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Real-time Indirect Illumination of Emissive�Inhomogeneous Volumes using Layered Polygonal Area Lights

1

Takahiro Kuge^†　Tatsuya Yatagawa^††　Shigeo Morishima^†

^†Waseda University

^††The University of Tokyo

PACIFIC

GRAPHICS

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Our Goal

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Reflection of volume

(Indirect Illumination)

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Our Goal

3

Arbitrary roughness

Arbitrary shape

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Our Goal

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Arbitrary roughness

Arbitrary shape

Please refer to our demo movie for Sponza result!

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Our Motivation

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Entire body of the volume is reflected

No longer the same appearances

Real world

Interactive Application

[2] “ACE COMBAT 7 SKIES UNKNOWN”, BANDAI NAMCO Entertainment

[3] https://www.yahoo.com/news/fiery-explosion-sinks-alaska-boat-203941004.html

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Previous Works

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Offline rendering

・Volumetric path tracing (ex. Woodcock tracking [4])

・Volumetric photon mapping [5]

Real-time rendering

・Simulate light diffusion in volume [6]

・e.g., Light propagation volume [7]

[4] Woodcock et al., “Techniques used in GEM code for Monte Carlo neutronics calculation”, Conf. Applications of Computing Methods to Reactors, 1965.

[5] Jensen et al., “Volumetric photon mapping”, SIGGRAPH, 1998.

[6] Stam, “Multiple Scattering as a Diffusion process”, Rendering Techniques, 1995.

[7] Kaplanyan et al., “Cascaded Light Propagation Volumes for Real-time Indirect Illumination”, I3D, 2010.

Too complex for real-time applications

Renders only directly visible volume

[4]

[5]

[7]

Real-time Indirect Illumination of volumes is not yet well established

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Difficulties of Indirect Illumination

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Direct Illumination

Viewer

Reflective surface

Image plane

Volume

Evaluate incident radiance along rays (Ray marching)

1 ray for 1 pixel

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Difficulties of Indirect Illumination

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Indirect Illumination

Evaluate radiance from “whole volume” to “every surface point”

Reflective surface

BRDF lobe

Viewer

Volume

Image plane

Multiple rays for 1 pixel

However, indirect illumination does not go as simple as direct illumination.

This is because, we have to evaluate the radiance from the entire volume to every surface point, while considering the BRDF lobes over the reflective surface.

For instance, the straightforward way for indirect illumination is to trace multiple rays from the point of reflection on the surface.

In this approach, a large number of rays are needed to be traced depending on the roughness of surface, the rougher the surface the larger number of rays are needed.

By casting rays for each pixel in the same manners,

It is possible to render the indirect illumination of volume.

This multiple ray tracing are typically combined with Monte-Carlo method that prohibits the real-time performance even by using modern high-performance graphics hardware.

Therefore, we have to come up with another idea to achieve the real-time indirect illumination of volume.

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Indirect Illumination using LPAL

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Radiance from the whole volume

Incident radiance from LPALs

LPALs

“Layered Polygonal Area Lights”

Volume slicing

Cutting section is an area light

Volume consists of multiple area lights

Our approach

Volume

(3D texture)

・

Approximate volume as a set of parallel area lights

Sorry for the long story and finally let us explain our approach from after.

Suppose that a 3D texture of a volume and a reflective surface as shown in the slide.

To tell the conclusion first, our idea is to approximate a volume as a set of area lights which are all parallel to each other.

In this slide, the area lights are illustrated in green polygons.

The representation using these area lights is natural because every cutting section in a volume can be considered as an area light.

Here, as these area lights are literally “layered” in the volume, we refer to this set of parallel area lights as Layered Polygonal Area Lights, and LPALs in short.

Therefore, the radiance from whole volume are now calculated by accumulating the contributions from these LPALs.

This is the basic concept of our method.

