16-825 Assignment 1: Rendering Basics with PyTorch3D (Total: 100 Points + 10 Bonus)

andrew id: danielya

Table of Contents

1. Practicing with Cameras (15 Points)
2. Practicing with Meshes (10 Points)
3. Re-texturing a mesh (10 Points)
4. Camera Transformations (10 Points)
5. Rendering Generic 3D Representations (45 Points)
6. Do Something Fun (10 Points)
7. Extra Credit (10 Points)

1. Practicing with Cameras (15 Points)

1.1. 360-degree Renders (5 points)

1.2 Re-creating the Dolly Zoom (10 points)

2. Practicing with Meshes (10 Points)

2.1 Constructing a Tetrahedron (5 points)

A tetrahedron should have 4 vertices and 4 faces.

Inspired by (Come bouldering with me!)

2.2 Constructing a Cube (5 points)

A cube should have 8 vertices and 12 faces (each square face needs 2 triangular faces).

3. Re-texturing a mesh (10 points)

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

4. Camera Transformations (10 points)

World coordinate to camera coordinate: $$ X_c = R_0 X_w + T0 $$ Camera coordinate 0 (before transform) to camera coordinate 1: $$ X{c1} ​= R{rel} X{c0} + T{rel​}\ X{c1} ​= (R_{rel} R_0) Xw + R{rel} T0 + T{rel​} $$

• No transform:
• Rotate camera -90 degrees along the z axis:
• Rotate camera +90 degrees along the y axis, and translate by (-3, 0, 3):
• Translate camera by (0, 0, 3):
• Translate camera by (0.5, -0.5, 0):

Submission: In your report, describe in words what R_relative and T_relative should be doing and include the rendering produced by your choice of R_relative and T_relative.

5. Rendering Generic 3D Representations (45 Points)

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

3 different point clouds:

1. The point cloud corresponding to the first image
2. The point cloud corresponding to the second image
3. The point cloud formed by the union of the first 2 point clouds.

5.2 Parametric Functions (10 + 5 points)

Torus

Ellipsoid

Some kind of Meta logo-like shape. I love Meta. Please give me a return offer. PLEASE. 👁️❤️♾️

5.3 Implicit Surfaces (15 + 5 points)

Tradeoffs for renderings as mesh vs point clouds

Mesh

• Pros:
  • Looks continusous and visually appealing without holes on the surface
  • Render fast with large geometries and large faces
  • Easier to convert to point cloud if needed
• Cons:
  • Need faces and UV as input. Less convenient to setup

Point clouds

• Pros:
  • More flexible for geometries
  • Readily available for most commercial lidar or depth cameras
• Cons:
  • May be discontinuous
  • Harder to convert to meshes
  • Doesn't scale well with large geometries

    Implicit Torus

    

    A Tanglecube

    

(Ref: https://mathworld.wolfram.com/Tanglecube.html)

6. Do Something Fun (10 points)

No more boring toruses. An actually appetizing-looking glazed donut!

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

10 points

100 points

1000 points

10000 points