1.1. 360-degree Renders (5 points)
1.2 Re-creating the Dolly Zoom (10 points)
2.1 Constructing a Tetrahedron (5 points)
- Q: List how many vertices and (triangle) faces your mesh should have.
- A: The tetrahedron mesh should have 4 vertices and 4 faces.
2.2 Constructing a Cube (5 points)
- Q: List how many vertices and (triangle) faces your mesh should have.
- A: The Cube mesh requires 8 vertices and 12 faces.
3. Re-texturing a mesh (10 points)
- Q: Describe your choice of color1 and color2.
- A: In the GIF above, color1 was chosen as blue and color2 was chosen as red. Same colors as given in the example were chosen.
4. Camera Transformations (20 points)
T_relative=[0, 0, 0]
R_relative=[
[0, -1, 0],
[-1, 0, 0],
[0, 0, 1]
]
T_relative=[0, 0, 2]
R_relative=[
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]
]
T_relative=[0, 0, 0]
R_relative=[
[0.9969, 0.0062, 0.0782],
[0.0000, 0.9969, -0.0785],
[-0.0785, 0.0782, 0.9938]
]
T_relative=[-3, 0, 3]
R_relative=[
[0, 0, 1],
[0, 1, 0],
[-1, 0, 0]
]
- Q: Describe in words what R_relative and T_relative should be doing?
- A: R_relative indicates relative rotation matrix and hence should rotate the camera2 relative to camera1. T_relative indicates relative translation and hence should indicate the translation imposed on camera1 to generate camera2.
5.1 Rendering Point Clouds from RGB-D Images (10 points)
5.2 Parametric Functions (10 points)
5.3 Implicit Surfaces (15 points)
- Q: 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.
- A (Rendering speed): While pointclouds are just an unordered set or collection of 3D points, mesh on the other hand have faces (triangles) that generate a closed surface. Thus, in terms of rendering speed, pointclouds are relatively faster to render compared to meshes.
- A (Rendering quality): As mentioned earlier, since meshes have a closed continuous surface due to the faces created by vertices of triangles, the representation is of higher quality and conveys more information compared to pointclouds. Since pointclouds are just an unordered collection of 3D points, they are rather discrete and hence the quality of rendering is subpar compared to meshes.
- A (Ease of Use): Since there is no face (surface connectivity) information in pointclouds, it is easier to visualize as well as define the losses if we want to use them within optimization frameworks. On the other hand, since mesh has continuous surface representation consisting of ordered vertices, it is not agnostic to permutations since the ordering of vertices needs to be maintained.
- A (Memory): Since mesh needs to store the continous surface information, or simply put - since it needs to store the connectivity information, it takes larger memory compared to pointclouds. Pointclouds just need to store 3D points information (and color if available).
6. Do Something Fun (10 points)
I took the Indian Tunnel raw points in space from (https://ti.arc.nasa.gov/dataset/caves/) and leveraged the PyTorch3D tools to visualize the pointcloud data. Indian Tunnel is the largest of the lava tubes in the caves area of Craters of the Moon park. It was formed by the Blue Dragon Flow 2100 years ago. The tunnel is over 10m in diameter and 250m long. Critical portions of the interior were mapped, though it would have been prohibitive to map the entire length. Special illumination was designed for the scanner to enable quality color data in the dark underground portions.
-
(Extra Credit) 7. Sampling Points on Meshes (10 points)
N = 10000
N = 1000
N = 100
N = 10
