Question 1

Q1.1

Q1.2

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Question 2

Q2.1

The tetrahedron should have 4 verticies and 4 faces

Q2.2

The cube should have 8 verticies and 12 faces

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Question 3

I went with similar colors as in the handout that produces a color gradient from blue to red.

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Question 4

To achieve this

transform we rotate about the z axis

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

$T_{\text{relative}} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$

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To achieve this

transform we have to rotate about y (yaw) and translate about x and z:

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

$T_{\text{relative}} = \begin{bmatrix} -2.5 \\ 0 \\ 3 \end{bmatrix}$

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To achieve this

we simply translate along the z axis

$R_{\text{relative}} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

$T_{\text{relative}} = \begin{bmatrix} 0 \\ 0 \\ 5 \end{bmatrix}$

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To achieve this

we simply translate along the x axis:

$R_{\text{relative}} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

$T_{\text{relative}} = \begin{bmatrix} 0.8 \\ 0 \\ 0 \end{bmatrix}$

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Question 5

Q5.1

Q5.2

Q5.3

Question: Point clouds are faster to render and use less memory since they store only points without connectivity. However, they can appear sparse and lack surface continuity. Meshes provide higher visual quality with continuous surfaces and better shading, but require more memory and are slower to render.

Response: Point clouds are faster to render and use less memory since they store only points without connectivity. However, they can appear sparse and lack surface continuity. Meshes provide higher visual quality with continuous surfaces, but require more memory and are slower to render.

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Question 6

Star like parametric function

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Question 7

Cow with 10 points sampled

Cow with 100 points sampled

Cow with 1000 points sampled