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LPALs to Slice

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Out-of-slice attenuation

Slice

Out-of-slice attenuation

Light attenuation by frontal regions

Slices are occluded by regions at front

Slice-based calculation by filling the gap between LPALs

However, to accurately evaluate the radiance from the volume, <click> we also have to consider the emissive media in between the LPALs.

We refer to this domain between two LPALs as a “””slice”””, which is depicted in light green color.

To obtain an incident radiance from the slice, we interpolate the radiance of two LPALs located at the both ends of the slice.

In addition, there is another important point that must be considered.

That is the attenuation by the frontal slice, or what we call out-of-slice attenuation.

As shown in the slide, slices also exist in front of the slice of interest.

Since the frontal yellow slice also contains participating media, the radiance from green slice is attenuated through the yellow slice.

So, these two factors, namely the radiance from a slice and out-of-slice attenuation, are needed to be considered for evaluating the contribution from a slice.

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LPALs to Slice

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Slice

Out-of-slice attenuation

Light attenuation by frontal regions

Slices are occluded by regions at front

Slice-based calculation by filling the gap between LPALs

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Integration for Slice

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Slice-based calculation by filling the gap between LPALs

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Integration for Slice

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In-slice

attenuation

Function of normalized distance

Slice-based calculation by filling the gap between LPALs

The functions to be integrated can be divided into two parts.

The first part is the radiance of the area light L_A, which is depicted in blue.

Strictly speaking, L_A is a function of <click> distance “r” between the frontal LPAL and the area light in the middle of the slice.

And, the other part is the in-slice attenuation, which is illustrated in yellow.

In-slice attenuation describes the attenuation of area light radiance before reaching the frontal LPAL of the slice.

In the same manner with L_A, in-slice attenuation is also a function of distance between the frontal LPAL and area light in the middle of a slice.

Speaking of the illustration, <click> radiance from the blue polygon is in-slice attenuated by the yellow part in the slice.

<click>

What is important here is that, these two functions are both represented as functions of normalized distance r.

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Integration for Slice

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In-slice

attenuation

Slice-based calculation by filling the gap between LPALs

Ext. coeff. :

Radiance :

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Integration for Slice

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In-slice

attenuation

Slice-based calculation by filling the gap between LPALs

Ext. coeff. :

Radiance :

Compute instantly by recent studies [8][9]

[8] Heitz et al. “Real-Time Polygonal-Light Shading with Linearly Transformed Cosines”, SIGGRAPH, 2016.

[9] Heitz et al. “Linear-light Shading with Linearly Transformed Cosines”, GPU ZEN, 2017.

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Integration for Slice

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Ext. coeff. :

Radiance :

Slice

Slice-based calculation by filling the gap between LPALs

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Combining Radiance and Attenuation

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Out-of-slice attenuation

Light attenuation by frontal regions

Slices are occluded by regions at front

Slice-based calculation by filling the gap between LPALs

Slice

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Combining Radiance and Attenuation

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Slice

Out-of-slice attenuation

Light attenuation by frontal regions

Slices are occluded by regions at front

Slice-based calculation by filling the gap between LPALs

Final contribution from a slice

Attenuated

radiance

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Gathering Contributions

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Slice

Attenuated

radiance

Out-of-slice attenuation

Light attenuation by frontal regions

Slices are occluded by regions at front

Summation of contribution from slices

Slice-based calculation by filling the gap between LPALs

Evaluate in front-to-back order

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Gathering Contributions

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Slice

Attenuated

radiance

Out-of-slice attenuation

Light attenuation by frontal regions

Slices are occluded by regions at front

Out-of-slice attenuation

Slice-based calculation by filling the gap between LPALs

Summation of contribution from slices

Evaluate in front-to-back order

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Gathering Contributions

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Slice

Attenuated

radiance

Out-of-slice attenuation

Light attenuation by frontal regions

Slices are occluded by regions at front

Out-of-slice attenuation

Slice-based calculation by filling the gap between LPALs

Summation of contribution from slices

Evaluate in front-to-back order

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Gathering Contributions

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Slice #2

Attenuated

radiance

Slice-based calculation by filling the gap between LPALs

#1

Calculation of out-of-slice atte.

