Global Illumination using Precomputed Light Paths for Interactive LightCondition Manipulation (sap 0275)

Yonghao YueUniv. Tokyo

Kei IwasakiWakayama Univ.

Yoshinori DobashiHokkaido Univ.

Tomoyuki NishitaUniv. Tokyo

In this document, we would like to describe results and limitations in more detail. Before that, some details of our method are described. All

the results shown in this document and the one-page abstract are rendered by using a desktop PC with a Pentium D 3.0GHz CPU, 2.0 GB of

main memory and an NVIDIA GeForce 7800 GTX GPU.

1 Precomputation

Particle Tracing In order to make the computation during rendering correct, entry points must be appropriately weighted according to the

density of their distribution. We sample entry points uniformly on the surfaces of the scene, thus each entry point will have a same area.

To sample each entry point, we first choose a polygon with a probability proportional to its area, and then randomly select a point on the

polygon. After each entry point is determined, we build the light path by iteratively extending a light sub-path. If we do not need to modify the

characteristics of materials, we can utilize the importance sampling from the BRDFs. Otherwise, the cos term is accounted for the importance

sampling.

Final Gathering To construct final gathering paths, we have to determine the locations of cache points for (ir)radiance caching in the scene.

We use rejection-sampling technique to do this. That is, we first densely sample candidate locations, and reject those where the energy can

likely be interpolated using energies at other locations. We do this rejection based on the error metric proposed by Tabellion et al [Tabellion

and Lamorlette 2004]. After we obtain the set of caching locations, we sample final gathering rays from each location.

2 The Hierarchical Volumetric Data Structure

We construct the hierarchical volumetric data structure (HVDS) in the same fashion as an octree. First, the energies are stored in the highest

resolution, which we call the base level. The resolutions of the base level is changed with respect to the need of accuracy. Since each grid-cell

in the HVDS may contain several faces or curved surfaces, we cluster the normal directions of the faces in the grid and store the energies

per the clustered direction of the normal. We store the outgoing radiance or irradiance rather than the incident radiance in order to use the

stored radiance or irradiance directly in final gathering. To deal with glossy surfaces, the outgoing directions are discretized and energies are

accumulated per each discretized outgoing direction. After all the energies are stored in the base level, we normalize the stored radiance or

irradiance in order to take into account the surface area within a grid-cell and the solid angle of the outgoing direction.

After the normalization for the base level is completed, coarser resolution levels are constructed in the same manner as the bottom up

construction of octrees from leaf nodes. That is, we accumulate the energies stored in higher resolution hierarchies into their corresponding

coarser resolution hierarchies. To take into account the occlusion due to surfaces in a grid-cell (Figure 1), we make an assumpotion that the

energy has an invariant distribution in each grid-cell. Then we calculate the occlusion ratio for each discretized direction.

OccluderSelected grid-cell

Cache point

Figure 1: Occulusion prob-

lem in the HVDS.

grid-cellA

Figure 2: Choose the grid-

cell with appropriate level in

the hierarchy.

Light sourceOccluder Selected grid-cell

Cache point

Figure 3: Limitation of the assumption for solving the

occulusion problem in the HVDS.

3 Rendering

When the locations of light sources are determined during rendering, we can calculate the form factor between each sampling point on a light

source and each entry point. Since each entry point is uniformly distributed in the scene, the differential area per an entry point is determined.

By calculating form factors, we can calculate the energy distributed to each entry point, and the energy at the rest of vertices of light paths

can also be calculated consequently.

For the final gathering, we must determine the grid-cell with appropriate level in the hierarchy for each final gathering ray. We do this by

projecting the solid angle of each final gathering ray onto its corresponding intersection point (A in Figure 2), and use the grid-cell in the

level where the grid-cell has nearly equal size compared to the projected area.

