16-889: Learning for 3D Vision (Spring 2022)


Assignmenet 1


Qichen Fu

0. Reproduce all the results below


Simply run "python -m starter.main"

1. Practicing with Cameras


1.1. 360-degree Renders (5 points)



1.2 Re-creating the Dolly Zoom (10 points)

2. Practicing with Meshes


2.1 Constructing a Tetrahedron (5 points)



The Tetrahedron has 4 vertices and 4 (triangle) faces. See tetrahedron.obj for details.

2.2 Constructing a Cube (5 points



The cube has 8 vertices and 12 (triangle) faces. See cube.obj for details.

3. Re-texturing a mesh (10 points)


The color1 = [0, 0, 1] and color2 = [1, 0, 0].

4. Camera Transformations (20 points)


This transformation rotate along Z axis (in NDC coordinate system) by 90 degree clockwise (look in positive Z axis)
R_relative=[[0, 1, 0], [-1, 0, 0], [0, 0, 1]], T_relative=[0, 0, 0]

This transformation move the camera along the negative Z axis (in NDC coordinate system)
R_relative=[[1, 0, 0], [0, 1, 0], [0, 0, 1]], T_relative=[0, 0, 3]

This transformation move the camera along the positive X and negative Y axis (in NDC coordinate system)
R_relative=[[1, 0, 0], [0, 1, 0], [0, 0, 1]], T_relative=[0.5, -0.5, 0]

This transformation rotate along Y axis (in NDC coordinate system) by 90 degree counter-clockwise (look in positive Y axis)
R_relative=[[0, 0, 1], [0, 1, 0], [-1, 0, 0]],T_relative=[-3, 0, 3]

5. Rendering Generic 3D Representations


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



The above gifs are in the order of:

  1. The point cloud corresponding to the first image
  2. The point cloud corresponding to the first image
  3. The point cloud formed by the union of the first 2 point clouds.

5.2 Parametric Functions (10 points)



5.3 Implicit Surfaces (15 points)



For a corse representation (number of sampling points are small), rendering point cloud will be much faster because it only needs to compute the number of samples whilethe mesh needs to look at each voxels, which is usually much more than the number of points. It will also use less memory becuase the number of samples are much less than the number of voxels.

The mesh is more easy to use because it includes the extra face information. It also has better visual quality because there will be no holes like the point cloud.

6. Do Something Fun (10 points)


I rendered the point cloud and mesh for the Möbius strip Since there is no perfect implicit functions in cartesian coordinate for Möbius strip, I compute the voxel value for marching cubes by computing the minimum distance from each voxel to the point cloud to construct the mesh (see code for details).

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



The above gifs are in the order of:

  1. Randomly sample 10 points
  2. Randomly sample 100 points
  3. Randomly sample 1000 points
  4. Randomly sample 10000 points