically converge faster to a solution to the rendering equation than ray tracers but cannot account for specular reflection and refraction. Moreover, they are mainly used with planar geometry. Ray tracers obviate both these limitations but require path tracing[9] to get indirect illumination effects which introduces noise and is computationally expensive. Many interactive environments such as Virtual Building Systems[1] rely on precomputation of static environments to form progressive radiosity solutions. These suffer from large computational overhead and ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

.... by simulating the flow of light due to its physical behavior formulated by two relationships the bidirectional reflection distribution function (BRDF) on one hand, which describes the reflection properties of the objects surface points, and the rendering equation, on the other hand [1], which defines the propagation of light between separate instantiations of BRDFs. The BRDF on a certain point is a four dimensional function of the incident and reflected direction of light. Due to the amount of possible BRDF instantiations to guarantee an adequate result, approximations of the ....

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

....rendering operator can be thought of as existing for each chosen geometry. We denote this operator as: RG (L( u) I : 2) If one is willing to discount physical and quantum optics and work with static scene geometries, the rendering operation is linear with respect to the illumination [11, 8, 4] operator. More specifically, rendering obeys the rules of superposition: the image resulting from an additive combination of two illuminants is just the sum of the images resulting from each of the illuminants independently, multiplying the intensity of the illumination sources by a ....

James T. Kajiya. The rendering equation. In Computer Graphics (SIGGRAPH '86 Proceedings) , volume 20, pages 143--150, August 1986.

....the full repertoire of light. Ray tracing [61] and radiosity [13, 38] feature nearly mutually exclusive models of light reflection: each valid in itself, but incomplete. Methods that combine ray tracing and radiosity typically neglect more complex modes of reflection [53] The rendering equation [19] and methods that incorporate complex surface reflection [4, 52] still neglect light scattering by participating media such as smoke. Methods that model participating media have thus far limited the forms of surface reflection [46, 47, 21] Finally, absent from all of the cited approaches are ....

....and physically similar effects [24] as well as subsurface scattering [15] But its usefulness extends beyond these applications. Because of the generality of the equation of transfer, it subsumes many of the equations used in global illumination and volume rendering. Just as the rendering equation [19] unifies an array of rendering techniques, the equation of transfer encompasses an even larger class. We now consider some of the special cases that it subsumes. 3.2.1 Vacuum Conditions If the space separating the surfaces is a vacuum, there can be no volume emission and no particle collisions ....

[Article contains additional citation context not shown here]

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

No context found.

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH 86 Conference Proceedings), volume 20, pages 143--150, August 1986.

No context found.

James T. Kajiya. The Rendering Equation. In volume 20, pages 143--150, August 1986.

No context found.

James T. Kajiya. The rendering equation. In Computer Graphics (Proceedings of ACM SIGGRAPH 86), pages 143--150, 1986.

No context found.

James T. Kajiya. The rendering equation. In Computer Graphics (Proceedings of ACM SIGGRAPH 86), volume 20, pages 143--150, 1986.

No context found.

James T. Kajiya. The rendering equation. Computer 20(4):143--150, August 1986. Held in Dallas (TX), USA.

No context found.

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

No context found.

James T. Kajiya. The rendering equation. Proc. SIGGRAPH 86, pages 143--150, Aug. 1986.

No context found.

James T Kajiya. (1986), "The rendering equation" ACM Computer Graphics , (Proc. SIGGRAPH 86), vol.20.,no.4, pp.143-150.

No context found.

James T Kajiya. (1986), "The rendering equation" ACM Computer Graphics ACM Computer Graphics, (SIGGRAPH 86), vol.20.,no.4, pp.143-150.

No context found.

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

No context found.

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH 86 Conference Proceedings), volume 20, pages 143--150, August 1986.

No context found.

James T. Kajiya, "The rendering equation," Computer Graphics, vol. 20, no. 4, pp. 143--150, Aug. 1986.

No context found.

James T. Kajiya. The rendering equation. In Computer Graphics (ACM SIGGRAPH '86 Proceedings), pages 143--150, August 1986. Published as Computer Graphics (ACM SIGGRAPH '86 Proceedings), volume 20, number 4.

No context found.

James T. Kajiya. The Rendering Equation. In Computer Graphics (ACM SIGGRAPH '86 Proceedings), volume 20, pages 143--150, August 1986.

No context found.

James T. Kajiya. The rendering equation. Computer Graphics, 20(4):143--150, August 1986.

No context found.

James T. Kajiya. The rendering equation. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 143--150, 1986.

No context found.

James T. Kajiya. The rendering equation. In Computer Graphics (SIGGRAPH '86 Proceedings), pages 143-- 150, 1986.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC