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Interactive Global Illumination Using Selective Photon Tracing

Interactive Global Illumination Using Selective Photon Tracing
Interactive Global Illumination Using Selective Photon Tracing

Thirteenth Eurographics Workshop on Rendering(2002) P

1.Introduction

Synthesis of realistic images which predict the appearance of the real world has many important engineering applica-tions including product design,architecture and interior de-sign,and illumination engineering.One of the major com-ponents of such predictive image synthesis is global illumi-nation.Even for less rigorous applications such as special effects,?lm production,and computer games global illumi-nation greatly improves the appearance and believability of rendered images.

The vast majority of existing global illumination solutions are designed for off-line computations and for static scenes. The response times required by such solutions to update illumination information in dynamically changing environ-ments are prohibitively large even for minor changes in the scene,because the whole computation is usually repeated from scratch.Some successful attempts have been made to upgrade those algorithms to exploit the temporal coherence and reuse valid lighting information computed previously. While interactivity is often achieved for some simple scene changes,the storage costs involved in the data structure ex-tensions into the temporal domain are intractable for practi-cal applications dealing with complex scenes.

In this paper we propose a novel global illumination tech-nique designed speci?cally for interactive applications.Our algorithm exploits a periodicity property29of the multi-dimensional Halton sequence,which provides immediate in-formation on the similarity of photon paths in the scene. This enables selective photon tracing into the scene regions whose illumination must be updated due to the user interac-tion.To improve the progressivity of such update energy-and perception-based criteria are introduced whose main goal is to minimize the image artifacts as perceived by the observer.The unique feature of our selective photon tracing is that while the temporal coherence in lighting computa-tions is strongly exploited,no additional data structures in-

c The Eurographics Association2002.

volving photon paths in the dynamically changing scene are required.Moreover,since the photon hit points are bucketed on-the-?y directly into the corresponding elements of dense mesh the photon storage is completely avoided.In practice this means that if the mesh data structures required for ef-?cient ray(photon)tracing?t into the computer memory the global illumination computation can be performed using our method.This makes our technique suitable for interac-tive global illumination even for complex scenes.In terms of hardware requirement a simple PC-class computer equipped with a graphics board offers suf?cient performance for our technique,and expensive multiprocessor computers or com-puter clusters are not required.

Our rendering technique is optimized for interactivity and some of its design decisions clearly trade off image qual-ity for computation speed.The most severe limitation of our technique is the use of simple photon bucketing for the mesh-based reconstruction of indirect illumination(direct il-lumination and resulting shadows are rendered using graph-ics hardware).Obviously,by storing photon hit points and using more advanced density estimation techniques15264118 less bias could be obtained but then the rendering interactiv-ity would be compromised.

The paper is organized as follows.Section2reviews the previous approaches to global illumination in dynamic en-vironments.In Section3we introduce our new framework. We discuss the periodicity property of the Halton sequence which is the foundation for our selective photon tracing in Section4.The algorithm of interactive global illumination computation is explained in Section5.In Section6we pro-vide some implementation details of our interactive system. We discuss the results obtained by our techniques in Sec-tion7.Finally,we conclude the paper and propose some fu-ture directions for this research.

2.Previous Work

The problem of global illumination solutions for dy-namic environments has attracted signi?cant attention of re-searchers,resulting in various solutions which can roughly be categorized as off-line or interactive.In the following sec-tion we brie?y overview representative examples of off-line algorithms.Then we focus on interactive algorithms,which are more relevant for this paper.

2.1.Off-Line Techniques

Off-line global illumination algorithms are used in the pro-duction of high quality animations in which the accuracy of lighting simulation cannot be compromised.Many existing solutions resulted from extending hierarchical radiosity al-gorithms into the time domain,however,they involve huge storage costs which makes them impractical for complex scenes724.In Global Monte Carlo Radiosity2the temporal coherence of costly visibility computations is ef?ciently and conservatively exploited,but then the radiosity solution is performed independently for each frame and all radiosity solutions are stored simultaneously in the memory.In the range-image framework30,direct and indirect lighting are independently sampled in time for selected keyframes.The temporal frequency of sampling is adaptive to the changes in scene illumination.Interpolation is performed between the obtained solutions to derive lighting for inbetween frames, but some important lighting events between keyframes can be overlooked.To avoid this problem,sparse sampling of the scene illumination can be performed for all animation frames27.However,to reconstruct lighting for a given frame Myszkowski et al.27utilize information not only from pre-ceding but also from the following frames,which are not available in the interactive scenario.

In general,it is dif?cult to adapt a typical off-line algo-rithm for interactive applications.All discussed algorithms require that the complete information on all animated scene elements is known in advance.Also,since the main goal of the off-line algorithms is to reduce the overall computation time required for rendering of the whole animation,the dif-ferences in the rendering time of particular frames are per-fectly acceptable.Thus,the constant frame rate usually can-not be kept,which is not acceptable for an interactive sce-nario.

2.2.Interactive Techniques

A number of techniques handling global illumination com-putation for dynamic environments at interactive speeds have been presented.The techniques have been designed to trade the image quality for the response speed,and their main objective is to provide a fast response for frame-to-frame changes in the environment.Early solutions41125 were embedded into the progressive radiosity framework and relied on shooting the corrective energy(possibly neg-ative)to the scene regions affected by the environment changes.

Much better performance was obtained for more re-cently introduced techniques that are based on hierarchical radiosity31833.Those algorithms introduce mechanisms for controlling the frame rate and ef?ciently identifying which part of the scene is modi?ed.However,the hierarchical ra-diosity framework poorly supports the light transfer between glossy and specular surfaces.This drawback can be elimi-nated by adding photon tracing12atop of the line-space hi-erarchy,used for diffuse surfaces8.The photons traversing changed scene regions are identi?ed using a dynamic spa-tial data structure and are selectively updated.But still,the memory requirements in all those hierarchical approaches are extremely high due to the storage of the link structure. Keller introduced the instant radiosity technique19,which, although originally proposed for ef?cient rendering of static scenes,can easily be extended to handle dynamic environ-

c The Eurographics Association2002.

ments.The technique utilizes the quasi-random walk of pho-tons based on Quasi-Monte Carlo integration.Then each photon hit point is considered as a point light source which is processed by graphics hardware.The?nal image is obtained through the view-dependent accumulation of partial images generated for each resulting light source.Keller uses the Hal-ton sequence to generate the photon hit points.A drawback here is that Keller updates the photon paths merely based on their age criterion,ignoring whether they became invalid due to the changes in the scene or not.

The algorithms proposed by Pueyo et al.31and Keller19 are view-dependent which precludes interaction involving changes of camera parameters.This de?ciency is eliminated by view-independent algorithms833,however,the whole scene illumination is always updated with equal priority, without taking into account the current camera parameters and other“importance”factors.If a complete update of the scene illumination cannot be performed during a sin-gle frame refresh cycle,then what becomes important is the order in which the progressive re?nement in various scene regions must be performed for the subsequent frames.The main goal of such an ordering of computation is to minimize the perceivable artifacts at the intermediate stages of a global illumination update,and this problem has basically not been addressed in existing solutions.In this paper we present a view-independent approach,in which the priority of update is based on the current view and the perceivability of illumi-nation artifacts.

Recently,various image caching schemes have been pro-posed,which allow for rendering of non-diffuse surfaces for changing camera positions at interactive speeds403536. Our approach could bene?t signi?cantly from such solutions which could be incorporated into our interactive global illu-mination system.In this paper we focus on global illumina-tion for diffuse environments due to the limitations of illu-mination storage in the mesh.However,during our photon tracing,arbitrary surface re?ectance functions are properly processed.

3.Overview

As a framework for global illumination computation,we chose the Density Estimation Photon Tracing(DEPT) algorithm37.The DEPT is similar to other solutions in which photons are traced from light sources towards surfaces in the scene,and the lighting energy carried by every photon is de-posited at the hit point locations on those surfaces1541.We extend the DEPT for handling dynamic environments.Also, we replace stochastic pseudo-random sequences,which are used in the DEPT to generate photon paths,by deterministic quasi-random sequences.

In our algorithm we consider the same big pool Z of pho-tons(which are traced at the initialization stage)for the whole interactive session.We update the photons computed for previous frames,which became invalid for the current frame due to interactive changes in the scene.The main problem is to identify each invalid photon in Z and to re-place it by the corresponding photon,which is traced for the current scene con?guration.Our photon tracing is based on Quasi-Monte Carlo sampling with the multi-dimensional Halton sequence.We show how the periodicity property29of this sequence,allows for immediate identi?cation of photons that have similar paths in the scene.Thus,for any invalid photon,it is easy to identify indices of all similar photons in Z that are likely to be invalid as well.Since the Halton se-quence can be used to generate any photon path based on its index,the storage costs of photon data can be eliminated. Our algorithm of photon updating is iterative.The user decides upon the iteration duration,which imposes a limit on the number of photons that can be traced per iteration. The photon update iteration consists of two stages.In the ?rst stage a subset of photons from Z are traced from the light sources to the whole environment in order to identify invalid photons.In the second stage,based on the periodic-ity property of the Halton sequences,those invalid photons are used to generate similar photons in Z,which are likely to traverse modi?ed scenes regions.Since it might be impossi-ble to update all those potentially invalid photons in a single iteration,the photon update in various scene regions is or-dered by inexpensive energy-and perception-based criteria according to the importance of outdated lighting artifacts as perceived by the user.Our algorithm is conservative in the sense that?nally,after N g iterations since the last change in the environment,all photons in Z are updated.In practice, when changes in the environment are local,a small num-ber of iterations r N g is required to remove all perceiv-able problems with the outdated illumination.The constant frame refresh rate,which is required by many practical ap-plications,is achieved by letting the user control the iteration duration and the number of such iterations per frame.

4.Quasi-Monte Carlo Sampling

The global illumination problem involves solving high di-mensional integrals.An ef?cient way to solve such integrals is to apply Monte Carlo techniques,which have an advan-tage over other integration methods because their conver-gence speed does not depend on the dimension of the in-tegral.

Monte Carlo(MC)techniques are traditionally based on pseudo-random sequences.However,it was proven that for functions with bounded variation,faster convergence can be achieved using Quasi-Monte Carlo(QMC)techniques based on quasi-random sequences17.Although integrands usually have unbounded variation in global illumination tasks,nu-merical evidence has been presented that the QMC tech-niques still have advantage over the MC techniques for real-world scenes16.

In the following section we examine basic properties of

c The Eurographics Association2002.

the Halton sequence,which is an example for the quasi-random sequence that proved to be useful in photon tracing19 and stochastic radiosity28applications.

4.1.The Halton Sequence

The Halton sequence generation is based on the radical in-

verse function,applied to an integer i.The radical inverse Φb i is the number obtained by expressing i in the base b, then reversing the order of the resulting digit sequence and

placing the?oating point at the sequence beginning13:

Φb i∑

j0a j i b j1i∑

j0

a j i

b j(1)

where a j i are subsequent digits of i.For instance Φ10123404321.

For photon shooting we need to associate the index of each photon with a sequence of numbers,thus the multi-dimensional Halton sequence must be considered.Such a se-quence is usually obtained by using prime numbers as bases for different dimensions.For example,for integer i the fol-lowing sequence can be considered:

iΦ2iΦ3iΦ5iΦ7iΦ11i(2)

When sampling discrete events,a single quasi-random number can be re-used via the remapping procedure(refer to Shirley et al.34,Fig.8).In this way we use the two?rst quasi-random numbersΦ2i andΦ3i to choose a light source and the photon emission direction,the next two num-bersΦ5i andΦ7i to determine the photon-material event (photon absorption or scattering)and the re?ection direction for the?rst photon bounce,and so on.

4.2.Periodicity of the Halton Sequence

The observation that the Halton sequence has a highly periodic nature is hardly new29.Note for example how similar the values of following base-10radical inverses are:Φ10123404321,Φ101234100004322,and Φ101234200004323.We express this periodicity property in a form which is well suited for the task of?nding similar photons(paths)in photon(path)tracing algorithms:

Φb iΦb i mN g

1

Figure1:Distribution of photons between groups for N g 4.Each row represents one group.Each group contains a number of pilot photons(rectangle)as well as a number of corrective photons(vertical lines)whose indices are spaced with interval N g.

time moment.We denote such scene properties as scene phantoms.The algorithm can consider different dynamic scene properties.The most obvious are object positions and surface BSDFs(Bidirectional Scattering Distribution Functions).

According to the periodicity property discussed in Sec-tion4.2,corrective photons are concentrated in a tight sub-space of the multi-dimensional photon space.In practice this means that corrective photons of the same group are usually emitted by the same light source,traced in similar directions, have similar probability of being absorbed when they hit a given surface,and so on.Increasing N g increases the num-ber of groups and simultaneously decreases the space span occupied by every group.Note that when changing N g it is important to keep it factorized according to Equation(5). The size and space?lling characteristics of photon groups can be tuned according to the desired properties of the global illumination update using the following parameters:

N g de?nes the photon groups number and simultaneously the span between the indices of corrective photons

N p de?nes the number of the pilot photons in each group R de?nes the ratio between the total number of photons in each group and N p.

Given those parameters,the total number of photons uti-lized by the algorithm is equal to N g N p R.All photons with indices i0N g N p are the pilot photons,and all photons with indices i N g N p N g N p R are the corrective photons.

5.2.Illumination Update

Our algorithm is fully interactive,which means that it does not require any a priori knowledge on changes in the scene. In the following discussion we assume that user interaction consists of changing object positions(the case of surface BSDF changes is easier to handle and will be

explained Figure2:The bounding volume of corrective photons from a single group starts as a pyramid,but then its shape might become more complicated as the result of photon interaction with scene objects.For the?gure clarity we marked just one bounce of photons(grey pyramids re?ected from white ob-jects)but obviously all higher bounces are also considered as required for the global illumination computation. later).Updating illumination after scene change requires that photons intersecting moving objects must be reshot. Reshooting of a photon consists of tracing it for the old scene con?guration with negative energy and then tracing it for the new scene con?guration with positive energy.Since usually only a small number of photons intersect moving objects, such double effort is justi?ed compared to calculating the solution anew.

Ef?cient searching of invalid photons is a hard problem. We attempt to solve it by subdividing the multi-dimensional photon space into relatively small volumes and searching for those volumes,which intersect the moving object.Accord-ing to the periodicity property discussed in Section4.2,the corrective photons in a single group which are emitted by a light source are bounded by a pyramid with its apex lo-cated at this light source position(Figure2).The pyramid shape might become more and more complicated as the re-sult of interaction between scene objects and the corrective photons.However,even if the pyramid is split into a number of subpyramids,the resulting bundles of photon paths still remain coherent in space and are fully bounded by those subpyramids.

The computation of intersection between bounding vol-umes of complex shape(as depicted in Figure2)and moving

objects is required to identify invalid photons.Additionally it is important to estimate the impact of those invalid photons on the correctness of rendered images.Such an estimate is required to?nd out the order in which to reshoot the photon groups,which reduces image artifacts as perceived by the human observer.We address those problems by shooting the pilot photons.

In contrast to the corrective photons,the pilot photons are not coherent and uniformly sample the space of vectors de-?ned in Equation(2).The shooting of pilot photons is in-terleaved with the shooting of corrective photons by placing them in the same group(see Figure1).Let i be the pilot photon,which intersected the moving object.We then claim that the bounding volume of corrective photons belonging to group i g with

i g i mod N g(6) intersects this object as well.Indeed,all corrective photons of that group are given by indices N g N p i g cN g,where c

is a non-negative integer.The index i given by Equation(6) differs from the index of any corrective photon of group i g by some multiple of N g.Thus,according to Equation(3),this photon is inside of the multi-dimensional pyramid,which bounds all corrective photons of that group.This means that it also is inside of the bounding volume,created when this pyramid intersects scene objects.Since the pilot photons sample the multi-dimensional vector space(de?ned in Equa-tion(2))uniformly,the number of their hits with moving ob-jects provides an approximate measure how important it is to update the group(in Section5.3we discuss in detail the corresponding problem of photon updates ordering).

Our approach to identify moving objects is not conserva-tive(refer to Briere and Poulin3and Bala et al.1for discus-sion of the conservative solutions).Even if no pilot photon detects the intersection of a group of corrective photons with a moving object,it is nevertheless possible that such an inter-section takes place.However,this typically happens if the in-tersected volume is very small and does not contribute much to the changes of global illumination.Also,when scene ob-jects stop their motion,all N g groups are?nally updated, which means that all invalid photons will be corrected,and then the only negative consequence of such undetected in-tersections is a non-optimal ordering of the group update. One may advocate that it is easy to conservatively?nd the intersection between moving objects and the?rst segment of a pyramid with the apex at the light source position(e.g., such an approach is used to reinforce the caustic photons in the photon mapping technique18),however,we are aiming for a general solution that has some potential to detect invalid photons bouncing an arbitrary number of times in the scene. Also,the density and coherence of the pilot photons in the ?rst pyramid segment is very good,which usually results in the high probability of detecting moving objects.