4 Results

We show the rendered results in Figures 4, 5, and 6. Figures 4 and 5 contain the comparisons with reference solutions obtained by Photon

Mapping and pure Monte Carlo. Figure 6 shows an rendered example of a complex scene. Scene descriptions are shown in Table 1.Table 2

summarizes the computational time (all measured respect to ms) of each step in various cases. In the case where the materials are fixed, the

rendering process consists of the calculation of direct illumination (shown as Tdi in Table 2), recalculation of energies of light paths (Tlpe),

the construction of the HVDS (Thvds), the final gathering (Tfg), (ir)radiance splatting (Tsplat ), and the total time to render a single frame (Ttot).

Note that most time during rendering is spent on (ir)radiance splatting. We also show in Table 2 computation time when we move a light

source (Tlight), the viewpoint (Tview), and modify a material (Tmat ).

Table 3 shows the decrease in the rendering performance as we increase the number of light sources in a scene. For each scene, 400k entry

points are sampled, and up to 40k cache points are used. We emitted 256 final gathering rays from each cache point.

Please refer to the accompanied animations that are movies of the Box scene and the Sponza scene. In the movie of the Box scene, we

demonstrate the features of our algorithm. We first move the viewpoint to show around the Box scene. Then we change materials, including

the BRDF of the teapot from a diffuse one to a glossy one. We then move the viewpoint around the Box scene again to show the glossy

surface. After that, we move the point light source, and add an area light source. We show that we can deal with several light sources.

The area light source is approximated by using 10 spot light sources. Finally, we switch off the point light source and move the area light

source to show the indirect illumination due to the leftside wall. In the movie of the Sponza scene, we show the interactive rendering of the

Sponza scene. We first move the viewpoint, and then move the point light source and add an area light source. These movies were made by

recording the real-time interaction operations. We used a capture software and the resulting frame rates appear to be lower than that of the

actual interactive operations. Also Mach band artifacts appeared due to the capture software.

5 Limitations and Drawbacks

We will describe two main limitations and drawbacks of our method here. First, due to the discretization of directions for storing energies, we

can not handle high-frequency BRDF. From our experimental results, we find that Phong BRDF with the exponential up to 40 can be handled

without any noticeable differences with 256 discretized directions. Second, due to the assumption for solving the occulusion problem in the

HVDS, rendered results may be inaccurate under some special lighting conditions. If a final gathering ray gathers the energy form a grid-cell

with a blocker and a light source just behind the blocker, as illustrated in Figure 3, the energy computed at the final gathering point may be

wrong.

6 Future Work

In future work, we aim to achieve the interactive rendering of dynamic scenes, where objects in the scene move.

References

TABELLION, E., AND LAMORLETTE, A. 2004. An approximate global illumination system for computer generated films. ACM Transactions

on Graphics 23, 3, 469–476.

Direct illumination only. Photon mapping. Our method. Pure Monte Carlo.Figure 4: Comparison of a box scene.

Direct illumination only. Photon mapping. Our method. Pure Monte Carlo.

Figure 5: Comparison of the Sponza scene.

Direct illumination only. Our method.Figure 6: Examples of a room scene.

Table 1: Scene description.

Scene #Triangle Image size Precomp. Time Frame rate Memory usage

Box 2,914 512 � 512 32min 9.2 fps 165MB

Sponza 76,154 640 � 480 43min 5.1 fps 172MB

Room 141,287 640 � 480 50min 1.7 fps 197MB

Table 2: Detailed timings.

Scene Tdi Tlpe Thvds Tfg Tsplat Ttot Tlight Tview Tmat

Box 6 11 11 5 76 109 109 87 1271

Sponza 15 15 12 27 122 191 191 164 1310

Room 30 23 112 142 281 588 588 453 1807

Table 3: Fps vs. the number of lights.

Scene 1 light 2 lights 4 lights 8 lights

Box 9.1 8.6 8.2 7.2

Sponza 5.2 4.8 4.3 3.6

Room 1.7 1.5 1.2 1.0