16-825 Assignment 1: Rendering Basics with PyTorch3D

Chia Hui Yen (huiyenc) | Fall 2025

1. Practicing with Cameras (15 Points)

1.1. 360-degree Renders (5 points)

360-degree continuous view of the cow mesh from multiple viewpoints:

1.2 Re-creating the Dolly Zoom (10 points)

Recreated the famous dolly zoom effect by changing focal length while moving camera to keep subject size constant:

2. Practicing with Meshes (10 Points)

2.1 Constructing a Tetrahedron (5 points)

Manually constructed tetrahedron mesh with 4 vertices and 4 triangle faces:

2.2 Constructing a Cube (5 points)

Manually constructed cube mesh using triangle faces (8 vertices, 12 triangle faces):

3. Re-texturing a mesh (10 points)

Re-textured cow mesh with smooth color transition from front to back using linear interpolation:

Color choices: color1 = [0, 0, 1] (blue, front) → color2 = [1, 0, 0] (red, back)

4. Camera Transformations (10 points)

Found relative camera transformations (R_relative, T_relative) to produce specific target views:

Transformations applied:

• Rotation matrices: Apply 3D rotations to change viewing angles
• Translation vectors: Shift camera position in world coordinates
• Combined effect: R = R_relative @ R_0, T = R_relative @ T_0 + T_relative

5. Rendering Generic 3D Representations (45 Points)

Sample point cloud rendering of bridge:

5.1 Rendering Point Clouds from RGB-D Images (10 points)

Constructed point clouds from 2 RGB-D images using camera intrinsics/extrinsics and depth information:

Individual point clouds and combined result:

5.2 Parametric Functions (10 + 5 points)

Generated 3D point clouds by sampling parametric functions:

1. Parametric sphere (reference):

2. Torus point cloud (sampling torus parametric equations):

3. Helicoid point cloud (custom parametric surface):

5.3 Implicit Surfaces (15 + 5 points)

Generated meshes from implicit functions using marching cubes algorithm:

1. Torus mesh (from implicit function F(x,y,z) = 0):

2. Helicoid mesh (custom implicit surface):

3. Mesh vs Point Cloud Tradeoffs:

• Rendering quality: Meshes provide smooth surfaces with proper lighting/shading; point clouds show discrete samples
• Rendering speed: Point clouds faster (no triangle rasterization); meshes slower but more realistic
• Memory usage: Point clouds store only vertices+colors; meshes need vertices+faces+textures
• Ease of use: Point clouds simpler to construct; meshes require proper topology and face definitions

6. Do Something Fun (10 points)

DNA Double Helix Morphing Animation: Created a morphing animation from sphere to DNA double helix structure using custom parametric functions and point cloud interpolation. Features color transitions and 360° rotation.

7. Sampling Points on Meshes (10 points) [Extra Credit]

Implemented stratified sampling to uniformly sample points from triangle mesh surfaces using:

1. Face selection proportional to face area
2. Uniform barycentric coordinate sampling
3. Point computation via barycentric interpolation

Cow mesh vs sampled point clouds (10, 100, 1000, 10000 points):