The pseudo-code in Algorithm1summarizes the process of illumination update.

while there are groups containing scene phantoms do

among all such photon groups,?nd the one with highest priority;

place scene phantoms of that group into BSP grid and forbid scene changes;

for all photons i in the photon group do

perform Monte Carlo tracing of photon i according

to Equation(2)without updating the global illumi-

nation;

if photon i hit dynamic object or scene phantom then

if photon i is pilot then

if photon i hit dynamic object then

increase the priority of corresponding group;

else if photon i hit scene phantom then

increase the priority of corresponding group

only if it contains intersected phantom;

end if

end if

duplicate the photon and trace two resulting pho-

tons:

-photon,which ignores scene phantoms and has

positive energy;

-photon phantom,which ignores dynamic objects

and has negative energy;

end if

end for

display partially updated solution via OpenGL;

remove all scene phantoms from the BSP grid and from just reshot photon group,allow scene changes;

set the group priority to0;

end while

nore the phantom object at position M1,and rays that ignore

the actual object at position M2.

At the moment of time t3when the object changes its posi-tion to M3,the last update of some photon groups could have

been performed at t2,but there is also a chance that some

groups have been updated only at t1.The latter groups still contain the object phantom at position M1.Since any photon

group corresponds to a frozen scene con?guration at a par-

ticular moment in the past,it cannot contain two phantoms of the same object.This is why the newly created phantom

at position M2must be placed only in those photon groups,

which do not contain the phantom at position M1.

User interaction with surface BSDFs is processed in a similar way as described in Algorithm1.However,this does

not involve any update of the ray tracing acceleration data

structures.The scene phantoms store the surface BSDFs from the last iteration in which photons from the current

group were updated.

In our current implementation user interaction with light sources is not supported,although it is relatively easy to ex-

tend our algorithm for this purpose.A number of special

cases for changing the light source position,emitted energy, goniometric diagram and so on should be considered.For ex-

ample,user interaction changing the position of light sources

should result in increasing the update priority for all groups

for which photons are emitted by dislocated light sources. The old position of the light source should be stored as the

scene phantom.

5.3.Priority of Photon Groups Processing

An important issue is setting priorities of photon group pro-cessing in order to minimize the perceivability of illumina-

tion artifacts by the user.For this purpose we consider three

factors which affect the image appearance:

Changes in the scene detected by the pilot photons. Visual masking of lighting patterns by textures.

Current camera view frustum.

The pilot photons are used to compute the importance of

photon groups.If pilot photon i hits a dynamic object,the

importance P of the group i g is increased by increment?p. Also,if a scene phantom is hit by i and belongs to the list

of phantoms for i g,P is increased by the same increment

?p(some arbitrary value is chosen,e.g,?p1).The im-portance increment?p can be reduced for a given photon

hitting a texture as the result of visual masking.

Visual masking of lighting patterns by textures may sig-ni?cantly reduce the observer sensitivity to artifacts in the scene illumination.For surfaces with strong masking,the priority of illumination update can be reduced with respect to non-textured surfaces.We follow the approach by Du-mont et al.10in which the VDP proposed by Ramasub-ramanian et al.32is used to estimate the visibility thresh-old elevation T e for textures at the preprocessing stage.

We

a)b)

Figure3:Visual masking processing a)sample texture and

b)visibility threshold elevation map(brighter regions in the

map correspond to higher masking).

introduce one modi?cation to this procedure which is in-

spired by Luebke et al.23.For a given mesh density and texture mapping parameters for this mesh it is possible to

estimate the relation between the highest spatial frequency

of indirect illumination reconstructed using this mesh and the spatial frequencies in the texture.The visual masking

can be observed mostly between stimuli of similar spatial

frequencies6.Therefore,prior to the VDP processing we eliminate from the texture all frequencies higher than the

mesh imposed maximum frequency of indirect illumination.

This modi?cation makes our approach more conservative and excessive values of T e can be avoided.As a result of the

VDP processing we obtain a set of the average T e values for

a given texture at each MipMap level.In Figure3(see Ap-pendix/Color section)we show an example of the visibility

threshold elevation map obtained using our VDP.

During photon tracing we access textures assigned to

scene surfaces in order to estimate the probability of photon

absorption and to determine the color of scattered photons. While the texture is sampled at its original resolution,we

need to access T e at the proper MipMap level.For this pur-

pose we use a simple heuristic which takes into account the surface distance to the observer and its spatial orientation.

We use the T e value for the photon hit texture to modify the

importance P of the group i g by increment?p T e.This is an application example in which the perception-based error

metric is used to steer the global illumination computation

with negligible overhead costs.Also,the potential inaccura-cies of such perceptual steering are fully recoverable in our algorithm because only the computation ordering is affected. Although our algorithm is view-independent,better ef?-ciency of illumination update can be achieved by assigning higher priorities to the visible regions of the scene.We ef?-ciently combine visibility information with the group impor-tance P by controlling the visibility status V for every photon group.This visibility status is updated for every frame as a by-product of the pilot photons tracing.It is costly to deter-

c The Eurographics Association2002.

mine the visibility of the photon hit exactly,thus we only use view frustum culling here.Photon hits inside of view frus-tum can affect the image quality,so we increase V of the corresponding group.In contrast to the value P,V is view dependent and we have to reset it after each camera change. Thus,V is taken into account only if the number of pilot pho-tons,shot after the last camera change,is suf?cient for its robust estimate.Otherwise,we assume that V1for each group.

After the pilot photons of the current group are shot,and V and P are updated,the next group of corrective photons with the highest priority measured as V P is selected.

6.Implementation

We implemented our algorithm as a hybrid rendering sys-tem where graphics hardware is responsible for computing direct illumination,the corresponding hard shadows,and vi-sualizing the indirect illumination.The software part of our engine is mostly dedicated to calculating the indirect illumi-nation.Both parts run in parallel using multi-threading,and are synchronized by the important events(update of indirect illumination,user interaction etc.).

For scenes with multiple light sources,whose processing would require many rendering passes of graphics hardware, another strategy of direct lighting computation can be con-sidered.The user may select the most important for his ap-plication light sources to be processed by graphics hardware to obtain the good quality of shadows.The remaining light sources can be processed on the photon basis without any extra cost since photons are traced from the light sources anyway.The problem with such an approach is that the di-rect illumination is then reconstructed on the mesh basis and the resulting shadow boundaries are fuzzy with some possi-ble artifacts.

Shooting photons requires ef?cient ray tracing accelera-tion data structures for dynamic environments.Initially we relied on multi-level voxel grids.Recently,we switched to the axis-aligned BSP-tree with a cost function14,which allowed us to improve the computation performance sig-ni?cantly(up to3times).At present we do not use any hardware-dependent optimizations of ray tracing(e.g., SIMD,prefetching,and so on)as suggested by Wald et al.39. Obviously by adding such optimizations the ray tracing per-formance could be further improved.

6.1.Direct Illumination

For computing the effect of direct illumination we chose to use OpenGL-compliant graphics hardware.Instead of re-stricting ourselves to the?xed function pipeline of standard OpenGL we utilize programmable vertex and pixel hardware to gain the highest qualitative and most ef?cient rendering possible.Our current implementation is customized to run on NVIDIA GeForce3graphics cards,but can of course also be implemented on any other card with similar features(e.g. ATI’s Radeon series).

6.1.1.Shadows

One of the main aspects of image quality is an accurate rep-resentation of shadows.Although shadow mapping42is di-rectly supported by the graphics hardware it is problematic due to its sampling problems.Another disadvantage is that for dynamic environments shadow maps change very often which would lead to a huge amount of regeneration passes. We therefore prefer the shadow volume algorithm proposed by Crow5since it

generates very precise shadows by performing calcula-tions in object space,

can be ef?ciently implemented using graphics hardware, and

is appropriate for dynamic environments.

For complex scenes the generation of shadow volumes, which requires?nding the silhouette edges of all objects with respect to the light source,is quite expensive.By ex-ploiting temporal coherency of shadow volumes we can limit the regeneration of shadow volumes to those objects that are moving and reuse the volumes of all static objects from the previous frame.

Our shadow volume implementation is based on the hard-ware stencil buffer scheme presented21,which solves the problematic cases of shadow volumes intersecting the near clipping plane.

With normal OpenGL the shadow volume algorithm would require N1rendering passes where N is the num-ber of shadow casting light sources.However using pro-grammable features available on recent graphics hardware20 we are able to collapse up to4passes into a single one.This is done by?rst rendering the scene’s geometry as seen by the camera,resulting in having the depth values of the front most pixels in the depth buffer.After this we loop over the ?rst four light sources where in each step we?rst initialize the stencil buffer and draw shadow volumes with the corre-sponding stencil operation(increment/decrement).The con-tent of the stencil buffer,which corresponds to the shadow test result,is then copied to one of the color buffer channels (red channel for?rst light,green channel for second,etc.) and the stencil buffer is initialized for the next light source. After this loop we obtain a RGBA shadow mask containing the shadow information for up to four light sources.

In the?nal rendering pass we then render the scene once again but this time using a customized vertex program22 which instead of summing up all lighting contributions for a given vertex uses additional output attributes that hands out the illumination for light source L03separately.These values will then be linearly interpolated over the primitive (triangle)and passed to the texture blending stage.

c The Eurographics Association2002.

