16-825 Assignment 1: Rendering Basics with PyTorch3D

This repository contains solutions for Assignment 1 of the 16-825 course, focusing on rendering basics using PyTorch3D. The results for each question can be reproduced by uncommenting the corresponding function calls in main.py. Comments in the code indicate the relevant question numbers.

How to Run

To execute the code in main.py, follow these steps:

cd sragi_code_proj1
python -m starter.main

All results will be saved in the submissions folder.

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Table of Contents

1. Practicing with Cameras
   • 360-degree Renders
   • Re-creating the Dolly Zoom
2. Practicing with Meshes
   • Constructing a Tetrahedron
   • Constructing a Cube
3. Re-texturing a Mesh
4. Camera Transformations
5. Rendering Generic 3D Representations
   • Rendering Point Clouds from RGB-D Images
   • Parametric Functions
   • Implicit Surfaces
6. Do Something Fun

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1. Practicing with Cameras

1.1 360-degree Renders

1.2 Re-creating the Dolly Zoom

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2. Practicing with Meshes

2.1 Constructing a Tetrahedron

This mesh consists of 4 vertices and 4 faces, forming 4 triangles.

2.2 Constructing a Cube

This mesh consists of 8 vertices and 12 faces, with 2 triangles forming each of the 6 square faces.

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3. Re-texturing a Mesh

In this example:

• color1 = [0.5, 0, 1]
• color2 = [1, 0.5, 0]

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4. Camera Transformations

R_relative and T_relative describe the rotation and translation of the object's coordinate frame relative to the camera's coordinate frame. For example:

R_relative = [[0, 1, 0], [-1, 0, 0], [0, 0, 1]]
T_relative = [0, 0, 0]

This configuration means:

• No translation from the current position.
• Rotation aligns the object's x-axis with the camera's y-axis, the object's y-axis opposite to the camera's x-axis, and the z-axes remain aligned.

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5. Rendering Generic 3D Representations

5.1 Rendering Point Clouds from RGB-D Images

5.2 Parametric Functions

Mobius Strip Parametric Function:

• x = (2 + r/2 * cos(α/2)) * cos(α)
• y = r/2 * sin(α/2)
• z = (1.5 + r/2 * cos(α/2)) * sin(α)

Where:

• r ranges from -1.5 to 1.5
• α ranges from 0 to 2π

5.3 Implicit Surfaces

Comparison of Meshes and Point Clouds:

1. Rendering Quality: Meshes appear smoother but may lose finer details, while dense point clouds retain high-resolution data.
2. Storage: Meshes are compact, whereas point clouds require more memory. High-precision meshes, however, also demand significant storage.
3. Editing: Meshes are easier to edit and widely supported by CAD software. Point clouds, though harder to edit, are directly captured by sensors like LiDAR.

Barth Sextic Implicit Function:

• Equation:

  4 * (φ² * x² - y²) * (φ² * y² - z²) * (φ² * z² - x²) - (1 + 2 * φ) * (x² + y² + z² - 1)² = 0
  

• Ranges:
  • x, y, z range from -1.5 to 1.5
  • φ is the golden ratio (approximately 1.618)

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6. Do Something Fun

This is a Trefoil Knot that dynamically tightens and loosens over time. Additionally, colors flow through it:

• Red along the X-axis.
• Cyan along the Y-axis. 16-825 Assignment 1: Rendering Basics with PyTorch3D