Q1

1.1

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1.2

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Q2

2.1

The mesh should have 4 vertices and 4 triangle faces. alt text

2.2

The mesh would have 8 vertices and 12 triangle faces. alt text

Q3

My color 1 was red and color 2 was green.

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Q4

For this transformation, we are rotating camera by 90 degrees in clockwise direction with the z axis being the axis of rotation. T_rel remains 0. alt text

For this transformation, we are moving camera along the z-axis further away from the object. hence only z componenet of R_rel would change. R_rel remains identity. alt text

For this transformation, the axis seemed upright so only translation occurs in the x and y directions i.e. x and y component of T_rel changes and R_rel remains unchanged. alt text

Here, the axis of rotation is y-axis. So R_rel is 90degree rotation in counter-clockwise direction. Then we further move the camera by translating across z and x axis. alt text

Q5

Q5.1

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Q5.2

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Another Shape: Ellipsoid

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Q5.3

Memory requirements of pointcloud will typically be more since we have to store a lot more points inside a triangle rather than having three vertices and one face definied by 3 numbers as is the case with meshes.

Rendering meshes would be faster than rendering pointclouds, since pointclouds can have a lot of points near high-density areas.

Ease of use, rendering point cloud will be easier since it's only a set of points but in case of meshes we need to define triangles.

Rendering quality might be better for meshes since pointcloud may contian holes depending on the density and number of points captured.

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Q6

For this i used cylinder primitives to create a workout bar. alt text

Q7

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