Learning for 3D Vision [16889] - Assignment 1

NAME: Mayank Agarwal

ANDREW ID: mayankag

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"

Question 1.1

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"

Question 1.2

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"

Number of Faces = 4, Number of Vertices = 4

Question 2.1

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"

Number of Faces = 12, Number of Vertices = 8

Question 2.2

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"

Color choices:

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

Question 3

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 "q4"

Question 4.1

Description: The camera moves back (moves further in the negative z direction by 3 units)

T_relative = [0, 0, 3]

4.2

Question 4.2

Description: The new camera coordinate system w.r.t. the world coordinate system is such that X points in -Y direction, Y points in X direction, and Z remains the same. There is no translation.

R_relative = np.array([[0, -1, 0], [1, 0, 0], [0, 0, 1]]).T

4.3

Question 4.3

Description: The new camera coordinate system w.r.t the world coordinate system is such that X points in -Z direction, Y remains the same, Z points in the X direction. The final world origin w.r.t to the new camera frame should point to [0, 0, 3], and accordingly T_relative becomes [-3, 0, 3].

R_relative = np.array([[0, 0, -1], [0, 1, 0], [1, 0, 0]]).T
T_relative = [-3, 0, 3]

4.4

Question 4.4

Description: The camera moves in the -ve X-direction by 0.5 units and in the +ve Y-direction by 0.5 units.

T_relative=[0.5, -0.5, 0]

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.

python main.py --question "q51"

Question 5.1 Question 5.1 Question 5.1

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"

Number of points = 100

Question 5.2

Number of points = 1000

Question 5.2

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"

Trade-Offs -

Rendering Speed: Rendering speed is better with mesh than a point cloud given that we have to render similar quality.

Quality: Due to connectivity in the mesh, the quality of rendering appears to be better than the point cloud. The quality of the point cloud depends on how well they are sampled. Meshes better represent the surface information.

Ease of use: Meshes and implicit surfaces might be difficult for complex surfaces but point clouds are 3D coordinates therefore are easier to use.

Memory: Meshes are easier on memory since they need to only store the vertices and faces. In a point cloud representation, multiple points would be needed to be sampled per face for finer representation. In my opinion, meshes should require lesser memory for the same resolution rendering as compared to the point cloud. This is especially true for simple objects such as Cube which can be represented by 8 vertices and 12 faces, whereas we would need at least 100 points in a point cloud for a good representation.

Question 5

6. Do Something Fun (10 points)

python main.py --question "q6"

Question 6.1 Question 6.2

7. (Extra Credit) 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"

Question 7.1 Question 7.1 Question 7.3 Question 7.4