Having the shadow mask as an projective RGBA texture we can apply the shadow result separately for each of the four light sources and output the total illumination as the pixel value.

out indirect illum L0mask R illum L1mask G

(7) For more light sources this approach can be extended by sim-ple multi-pass rendering.So for N light sources we have to generate N4shadow masks.Another N4passes are needed to compute the illumination.These passes can then be summed up using additive blending or the accumulation buffer.

This shadow mask scheme is not only very ef?cient but also enhances image https://www.wendangku.net/doc/0b6360537.html,ing the normal loop scheme, the contributions of all light sources need to be summed up using either the accumulation buffer or additive blending. Since both operations are performed at the end of the pixel pipeline precision is limited to(normally)8bits per color channel,whereas our approach sums up at an earlier stage in the pipeline where precision is much higher.Accuracy is also increased for N4since we use the accumulation buffer(or additive blending)for groups of four light sources rather than summing up the contribution of individual lights. Another advantage is that our method does not suffer from z-?ghting artifacts which normally occur when rendering the scene several times.

6.1.2.Goniometric Diagrams

In order to achieve realistic image quality we also choose to support complex point light sources with non-uniform di-rectional power distribution.Description of these goniomet-ric diagrams are available in standardized formats and are essential for accurate lighting computations.

We include these distributions by re-sampling from the standard format to a cube map texture38,which can ef?-ciently store the complete360o view of a point light source and which is supported by the graphics hardware. Restricting ourselves to monochromatic goniometric dia-grams we can include these as an additional scaling factor for the local illumination of a given light source.Referring to Equation7the mask scaling factor,which was considered to be either1.0for lit and0.0for shadowed pixels,can be used to perform this additional scaling.In the?rst rendering pass we render using the appropriate cube map textures and store the scaling factors in one of the color https://www.wendangku.net/doc/0b6360537.html,ing four texture units and RGBA masking we are able to gener-ate these for4light sources simultaneously.When copying the result of the shadow test back to the color buffer we set all pixels to00where the shadow test succeeded.Although the dynamic range of these textures is limited to00to10 this method still improves image quality signi?cantly while introducing only a minimal overhead.7.Results

We present results that we obtained for the ROOM scene (about12,400mesh elements)and for the HOUSE scene (about377,900mesh elements).The ROOM scene is illumi-nated by four,the HOUSE scene by two light sources with goniometric diagrams.Figures4(see Appendix/Color sec-tion)show snapshots of the two scenes obtained during an interactive session.

All timings were measured on1.7GHz Dual P4Xeon computer with an NVIDIA GeForce364MB videocard.The frame rate is governed by the speed of OpenGL rendering. For the ROOM scene8fps and for the HOUSE scene1.1fps are achieved,which includes the display of indirect lighting, and direct lighting with shadow computations performed by the graphics hardware.Our current implementation does not support triangle strip generation which affects the refresh rate.This however is not a limiting factor for the perfor-mance of indirect lighting update because it is re?ned at an even slower pace.

As we mentioned in Section5.1,our algorithm perfor-mance can be tuned by the parameters N g,N p and R.The parameter N g controls the number of the Halton sequence dimensions,for which corrective photons of the same group remain coherent.We chose the initial factorization of N g for two dimensions to be2332.This splits the?rst and second di-mensions to8and9spans,respectively.The remapping pro-cedure(refer to Section4.1),applied after the light source selection step,effectively reduces the spatial coherence in the?rst dimension.To compensate for this,we increase the corresponding power k2proportionally to the number of light sources present in the scene.This results in factoriza-tions2532and2432for the ROOM and HOUSE scenes,re-spectively.

The graphs in Figure5demonstrate the in?uence of N g parameter on the speed of the global illumination update as the result of an object movement from one position to an-other.The ef?ciency of the update is measured by the num-ber of reshot relevant photons as a function of time.We call those photons relevant,whose hit points are dislocated as a result of scene changes.All relevant photons must be reshot to complete the illumination update.The algorithm perfor-mance is compared for N g288(factorization:2532)and N g10080(factorization:25325171).For N g288only direct photons belonging to a group are spatially coherent, while for N g10080also the?rst bounce of scattered pho-

tons is coherent.Two cases are considered for each of the N g values:the moving object is illuminated1)directly and2) indirectly.In the?rst case the number of groups has a small impact on the performance of illumination update.This can be explained by the fact that the moving object is mostly hit by the direct photons,which are coherent even for small N g. If the moving object is illuminated indirectly,a much better performance is obtained for larger N g because the coherence

c The Eurographics Association2002.

a)b)

Figure5:The number of found relevant photons as a function of time.The moving object is illuminated by a)both direct and indirect lighting,b)only indirect lighting.The horizontal line shows the total number of relevant photons,which must be updated.

of the?rst bounce of re?ected photons becomes important.

