Learning for 3D Vision

Assignment 1

1.1. 360-degree Renders

1.2 Re-creating the Dolly Zoom

2.1 Constructing a Tetrahedron

number of vertices: 4 number of faces: 4

2.2 Constructing a Cube

number of vertices: 8 number of faces: 6

3. Re-texturing a mesh

color1 = [0.00, 0.59, 1.00]

color2 = [0.86, 0.08, 0.24]

4. Camera Transformations

$$ R_{\text{relative}} = \begin{bmatrix} 0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \quad T_{\text{relative}} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} $$

$$ R_{\text{relative}} = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}, \quad T_{\text{relative}} = \begin{bmatrix} 0 \\ 0 \\ 3 \end{bmatrix} $$

$$ \theta = \frac{10 \pi}{180} $$

$$ R_{\text{relative}} = \begin{bmatrix} \cos\theta & 0 & \sin\theta \\ 0 & 1 & 0 \\ -\sin\theta & 0 & \cos\theta \end{bmatrix}, \quad T_{\text{relative}} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} $$

$$ \theta = \frac{90 \pi}{180} $$

$$ R_{\text{relative}} = \begin{bmatrix} \cos\theta & 0 & \sin\theta \\ 0 & 1 & 0 \\ -\sin\theta & 0 & \cos\theta \end{bmatrix}, \quad T_{\text{relative}} = \begin{bmatrix} -3 \\ 0 \\ 3 \end{bmatrix} $$

5.1 Rendering Point Clouds from RGB-D Images

5.2 Parametric Functions

5.3 Implicit Surfaces

Aspect	Point Cloud	Mesh	Comment
Rendering Speed	faster	slower	mesh needs rasterization, but using GPU could be fast
Rendering Quality	worse	better	mesh can apply the texture on it
Ease of Use	easier	harder	point cloud data are easier to collect with lidar
Memory Usage	less	more	for mesh we also have to store the vertices indices for faces

6. Do Something Fun

Cottage in a cottage in a cottage.

7. Sampling Points on Meshes