16-889 Assignment 1: Rendering Basics with PyTorch3D

Name: Rohan Agarwal

Andrew ID: rohanaga

You can run all files using: python main.py

0.1 Rendering your first mesh

If you run python -m q0 --image_size 256 --output_path images/q0/cow_render.jpg, you should see the following output:

1. Practicing with Cameras

1.1. 360-degree Renders (5 points)

If you run python -m src.q1_1 --image_size 256 --output_path images/q1/cow_render.gif, you should see the following output:

1.2 Re-creating the Dolly Zoom (10 points)

If you run python -m src.q1_2 --num_frames 10 --image_size 256 --output_file images/q1/dolly_gif.gif, you should see the following output:

2. Practicing with Meshes

2.1 Constructing a Tetrahedron (5 points)

Number of vertices = 4 Number of faces = 4

If you run python -m src.q2_1 --image_size 256 --output_path images/q2/tetrahedron_render.gif, you should see the following output:

2.2 Constructing a Cube (5 points)

Number of vertices = 8 Number of faces = 12 (2 triangular meshes for each side)

If you run python -m src.q2_2 --image_size 256 --output_path images/q2/cube_render.gif, you should see the following output:

3. Re-texturing a mesh (10 points)

color1 = [0,0,1] (blue) and color2=[1,0,0] (red)

If you run python -m src.q3 --image_size 256 --output_path images/q3/cow_texture.gif, you should see the following output:

4. Camera Transformations (20 points)

Relative Rotation and Relative Transalation:

Say, a camera is moving in a fixed environment. The environment is represented by the world coordinate system. The camera has its own coordinate system at each of its position. This system has its origin at the camera centre i.e. the origin keeps moving. Now, we are interested in defining the relationship between the camera coordinate systems observed in position 1 and position 2. Relative rotation and relative translation define this relationship.

Relative rotation describes the amount of rotation the camera must undergo(from position 1) such that the axes of the camera in position 1 aligns with the axes in position 2. Mathematically, R2 = R_relative @ R1

Relative translation is similary described as the amount of translation the camera must undergo(from position 1) for its centre in position 1 to align with the centre in position 2. Mathematically, T2 = T_relative @ T1

Please note: Pytorch3D accepts the transpose of what has been described as the relative rotation and translation above.

If you run python -m src.q4 --image_size 512 --output_path images/q4/camera_1.jpg images/q4/camera_2.jpg images/q4/camera_3.jpg images/q4/camera_4. jpg, you should see the following output:

R_rel = [[0,1,0],[-1,0,0],[0,0,1]] T_rel = [0,0,0]

The relative rotation sets the new X axis --> old Y axis and new Y axis --> negative of old X axis. The relative translation is zero as camera merely rotates in its position

R_rel = [[0,0,1],[0,1,0],[0,0,1]] T_rel = [0,0,3]

The relative rotation is identity (actually, the transpose of it) i.e. has no effect on the original rotation of the camera. The relative translation moves the object away by 3 units along the positve z direction.

R_rel = [[0,0,1],[0,1,0],[0,0,1]] T_rel = [0.5,-0.5,0]

The relative translation moves the new camera coordinates to (-0.5, 0.5) which is equivalent to the object moving diagonally towards bottom left corner. The rotation matrix remains unchanged

R_rel = [[0.,0.,1],[0,1,0],[-1.,0,0]] T_rel = [-3,0,3]

The relative rotation sets the new X-axis --> old Z-axis and the new Z-axis --> old negative X-axis. The relative translation moves the the camera origin diagonally in the X-Z plane.

5. Rendering Generic 3D Representations

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

If you run python -m src.q5_1 --render point_cloud --image_size 256 --output_path images/q5/plants1.gif images/q5/plants2.gif images/q5/plants3. gif, you should see the following output:

5.2 Parametric Functions (10 points)

If you run python -m src.q5_2 --render parametric --num_samples 100 1000 --image_size 256 --output_path images/q5/, you should see the following output:

100 samples

1000 samples

5.3 Implicit Surfaces (15 points)

Memory Efficiency: Meshes are less memory efficient as they require storing face representations in addition to vertices. Rendering Speed: Points clouds are easier/faster to render as they don't require rendering the surface between the points. Rendering Quality: Given we use sufficient number of faces, mesh will provide a better visually quality as it allows for observing surfaces. It is easier to reason about the shape because of the connectivity. Points clouds may not be able to accurately represent fine details of an object (e.g. horn of the cow )

If you run python -m src.q5_3 --render implicit --num_samples 100 --image_size 256 --output_path images/q5/torus_implicit.gif, you should see the following output:

6. Do Something Fun (10 points)

Nothing fancy here, just a parametric rendering of a spiral spiralling.

If you run python -m src.q6 --render parametric --num_samples 100 --image_size 256 --output_path images/q6/spiral_parametric.gif, you should see the following output:

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

If you run python -m src.q7 --image_size 256 --output_path images/q7/, you should see the following output:

10 samples

100 samples

1000 samples

10000 samples