Learning for 3D Vision [16889] - Assignment 1

NAME: Shefali Srivastava

ANDREW ID: shefalis

Instructions:

Change to folder solutions to run the below mentioned commands.

1. Practicing with Cameras

1.1. 360-degree Renders (5 points)

On your webpage, you should include a gif that shows the cow mesh from many continously changing viewpoints.

python main.py --question "q11" --input-path "../data/cow.obj" --output-path "../output_final/q11.gif"

1.2 Re-creating the Dolly Zoom (10 points)

On your webpage, include a gif with your dolly zoom effect.

python main.py --question "q12" --input-path "../data/cow_on_plane.obj" --output-path "../output_final/q12.gif"

2. Practicing with Meshes

2.1 Constructing a Tetrahedron (5 points)

On your webpage, show a 360-degree gif animation of your tetrahedron. Also, list how many vertices and (triangle) faces your mesh should have.

python main.py --question "q21" --output-path "../output_final/q21.gif"

Number of Faces = 4, Number of Vertices = 4

2.2 Constructing a Cube (5 points)

On your webpage, show a 360-degree gif animation of your cube. Also, list how many vertices and (triangle) faces your mesh should have.

python main.py --question "q22" --output-path "../output_final/q22.gif"

Number of Faces = 12, Number of Vertices = 8

3. Re-texturing a mesh (10 points)

In your submission, describe your choice of color1 and color2, and include a gif of the rendered mesh.

python main.py --question "q3" --input-path "../data/cow.obj" --output-path "../output_final/q3.gif"

Color choices:

color1 = torch.tensor([255/255, 242/255, 0/255])
color2 = torch.tensor([255/255, 82/255, 82/255])

4. Camera Transformations (20 points)

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.

4.1

python main.py --question "q41" --input-path "../data/cow.obj" --output-path "../output_final/q41.jpg"

Description: For this view, the cow is rotated by -90 degrees with z axis as the axis of rotation. There is no translation.

R_relative = pytorch3d.transforms.euler_angles_to_matrix(
        torch.tensor([0, 0, -1 * np.pi / 2]), "XYZ"
    )
T_relative = [0, 0, 0]

4.2

python main.py --question "q42" --input-path "../data/cow.obj" --output-path "../output_final/q42.jpg"

Description: There is no rotation. For translation, the camera moves back by 3 units along the z axis.

R_relative = [[1.0, 0, 0], [0, 1, 0], [0, 0, 1]]
T_relative = [0.0, 0, 3]

4.3

python main.py --question "q43" --input-path "../data/cow.obj" --output-path "../output_final/q43.jpg"

Description: There is no rotation. For translation, the camera moves in the right by 3 units along the -x axis and up by 3 units along with +y axis.

R_relative = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
T_relative = [0.5, -0.5, 0]

4.4

python main.py --question "q44" --input-path "../data/cow.obj" --output-path "../output_final/q44.jpg"

Description: For this view, the cow is rotated by 90 degrees with y axis as the axis of rotation. To position the camera to view the object now, the camera moves 3 units along +x axis and -3 units along -z axis.

R_relative = pytorch3d.transforms.euler_angles_to_matrix(
        torch.tensor([0, np.pi / 2, 0]), "XYZ"
    )
T_relative = [-3, 0, 3]

5. Rendering Generic 3D Representations

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

In your submission, include a gif of each of these point clouds side-by-side.

5.1.1 The point cloud corresponding to the first image

python main.py --question "q511" --input-path "../data/rgbd_data.pkl" --output-path "../output_final/q511.gif"

5.1.2 The point cloud corresponding to the second image

python main.py --question "q512" --input-path "../data/rgbd_data.pkl" --output-path "../output_final/q512.gif"

5.1.3 The point cloud formed by the union of the first 2 point clouds.

python main.py --question "q513" --input-path "../data/rgbd_data.pkl" --output-path "../output_final/q513.gif"

5.2 Parametric Functions (10 points)

In your writeup, include a 360-degree gif of your torus point cloud, and make sure the hole is visible. You may choose to texture your point cloud however you wish.

python main.py --question "q52" --output-path "../output_final/q52.gif" --num-points 100

Number of points = 100

Number of points = 1000

5.3 Implicit Surfaces (15 points)

In your writeup, include a 360-degree gif of your torus mesh, and make sure the hole is visible. In addition, discuss some of the tradeoffs between rendering as a mesh vs a point cloud. Things to consider might include rendering speed, rendering quality, ease of use, memory usage, etc.

python main.py --question "q53" --output-path "../output_final/q53.gif"

Trade-Offs:

Rendering Speed: Rendering speed is better with mesh than a point cloud given that we have to render similar quality since there is connectivity.
Quality: Quality of the rendering is better with mesh because point cloud might sometimes be sparse and depend on the number sampled. Mesh has connectivity.
Ease of use: Point Clouds are just coordinates in the 3D world and are more intuitive and easy to use, even for complex surfaces for which meshes, implicit surfaces might be very difficult to construct.
Memory: Meshes need to store faces and vertices only while point clouds if sampled in a huge number can be multiple per face and therefore take more storage.

6. Do Something Fun (10 points)

python main.py --question "q6" --output-path "../output_final/q6.gif"

Trefoil

x = (2 + torch.cos(2 * t)) * torch.cos(3 * t)
y = (2 + torch.cos(2 * t)) * torch.sin(3 * t)
z = torch.sin(4 * t)

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

For this part, write a function that takes a triangle mesh and the number of samples and outputs a point cloud. Then, using the cow mesh, randomly sample 10, 100, 1000, and 10000 points. Render each pointcloud and the original cow mesh side-by-side, and include the gif in your writeup.

python main.py --question "q7" --input-path "../data/cow.obj" --output-path "../output_final/q7.gif" --num-points 100