## Path-Space Differentiable Rendering of Participating Media

# Supplemental Materials

Cheng Zhang*, Zihan Yu*, and Shuang Zhao
University of California, Irvine (* equal contribution)

In this supplemental material, we show animated versions of a few inverse-rendering optimizations. For each example, we visualize derivatives with respect to one of the parameters.

Scene | # Param. | # Iter. | Time (per iteration)
Branches (Fig 10) | 1 | 100 | 39s
Bust (Fig 10) | 1 | 120 | 3m 24s
Bumpy sphere (Fig 10) | 2 | 125 | 22.77s
Point Light | 2 | 125 | 34s
Bunny0 | 3 | 200 | 3m 47s
Spheres (Fig 11) | 2 | 150 | 3m 15s
Bunny (Fig 11) | 17 | 125 | 9m 35s
Pool (Fig 11) | 100 | 300 | 5m 52s

Left click the images below to start/pause; right click to reset the animations.
Inverse-Rendering Comparisons

#### Branches

- This example contains a few twisted pipes lit by a small area source. The space around the branches is filled with heterogeneous medium.
- We search for the rotation angle of the tree (around the vertical axis) by looking at its shadow.

#### Bust

- This example contains a marble bust, modeled by rough dielectric surface and medium of varying albedo inside.
- We search for the rotation angle of the bust (around the vertical axis).

#### Bumpy sphere

- This example contains a bumpy glass sphere lit by a small area source. The space around the sphere is filled with homogeneous medium.
- We search for the position of the emitter (expressed using 2 variables)

Additional Inverse-Rendering Results

#### Point Light

- This example contains a bumpy glass sphere lit by a point source. The space around the sphere is filled with homogeneous medium.
- We search for the position of the emitter (expressed using 2 variables)

#### Bunny0

- This example contains a silver bunny in the Cornell Box filled with homogeneous medium
- We search for the position of the bunny.

#### Spheres

- This example contains a big bumpy glass sphere and two smooth glass spheres lit by a small area source. The space around the spheres is filled with homogeneous medium.
- We search for the position of the larger sphere (expressed using 2 variables).

#### Bunny

- This example contains a homogeneous translucent bunny that exhibits rough refraction on the surface and multiple scattering in the interior.
- We use a control cage with 16 vertices to deform the bunny in a non-rigid fashion.
- We search for the optical density of the medium, roughness of the surface and the positions of 5 visible cage vertices.

#### Pool

- This example contains a swimming pool lit by a small area light above.
- The interface between water and air (beyond field of view) is bumpy and parameterized with 100 parameters.
- We search for the control parameters of the interface by only looking at the casted caustics underwater.