**Nori Final Project - Loop**

Student name: Xingyu Su

Final render
============

![Figure [final]: Final render](final.png width="800px")

Motivation
==========

My final render contains a curious robot who is playing toy cars on a loop track. The car would slide down along the track for the
robot to pick up again, which is another sense of 'loop'.

Feature list
============

<table>
    <tr>
        <th>Feature</th>
        <th>Standard point count</th>
        <th>Adjusted point count</th>
    </tr>
    <tr>
        <td>Textures or Procedural Images</td>
        <td>10</td>
        <td>10</td>
    </tr>
    <tr>
        <td>Depth of Field</td>
        <td>10</td>
        <td>10</td>
    </tr>
    <tr>
        <td>Bump mapping / Normal mapping</td>
        <td>10</td>
        <td>10</td>
    </tr>
    <tr>
        <td>Simple extra BSDFs</td>
        <td>10</td>
        <td>10</td>
    </tr>
    <tr>
        <td>Image Based Lighting</td>
        <td>30</td>
        <td>10</td>
    </tr>
    <tr>
        <td>Homogeneous participating media</td>
        <td>30</td>
        <td>30</td>
    </tr>
    <tr>
        <td><strong>Total</strong></td>
        <td>100</td>
        <td>80</td>
    </tr>
</table>

**Note:**

All of the implemented features are validated with `Mitsuba2` using equivalent/similar parameters.

Textures or Procedural Images
=============================

**Related code:**

- `include/nori/project/texture.h`
- `src/project/imagetex.cpp`

`texture.h` is a common interface for all kinds of textures. In `imagetex.cpp`, I implement the bitmap texture which uses bilinear
interpolation to get texels from image based on UV coordinates. Each `Texture` is a child bind to a `BSDF` instance. When evaluating
or sampling a `BSDF`, `getTexel()` is called simultaneously if the `BSDF` has a texture.

**Validation:**

- Left: Mitsuba, `scenes/project/texture/test2/cbox_mats_mitsuba.xml`
- Right: Mine, `scene/project/texture/test2/cbox_mats.xml`

<div class="twentytwenty-container">
    <img src="validation/texture/cbox_mats_mitsuba.png" alt="Mitsuba">
    <img src="validation/texture/cbox_mats.png" alt="Mine">
</div>

Depth of Field
==============

**Related code:**

- `src/project/thinlens.cpp`

When sampling rays, instead of shooting rays from a pinhole, generate points on the aperture and calculate the correspoinding rays.

**Validation:**

- Left: Mitsuba, `scenes/project/depth/test1/cbox_mats_mitsuba.xml`
- Right: Mine, `scene/project/depth/test1/cbox_mats.xml`

<div class="twentytwenty-container">
    <img src="validation/depth/cbox_mats_mitsuba.png" alt="Mitsuba">
    <img src="validation/depth/cbox_mats.png" alt="Mine">
</div>

Normal Mapping
==============

**Related code:**

- `include/nori/project/surface.h`
- `src/project/normalmap.cpp`

`surface.h` is a common interface for additional surface description. In `normalmap.cpp`, for evaluation of a surface point, I
first find the normal based on UV coordinate using bilinear interpolation. Then I do transformation based on the original normal.
Each `Surface` is bind to a `Mesh` instance, and the adjust of normal is done in each integrator when a ray hits a mesh with a
`Surface` instance.

**Validation:**

- Left: Mitsuba, `scenes/project/normal/test1/normal_mitsuba.xml`
- Right: Mine, `scene/project/normal/test1/normal.xml`

<div class="twentytwenty-container">
    <img src="validation/normal/cbox_mats_mitsuba.png" alt="Mitsuba">
    <img src="validation/normal/cbox_mats.png" alt="Mine">
</div>

Simple Extra BSDF
=================

**Related code:**

- `src/project/roughconductor.cpp`
- `src/project/roughdielectric.cpp`

For each BSDF, I implement the `sample()`, `eval()` and `pdf()` method and make them consistent to pass the warptest. The sampling
basically follows Mitsuba.

