Fast Global Illumination Baking via Ray-Bundles (sap 0046)

Yusuke Tokuyoshi∗

Square Enix Co., Ltd.Takashi Sekine†

Square Enix Co., Ltd.Shinji Ogaki‡

Square Enix Co., Ltd.

Figure 1: Left: real-time rendering using light maps (122640 triangles scene). Right: the light maps generated by our renderer (1024×1024pixels per image). The total rendering time for the light maps is 181 seconds (ray-bundle resolution: 2048×2048 pixels, 10000 directionalsamples, GPU: NVIDIA GeForce GTX 580).

1 Introduction

In interactive applications such as video games, light maps are of-ten used to generate realistic images. However, baking light mapsis time consuming because it is necessary to compute global illu-mination. This sketch presents a simple and fast rendering systemfor light maps. Our system exploits ray-bundles on DirectX R©11capable GPUs and outperforms ray tracing based methods. Fur-thermore, it supports tessellation for DirectX 11 games.

1.1 Related Work

Ray-bundles The use of global ray-bundles was introduced bySbert [1996]. Szirmay-Kalos and Purgathofer [1998] used globalray-bundles for global illumination algorithm based on finite ele-ments. They compute radiance exchange between visible surfacesusing rasterization. Hachisuka [2005] proposed ray-bundles usingrasterization for final gathering. To obtain each depth fragment,depth peeling [Everitt 2001] was used. Hermes et al. [2010] usedk-buffer [Callahan et al. 2005] and they demonstrated high-qualityglobal illumination with multiple glossy reflections using their ra-diance exchange.

Per Pixel Linked-list Everitt [2001] introduced a multi-pass ren-dering method called depth peeling for order independent trans-parency. Ideally, we would need to store a list of fragments perpixel as A-buffer [Carpenter 1984] in a single-pass. Callahan etal. [2005] proposed k-buffer. Although it can be created in asingle-pass, the number of fragments per pixel is fixed. Yang etal. [2010] introduced a method to dynamically construct highlyconcurrent linked-list on DirectX 11 GPUs. This method is fasterthan depth peeling for calculating order independent transparency,and provides unlimited storage per pixel unlike k-buffer. However,the fragments in the list need to be sorted for order independenttransparency.

Tessellation DirectX 11 GPUs support hardware tessellation. Itenables real-time graphics to use arbitrary tessellation methods.However, it is not easy for offline rendering. In order to obtainexactly the same appearance both in real-time graphics and offlinerendering, offline renderers and real-time rendering engines have touse the same tessellation method. The simplest solution is to firsttessellate the polygons. However, this is memory consuming. A

∗e-mail:tokuyosh@square-enix.com†e-mail:sekine@square-enix.com‡e-mail:ogaki@square-enix.com

complex and costly out-of-core rendering system may be needed.Direct ray tracing [Smits et al. 2000; Ogaki and Tokuyoshi 2011] isone of the solutions, but arbitrary tessellation methods are still dif-ficult. Our renderer is able to support the same tessellation methodsfor real-time graphics without a complex implementation.

2 Method

2.1 Ray-Bundle Tracing on the GPU

Our algorithm is based on ray-bundle tracing. It focuses on a sin-gle global direction, and computes the visibility for all fragmentsin a scene in parallel as shown Figure 2 (left). This can be done byrendering the scene from the sample direction using parallel pro-jection, similar to rendering a shadow map from a directional lightsource. In this pass, the fragment data is stored to a buffer. Then,in the next pass, the radiance of a fragment is obtained from thebuffer for each shading point. We create ray-bundles using per pixellinked-list construction on DirectX 11 GPU [Yang et al. 2010]. Foropaque objects, this can be done much faster because there is noneed to sort the fragments unlike order independent transparency.

