Assignment 1: Rendering Basics with PyTorch3D

1. Practicing with Cameras

1.1. 360-degree Renders

My 360-Degree Cow Mesh Below

1.2. Re-creating the Dolly Zoom

My Dolly Zoom Below

2. Practicing with Cameras

2.1. Constructing a Tetrahedron

My Tetrahedron Below. This has 4 vertices and 4 faces.

2.2. Constructing a Cube

My Cube Below. This has 14 vertices and 18 faces.

3. Re-texturing a mesh

My textured mesh is below. The choice of colors that I chose were in remembrance of Kobe Bryant - purple and gold. color1 = [93/255, 63/255, 211/255] and color2 = [255/255, 215/255, 0]

4. Camera Transformations

R_relaivee rotates the camera in the xyz-coorinate frame to the conanical identical rotation matrix

T_relative translates moves thee camera in the xyz-coordinate frame relative to the conanical translation vector [0,0,0]

R_relaivee = [[np.cos(np.deg2rad(-90)), -np.sin(np.deg2rad(-90)), 0], [np.sin(np.deg2rad(-90)), np.cos(np.deg2rad(-90)), 0], [0,0,1]]

T_relative = [0, 0, 0]

R_relaivee = [[1,0,0], [0, 1, 0], [0,0,1]]

T_relative = [0, 0, 2]

R_relaivee = [[1,0,0], [0, 1, 0], [0,0,1]]

T_relative = [0.5, -0.5, 0]

R_relaivee = [[np.cos(np.deg2rad(90)), 0, np.sin(np.deg2rad(90))], [0, 1, 0], [-np.sin(np.deg2rad(90)), 0, np.cos(np.deg2rad(90))]]

T_relative = [-3, 0, 3]

5. Rendering Generic 3D Representations

5.1. Rendering Point Clouds from RGB-D Images

RGB-D Point clouds (left-to-right: point cloud from 1st image, point cloud from 2nd image, union of point clouds)

5.2. Parametric Functions

Torus as parametric function

5.3 Implicit Surfaces

Torus as implicit surface. The tradeoffs between rendering as a mesh vs. a point cloud in terms of rendering speed is that it is faster to render a point cloud than a mesh. Point clouds are also easier to use. They also use less memory because for meshes, you have to store vertices, faces, and edges info.

6. Do Something Fun

My mesh of a human face is below