16-889 Assignment 1: Rendering Basics with PyTorch3D

0. Setup

Folder structure:

ROOT
├── data
│   └── ...
├── images
│   └── ...
├── __init__.py
├── README.md
├── requirements.txt
├── starter
│   └── ...
└── yukunx_code_proj1
    ├── data
    │   ├── Castle.obj
    │   └── Dragon.obj
    ├── images
    │   ├── 1-1-360-degree-renders.gif
    │   ├── 1-2-dolly-zoom.gif
    │   ├── 2-1-tetrahedron.gif
    │   ├── 2-2-cube.gif
    │   ├── 3-re-texturing-a-mesh.gif
    │   ├── 4-textured_cow_transform0.jpg
    │   ├── 4-textured_cow_transform1.jpg
    │   ├── 4-textured_cow_transform2.jpg
    │   ├── 4-textured_cow_transform3.jpg
    │   ├── 5-1-1-point-cloud-first-two-images.gif
    │   ├── 5-1-point-cloud-first-image.gif
    │   ├── 5-1-point-cloud-second-image.gif
    │   ├── 5-2-torus-point-cloud.gif
    │   ├── 5-3-torus-implicit-surface.gif
    │   ├── 6-fun.gif
    │   ├── 7-sampling-cow-points-10000.gif
    │   ├── 7-sampling-cow-points-1000.gif
    │   ├── 7-sampling-cow-points-100.gif
    │   └── 7-sampling-cow-points-10.gif
    ├── __init__.py
    ├── main.py
    └── README.md

1. Practicing with Cameras

1.1. 360-degree Renders

1.2 Re-creating the Dolly Zoom

2. Practicing with Meshes

2.1 Constructing a Tetrahedron

In total, there’re 4 vertices and 4 triangle faces.

2.2 Constructing a Cube

In total, there’re 8 vertices and 12 triangle faces.

3. Re-texturing a mesh

color0=[1.0, 1.0, 0.0]
color1=[0.0, 1.0, 1.0]

4. Camera Transformations

Transformation 0

R_relative= Rotation.from_euler('z', -90, degrees=True).as_matrix()
T_relative=[0, 0, 0]

Transformation 1

R_relative = [1, 0, 0], [0, 1, 0], [0, 0, 1]]
T_relative = [0.0, 0.0, 2.0]

Transformation 2

R_relative= Rotation.from_euler('y', 3, degrees=True).as_matrix(),
T_relative= [0.2, -0.5, 0.0]

Transformation 3

R_relative= Rotation.from_euler('y', 90, degrees=True).as_matrix(),
T_relative= [-3.0, 0.0, 3.0]

5. Rendering Generic 3D Representations

5.1 Rendering Point Clouds from RGB-D Images

Only the first point cloud

Only the second point cloud

Combining the first and the second point cloud

5.2 Parametric Functions

5.3 Implicit Surfaces

Comparing rendering torus with a point cloud and a implicit surface, the former one is much faster, because their time complexities are respectively quadratic and cubic to the adjacent element distance. Besides, the resultant surface of the former method perfectly matches the torus geometry, while marching cube algorithm generates torus with two spurious bulges. As for the advantage of the implicit surface, the marching cube method directly provides dense meshes, while point clouds require an extra reconstruction step to achieve that.

6. Do Something Fun

A dragon and a castle obj file were downloaded from Free3D. I merged their mesh vertices and faces together, and rendered them with different texture colors. Further, I tuned the transformation of the dragon to let it sit on top of the castle.

7. Sampling Points on Meshes

Original mesh	Point cloud with 10 points

Original mesh	Point cloud with 100 points

Original mesh	Point cloud with 1000 points

Original mesh	Point cloud with 10000 points