2.2 Radiance Exchange

We solve the light transport problem by radiance exchange de-scribed in [Hermes et al. 2010]. They used texture atlas for in-termediate data structures, whereas we use light maps directly. Thelight maps are updated in an iterative fashion. The light transfer iscomputed between all pairs of successive points. These pairs can befound using ray-bundles (see Figure 2). Let x1 and y1 be a pair ofsuccessive points. The pixel corresponding to x1 in the light mapsis updated using the radiance at y1. The approximated radiance aty1 can be obtained by light maps computed in the previous itera-tion. Similarly, the pixel corresponding to y1 in the light maps isupdated using the previous radiance at x1. Although this updat-ing scheme is a biased method, it allows an arbitrary number ofinterreflections and converges to the truth. The weight of a bounceis reduced according to number of interreflections. Therefore, thebias at the ith bounce is given by:

Bi ∝ min(i

m, 1)ρi, (1)

where m is the number of samples and ρ the albedo of surfaces.Since we can assume ρ < 1 in most scenes, the bias converges tozero.

Ray-bundle Light map

Figure 2: Ray-bundle tracing and radiance exchange. The sampledirection is randomly generated and the light maps are updated inan iterative fashion. A ray-bundle is created as a per pixel linked-list in each iteration. And light transport is computed by looking upthe radiance of visible fragments from the light maps which werecomputed in the previous iteration.

2.3 Sampling of Ray Directions

Ray-bundles transfer radiance not only into the direction ω, but alsointo −ω. If the orientation is sampled uniformly, then its probabil-ity density function is p(ω) = 1/2π. When a scene is lit by anenvironment map, importance sampling is done according to theemitted radiance of the environment map to reduce variance. Wecalculate the probability density function as follows:

p(ω) =Le(ω) + Le(−ω) + 2Lo∫

ΩLe(ω′) + Lodω′

, (2)

where Le(ω) is the emitted radiance from the direction ω of theenvironment map and Lo is the user-specified offset to account forindirect illumination.

2.4 Tessellation

Since our visibility test is done by rasterization on DirectX 11 GPU,our baking system can easily utilize hardware tessellation. In addi-tion, the domain shader can be shared with the real-time renderingengine. Therefore, we are able to render highly tessellated scenewithout complex implementation such as an out-of-core algorithm.

3 Results

Figure 1 shows generated light maps. The scene contains 122640triangles. 7 high-quality light maps are rendered in 181 secondswith NVIDIA GeForce GTX 580. The resolution of ray-bundle is2048×2048 pixels, and 10000 directions are sampled. The perfor-mance of our renderer is over 200 M rays per second on a commod-ity GPU.

4 Discussion and Future Work

The computational complexity of our method is O(mn), where mis the number of samples and n is the number of primitives. On theother hand, the complexity of general ray tracing based algorithmsisO((n+m) logn), because the acceleration structure constructionneeds O(n logn), and ray tracing needs O(m logn). Therefore, inthe case of enormously high-polygon scenes with a huge number ofsamples, our method may be slower than general ray tracing basedmethods. However, in real-time applications such as games, the

number of primitives is limited by memory size and run-time per-formance. If a scene is highly tessellated, ray tracing based systemmay need to use slow direct ray tracing methods or out-of-core al-gorithms. On the other hand, the use of hardware tessellation issimple and fast. For most scenes, we can achieve sufficient qualitywith less than 10 thousand samples and our system outperforms raytracing based baking systems.

Currently, our renderer only supports lambertian materials. How-ever, we can use arbitrary BRDFs with a slight modification asshown in [Hermes et al. 2010]. Ray-bundle based methods are weakin computing highly glossy reflections, especially perfect specu-lar surfaces. If a scene has perfect specular surfaces, we must useray tracing based methods for caustics. Since our renderer entirelyworks on the GPU, ray (or photon) tracing can be executed on theCPU in parallel.

If a scene is vast, artifacts may occur since the resolution of ray-bundles is limited by memory size. This problem is addressed bytiling [Thibieroz 2011]. We would like to investigate its effective-ness.

Acknowledgements

The authors would like to thank Toshiya Hachisuka, Arun Mehtaand Fabien Gravot for valuable comments, and Takashi Sugata forproviding the models.

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