Q1.1: 360 degree render

• the frame rate is 15

Q1.2: Dolly Zoom

Q2.1: Constructing a Tetrahedron

• 4 vertices and so 4 faces needed

Q2.2: Constructing a Cube

• 8 vertices needed for cube
• Each face of the cube need two triangle to represent, so need 12 faces

Q3: Re-texturing a mesh

• the purple color1 is [0.7, 0.1, 1]
• the green color2 [0.7, 1, 0.1]

Q4: camera transform

Fig.1 - Camera rotate 90 degree.

a = -90/180*np.pi
Rs = [[np.cos(a), -np.sin(a), 0],
    [np.sin(a), np.cos(a), 0],
    [0,0,1]]
Ts =  [0,0,0]

Fig.2 - Camera scale change.

Ts =  [0,0,2]
Rs = [[1, 0, 0],
      [0, 1, 0],
      [0, 0, 1]]

Fig.3 - Camera translate to upper right.

Ts =  [1,-1,0]
Rs = [[1, 0, 0],
      [0, 1, 0],
      [0, 0, 1]]

Fig.4 - Camera transform to right.

b = 90/180*np.pi
Ts = [-3,0,3]
Rs = [[np.cos(b), 0, np.sin(b)],
      [0, 1, 0],
      [-np.sin(b), 0, np.cos(b)]]

Q5.1

• point cloud 1

• point cloud 2

• point cloud 1 & point cloud 2

Q5.2

Q5.3

• Basically the more voxels used, the higher quality of the rendering. But the tradeoff is a slower rendering speed and higher memory consumption.
• The increment of the memory complexity is exponential, while the improvment of the rendering quality is smaller than the exponential.

Q6