**Validation:**

Rough Conductor

- $\alpha = 0.1$
- Left: Mitsuba, `scenes/project/rough/test2/ajax_mitsuba.xml`
- Right: Mine, `scene/project/rough/test2/ajax.xml`

<div class="twentytwenty-container">
    <img src="validation/roughconductor/ajax_mitsuba.png" alt="Mitsuba">
    <img src="validation/roughconductor/ajax.png" alt="Mine">
</div>

Rough Conductor Warptest

- $\alpha = 0.3$
- Default $eta$ and $k$

![Figure [warpconductor_a]: Warptest for rough conductor](validation/roughconductor/warpconductor_a.png width="800px")

![Figure [warpconductor_b]: Warptest for rough conductor](validation/roughconductor/warpconductor_b.png width="800px")

Rough Dielectric

- $\alpha = 0.2$
- Left: Mitsuba, `scenes/project/rough/test1/ajax_mitsuba.xml`
- Right: Mine, `scene/project/rough/test1/ajax.xml`

<div class="twentytwenty-container">
    <img src="validation/roughdielectric/ajax_mitsuba.png" alt="Mitsuba">
    <img src="validation/roughdielectric/ajax.png" alt="Mine">
</div>

Rough Conductor Warptest

- $\alpha = 0.3, intIOR = 1.5046, extIOR = 1.000277$

![Figure [warpdielectric_a]: Warptest for rough dielectric](validation/roughdielectric/warpdielectric_a.png width="800px")

![Figure [warpdielectric_b]: Warptest for rough dielectric](validation/roughdielectric/warpdielectric_b.png width="800px")

Image Based Lighting
====================

**Related code:**

- `src/project/environment.cpp`
- `src/project/envpath_ems.cpp`
- `src/warp.cpp`

For the image based lighting, since I did the bonus part in Assignment 3, I continue to use hierachical sampling instead of the
sampling method described in PBRT for this feature. The hierachical sampling and pdf function is defined in `warp.cpp`. 
`environment.cpp` is the image based lighting emitter derived from `Emitter` class. It behaves like all other emitters, except for
when a ray intersect with nothing in the scene, we would evaluate $Li$ based on the direction of the ray. `envpath_ems` is an
integrator supporting image based lighting with next event estimation.

**Validation:**

Image Based Lighting with Next Event Estimation

- Left: Mitsuba, `scenes/project/environment/test2/ajax_mitsuba.xml`
- Right: Mine, `scene/project/environment/test2/ajax.xml`

<div class="twentytwenty-container">
    <img src="validation/environment/ajax_mitsuba.png" alt="Mitsuba">
    <img src="validation/environment/ajax.png" alt="Mine">
</div>

Hierachical Sampling Warptest

![Figure [hierachical]: Warptest for hierachical sampling](validation/environment/hierachical.png width="800px")

Imaged Based Lighting Warptest

![Figure [ibl]: Warptest for image based lighting](validation/environment/ibl.png width="800px")

I do not pass the warptest for image based lighting emitter, but the $\chi^2$ statistic is quite close to the degree of freedom,
and the two images look very similar. Besides, the result of the integrator with next event estimation actually looks almost the
same as Mitsuba's rendering. So I think the implementaion is mostly correct.

Homogeneous participating media
===============================

**Related code:**

- `include/project/medium.h`
- `include/project/phase_function.h`
- `src/project/henyeygreenstein.cpp`
- `src/project/isotropic.cpp`
- `src/project/homogeneous.cpp`
- `src/project/mixpath.cpp`
- `src/project/nothing.cpp`

My implementaion of homogeneous participating media basically follows the guidance in Lecture 11 slides. `mixpath.cpp` is a path
tracer supporting volumetirc rendering and also all the features implemented before. `medium.h` and `phase_function.h` are the
base class for different medium and phase functions. `homogeneous.cpp` is the class for homogeneous participating media. The main
method it provides is `sampleT()`, which given current ray and $t_{max}$, samples within the medium either for a random distance or
reach the $t_{max}$. The main logic of volumetric rendering is implemented in `mixpath`. It records whether it's within medium or
not and does BSDF or medium sampling accordingly. Each `Medium` is a child bind to a `Mesh` instance, and each `PhaseFunction` is
a child of a `Medium` instance. I also add a new BSDF called nothing which causes no BSDF interaction to mark the boundry of
medium.

**Validation:**

Without Surface

- Left: Mitsuba, `scenes/project/volume/test3/cbox_mats_mitsuba.xml`
- Right: Mine, `scene/project/volume/test3/cbox_mats.xml`

<div class="twentytwenty-container">
    <img src="validation/volumenothing/cbox_mats_mitsuba.png" alt="Mitsuba">
    <img src="validation/volumenothing/cbox_mats.png" alt="Mine">
</div>

With Dielectric Surface

- Left: Mitsuba, `scenes/project/volume/test2/cbox_mats_mitsuba.xml`
- Right: Mine, `scene/project/volume/test2/cbox_mats.xml`

<div class="twentytwenty-container">
    <img src="validation/volumedielectric/cbox_mats_mitsuba.png" alt="Mitsuba">
    <img src="validation/volumedielectric/cbox_mats.png" alt="Mine">
</div>

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