16-825 Assignment 1 — Kunwoo Lee

Assignment 1 — Rendering Basics with PyTorch3D

Course	16‑825 (Learning for 3D Vision)
Student	Kunwoo Lee (kunwool@andrew.cmu.edu)

1. Practicing with Cameras

1.1 360° Turntable (Cow)

Your first task is to create a 360-degree gif video that shows many continuous views of the provided cow mesh. For many of your results this semester, you will be expected to show full turntable views of your outputs.

1.2 Dolly Zoom

Explain the change of FOV vs camera distance and how the subject size was kept constant.

Dolly zoom effect — Dolly Zoom — focal length & translation animation.

2. Practicing with Meshes

2.1 Tetrahedron

State vertex/face counts and any texture choices.

Vertices: 4
Triangle faces: 4

Tetrahedron 360° — Tetrahedron — 360° GIF.

2.2 Cube

State vertex/face counts and triangulation method (two tris per face).

Vertices: 8
Triangle faces: 12

3. Re‑texturing a Mesh (Cow)

Chosen colors: color1 = red → color2 = blue. Interpolation along z using alpha = (z - z_min)/(z_max - z_min).

Cow retextured gradient — Front‑to‑back gradient retexture result.

4. Camera Transformations

Describe R_relative and T_relative R_relative tells us the relative rotation of camera w.r.t the object, defined in camera coordinate. T tells us the position of object w.r.t the object, defined in camera coordinate system. Thus this never has to change with rotational matrix, where it was defined to change so, making it a bit complicated. I think we can simply patch the code to "T = T_relative + torch.tensor([0.0, 0, 3])" instead of "T = R_relative @ torch.tensor([0.0, 0, 3]) + T_relative to make it simpler.
NOTE: I used "R.from_euler(...).as_matrix()" from scipy to get rotation matrix from euler angles.

Transform 1
R_relative = R.from_euler('z', -90, degrees=True)
T_relative = [0, 0, 0]

Transform 2
R_relative = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
T_relative = [0, 0, 2].

Transform 3
R_relative = R.from_euler('y', 2, degrees=True)
T_relative = [0.5, 0, 0].

Transform 4
R_relative = R.from_euler('y', 90, degrees=True)
T_relative = [-3, 0, 3].

5. Rendering Generic 3D Representations

5.1 Point Clouds from RGB‑D

5.2 Parametric Functions

Parametric torus

Additional parametric object — Extra parametric object.

5.3 Implicit Surfaces

Define implicit torus F(x,y,z)=0

Implicit torus mesh — Implicit Torus Mesh — 360° GIF.

Mesh vs Point Cloud — Quick Notes

Quality: Mesh rasterization gives crisp silhouettes & shading; point size limits edge fidelity.
Speed: Point rendering is often simpler; high‑res marching cubes + meshes can be heavier.
Memory: Dense voxels ⮕ high memory; points can be streamed/sampled.
Ease: Points are trivial to build; watertight meshes require extraction or authoring.

6. Do Something Fun

Human mesh rendering via SMPL model

Extra Credit — Sampling Points on Meshes

Briefly describe stratified sampling by area, barycentric sampling, and show results for 10/100/1k/10k samples.