Such coherence is not ensured for N g288.

Figure6(see Appendix/Color section)shows the ability

of the algorithm to?nd the coherent photons after the?rst in-direct bounce from the surface.Photons from both depicted

groups re?ect diffusely from the?oor in the direction of the

moving objects.

The speed of the global illumination update depends

strongly on the pilot photon’s ratio in the pool,which de-?nes the precision of the group priority computation.If this

ratio is too small,important photon groups can be missed

and then reshot too late.Conversely,if the number of pilot photons is too large,the update ef?ciency is reduced because

the pilot photons are shot essentially in a random order.Fig-

ure7demonstrates this dependency for the ROOM scene.N p and R values are selected in such a way,that the total num-

ber of photons is constant and only the ratio of pilot photons

changes.We have found that R16,which corresponds to only6.25%of pilot photons in the pool,yields nearly op-

timal performance.As can be clearly seen in Figure7,for

R32(3.125%of pilot photons)the photon group ordering is not robust and the overall update performance is worse. According to our experiments,full recovery of perceiv-able illumination artifacts resulting from the furniture move-ments in the ROOM and HOUSE scenes usually takes2–4and 4–8seconds,respectively.The total number of photons in the pool for the ROOM scene was1,152,000and for the HOUSE scene1,728,000.

Storing the photon paths for all photons could be man-

ageable for the number of photons we presently use,which

could perhaps help to avoid some computation,e.g.,tracing some photons with negative energy.However,our experi-ments have shown that tracing changed photon paths twice introduces an overhead which on average was below25% (some initial segments of the photon path may be the same

Figure7:Number of found relevant photons as a function of time,depending on the ratio R between the total number of photons and the number of pilot photons.The total number of photons in the pool is constant.The dotted line shows the theoretical update progress under the assumption that the photons are updated in a random order.

and can be computed only once).Handling stored photon paths would incur some overhead,and the extension of our algorithm to handle more photons and a?ner mesh in or-der to obtain an even better quality of lighting reconstruc-tion would be more dif?cult(e.g.more than one proces-sor for photon tracing could be used or a faster ray tracing algorithm39could be implemented).

8.Conclusions

We propose a novel interactive global illumination technique for dynamic environments which is suitable for processing complex scenes.Based on the periodicity property of the Halton sequence we are able to trace photons coherently only into those scene regions which require the illumination

c The Eurographics Association2002.

https://www.wendangku.net/doc/0b6360537.html,ing our technique,the temporal coherence of the scene illumination can ef?ciently be exploited without any signi?cant storage of data involving the temporal domain. Progressive re?nement of rendered frames is steered using energy-and perception-based criteria in order to minimize image artifacts as perceived by the user.As a result subse-quent frames can be ef?ciently rendered and the temporal aliasing is practically reduced below the perceivability level. The quality of the direct lighting distribution and shadows signi?cantly bene?t from our ef?cient hardware implemen-tation.

Selective photon tracing has many potential applications which require local reinforcement of computations based on some importance criteria.An example of such an applica-tion is the ef?cient rendering of high quality caustics,which usually requires a huge number of photons.After identify-ing some paths of caustic photons,more coherent caustic photons can easily be generated using our approach.The drawback of many existing photon based methods is that too many photons are sent into well illuminated scene regions with a simple illumination distribution,and too few photons reach remote scene regions.This de?ciency could easily be corrected using our approach,by skipping the tracing of re-dundant photons and properly scaling the energy of the ac-tually traced photons.As future work we plan to pursue our research along those avenues.Also,we would like to include specular and glossy effects into our interactive renderer us-ing pixel-selective ray tracing.

9.Acknowledgments

We would like to thank Philippe Bekaert,Katja Daubert and Vlastiml Havran for their helpful comments and sug-gestions.This work was supported in part by the European Community within the scope of the RealRe?ect project IST-2001-34744“Realtime visualization of complex re?ectance behavior in virtual prototyping”.

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a)b)

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.

a)b)

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c The Eurographics Association 2002.

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