16-889 Assignment 1: Rendering Basics with PyTorch3D

Name: Neha Boloor

Andrew ID: (nboloor)

1. Practicing with Cameras

1.1. 360-degree Renders (5 points)

360-Degree View of Cow Mesh

1.2 Re-creating the Dolly Zoom (10 points)

Dolly Zoom on Cow Mesh

2. Practicing with Meshes

2.1 Constructing a Tetrahedron (5 points)

Tetrahedron mesh: 4 triangles, 4 vertices

2.2 Constructing a Cube (5 points)

Cube mesh : 12 triangles, 8 vertices

3. Re-texturing a mesh (10 points)

Gradient render of cow mesh. In this case, color1 = [1,0.9,0.8] and color2 = [0.7,0.4,0.05].

4. Camera Transformations (20 points)

The values of R_relative and T_relative wrt the code given that produces each of the following images are:

Transform 1: R_relative=[[0, 1, 0], [-1, 0, 0], [0, 0, 1]], T_relative=[0, 0, 0]

R_relative and T_relative for this transformation are doing this: The cow is rotated by -90 degrees about the z axis and there is no translation.

Transform 2: R_relative=[[0, 0, 1], [0, 1, 0], [-1, 0, 0]], T_relative=[-3, 0, 3]

R_relative and T_relative for this transformation are doing this: The cow is rotated by 90 degrees about the y axis and the translation for camera is 3 units along x axis and -3 units along z axis.

Transform 3: R_relative=[[1, 0, 0], [0, 1, 0], [0, 0, 1], T_relative=[0, 0, 2]

R_relative and T_relative for this transformation are doing this: There is no rotation. For translation, the camera is moved back by 2 units along the z axis.

Transform 4: R_relative=[[1, 0, 0], [0, 1, 0], [0, 0, 1]], T_relative=[0.5, -0.5, 0]

R_relative and T_relative for this transformation are doing this: There is no rotation. For translation, the camera moves by -0.5 units along the x axis and by 0.5 units along with y axis.

Transform 5 of my choice : R_relative=[[np.cos(-np.pi/10), 0, -np.sin(-np.pi/10)], [0, 1, 0], [np.sin(-np.pi/10), 0, np.cos(-np.pi/10)]], T_relative=[-1, -0.75, 0]

5. Rendering Generic 3D Representations

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

Construct 3 different point clouds:

5.2 Parametric Functions (10 points)



5.3 Implicit Surfaces (15 points)



Trade-Offs:

1. Rendering Speed : Rendering speed for a give set of points would be faster in the case of point clouds as it would be just rendering 3D points while meshes would need continuous connecting faces rendered too. However, for a given quality of rendering, mehses might have a higher rendering speed as opposed to point cloud as there would be a lot more points in the point cloud to match the mesh quality.
2. Rendering Quality : The quality of the rendering is better with mesh as they render continuous surfaces while point clouds have holes in them and also depend on the number of points sampled and are sparse in comparison to a mesh in general.
3. Ease of Use : Point Clouds are just 3D coordinates in the world and hence more intuitive and easy to use, even for complex surfaces which might not be easy to construct in the case of meshes.
4. Memory Usage : Point clouds are much heavier on memory than meshes. Because meshes need to only store faces and vertices while point clouds on the other hand to have a similar degree of continuous rendering would need a much larger number of points sampled which means more memory for storing them.

6. Do Something Fun (10 points)



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

10,100,1000,10000 sampled points, original mesh: