Section 1.1

Section 1.2

Section 2.1

The tetrahedron should have 4 vertices and 4 triangular faces.

Section 2.2

The cube should have 8 vertices and 12 triangular faces.

Section 3

color1 is cyan ([0, 1, 1]) and color2 is yellow ([1, 1, 0])

Section 4

R_relative=[[0, 1, 0], [-1, 0, 0], [0, 0, 1]] (this rotates the camera 90 degrees clockwise around z-axis)

T_relative=[0, 0, 0] (no translation)

R_relative=[[1, 0, 0], [0, 1, 0], [0, 0, 1]] (no rotation change)

T_relative=[0.25, -0.4, -0.5] (this moves the camera 0.5 units in direction of cow, 0.25 units to the right of the cow, and 0.4 units above the cow)

R_relative=[[1, 0, 0], [0, 1, 0], [0, 0, 1]] (no rotation change)

T_relative=[0, 0, 1] (move camera 1 unit farther from cow)

R_relative=[[0, 0, 1], [0, 1, 0], [-1, 0, 0]] (this rotates the camera 90 degrees counterclockwise along the y-axis)

T_relative=[-3, 0, 3] (the -3 becomes z-direction, so removes the original z translation, and the +3 becomes x-direction, so moves the camera 3 units right of the cow)

Section 5

Point Clouds

Parametric Functions - Torus

Parametric Functions - Moebius Strip

Implicit Functions - Torus

Implicit Functions - Heart

Tradeoffs Between Mesh and Point Cloud

1. Rendering Speed - Hard to compare because it depends on the number of 3d points vs the number of vertices and faces.

2. Rendering Quality - Meshes look better than Point Clouds because there's connectivity throughout the render, instead of scattered 3d points.

3. Ease of Use - Meshes are more easy to use than Point Clouds because they have connectivity and thus a more formalized shape than Point Clouds

4. Memory Usage - Meshes can use less memory because the number of faces and vertices needed to represent a surface can be significantly less than the number of individual 3d points. This is because a single face over several vertices can represent the same area that many 3d points would need to fill in.

Section 6

Extra Credit

10 Samples

100 Samples

1000 Samples

10000 Samples