Out-of-slice attenuation

In-slice attn. (#2)

Out. attn. (#1)

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Gathering Contributions

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Slice-based calculation by filling the gap between LPALs

Calculation of out-of-slice atte.

In-slice attn. (#2)

Attenuated

radiance

Out-of-slice attenuation

#2

#1

Slice #3

Out. attn. (#1)

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Gathering Contributions

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Slice-based calculation by filling the gap between LPALs

Calculation of out-of-slice atte.

=

Attenuated

radiance

Out-of-slice attenuation

#2

#1

Slice #3

In-slice attn. (#2)

Out. attn. (#1)

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Gathering Contributions

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Slice-based calculation by filling the gap between LPALs

Calculation of out-of-slice atte.

In-slice attn. (#3)

In-slice attn. (#2)

Out. attn. (#1)

Attenuated

radiance

Out-of-slice attenuation

#2

#1

Slice #3

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Gathering Contributions

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Slice-based calculation by filling the gap between LPALs

Calculation of out-of-slice atte.

Attenuated

radiance

Out-of-slice attenuation

#2

#1

Slice #4

#3

In-slice attn. (#3)

Out. attn. (#2)

=

In-slice attn. (#2)

Out. attn. (#1)

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Results and Performance

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Reflection on surface with arbitrary roughness

Volume

(Ray marching)

Reflective surface

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Results and Performance

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Time (ms)	5.38	6.57	8.81	12.74
fps	186	152	114	78

Performance in Sponza scene

Direct : 4.72%

Filtering : 6.15%

Indirect : 89.13%

(our method)

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Results and Performance

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Reflection with opaque obstacle

Variations : Occluded volume

Obstacle

Obstacle : Optically dense volume

Surface

Viewer

Please refer to our demo movie!

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Results and Performance

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Reflection of multiple volumes

Variations : Multiple volumes

Surface

Viewer

#1

#2

Slice the volumes in order (#1, then #2)

#2 is occluded by #1

(Radiance from #2 is influenced by #1)

Please refer to our demo movie!

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Results and Performance

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Insufficient tail

Brightness error

Insufficient tail

Brightness error

・3D isotropic gaussian filtered MIP map

・Access higher MIP-level for rougher surface

Limitation

Area light

2D filter

Filter over the light

LPAL

3D filter

Filter leakage

Despite the high practicability of our method, our method also has several limitations when we compared with path traced results. <click>

Please look at the two regions in the right figure marked by green and yellow circles.

Respectively, those circles describe the brightness error and insufficient reflection tail over the rough surfaces.

<click>

These limitations are basically coming from the recent study which we applied to compute the radiance from an area light.<click>

For example, the original method applied a <click> 2D gaussian filter over the area light to render the blurry indirect illumination. <click> But, in our case of using 3D volume texture, we have to apply an isotropic <click> 3D gaussian filter to obtain the blurry appearances, and the filter cannot be exactly applied over an LPAL.

Nevertheless the limitation, since these problems comes from the previous study, it is highly expectable to solve this problem by using more sophisticated approach to calculate the area light illumination because our method does not necessarily have to use a specific method for this part.

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Conclusion

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Indirect illumination using Layered Polygonal Area Lights

・Approximate volume as a set of parallel area lights (LPALs)

→ Real-time indirect illumination for arbitrary surface

Slice

LPALs

Fill the gap

Sum up

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Conclusion

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Future work

　Adaptive slicing depending on the position of reflection

Other parts

Visually rich part

Indirect illumination using Layered Polygonal Area Lights

・Approximate volume as a set of parallel area lights (LPALs)

→ Real-time indirect illumination for arbitrary surface

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Thank you for your attention!

MAIL : takahirolabo@gmail.com

HP : https://tatsy.github.io/projects/lpal19/

(Paper, source code and demo movie are available)