ASSIGNMENT 1 : Rendering Basics with PyTorch3D

andrewID : kgaddoba

TASK 0 : SETUP

0.1 Rendering a mesh

TASK 1 : Practicing with Cameras

1.1. 360-degree Renders

1.2 Re-creating the Dolly Zoom

TASK 2 : Practicing with Meshes

2.1 Constructing a Tetrahedron
A 360° rotating Tetrahedron with 4 vertices and 4 triangular faces.

2.2 Constructing a Cube
A 360° rotating Cube with 8 vertices and 12 faces.

TASK 3 : Re-texturing a mesh

color1 = [0, 0.5, 1] color2 = [1, 0.5, 0]

TASK 4 : Camera Transformations

R_relative: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
T_relative: [0.5, -0.5, 0]

R_relative: [[cos(pi/2), -sin(pi/2), 0], [sin(pi/2), cos(pi/2), 0], [0, 0, 1]]
T_relative: [0, 0, 0]

R_relative: [[cos(-pi/2), 0, sin(-pi/2)], [0, 1, 0], [-sin(-pi/2), 0, cos(-pi/2)]]
T_relative: [2, 0, 2]

R_relative: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
T_relative: [0, 0, 2]

TASK 5 : Rendering Generic 3D Representations

5.1 Rendering Point Clouds from RGB-D Images

5.2 Parametric Functions

1. Torus
   

2. Spiral Shell
   

5.3 Implicit Surfaces

1. Torus Mesh
   

2. Mobius Strip Mesh
   

3. Rendering as Mesh vs Point Cloud

a. Point clouds render faster; meshes are slower due to face and shading computations.
b. Meshes provide smooth surfaces and realistic lighting; point clouds can appear sparse.
c. Point clouds use less memory; meshes require more for vertices, faces, and textures.
d. Point clouds are easier to generate from raw data; meshes need reconstruction and preprocessing.
e. Meshes support advanced lighting and shadows; point clouds have limited shading effects.

TASK 6 : Do Something Fun

Double_Torus_Points

TASK 7 : Sampling Points on Meshes

1. 100 Points
   

2. 500 Points
   

3. 1000 Points
   

4. 10000 Points