1 Practicing with Cameras

1.1. 360-degree Renders

1.2 Re-creating the Dolly Zoom

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2 Practicing with Meshes

2.1 Constructing a Tetrahedron

The tetrahedron has 4 vertices and 4 faces

2.2 Constructing a Cube

The cube has 8 vertices and 12 faces

3 Re-texturing a mesh

I choose color 1 to be blue, i.e., [0, 0, 1] and color 2 to be red, i.e., [1, 0, 0]

4 Camera Transformations

# first transformation ,rotate along z-axis for 90 degree
R_relative = [[0, 1, 0], [-1, 0, 0], [0, 0, 1]]
T_relative = [0, 0, 0]
image = render_textured_cow(R_relative=R_relative, T_relative=T_relative)
media.show_image(image, border=True)

# second transformation, move camera farther
R_relative = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
T_relative = [0, 0, 3]
image = render_textured_cow(R_relative=R_relative, T_relative=T_relative)
media.show_image(image, border=True)

# third transformation, rotate along y for -5 degree (left), rotate along x for 5 degree (up), move camera
# closer
theta = np.deg2rad(-5)
R_relative = np.array([[np.cos(theta), 0, -np.sin(theta)], [0, 1, 0], [np.sin(theta), 0, np.cos(theta)]])
theta = np.deg2rad(5)
R_relative_2 = np.array([[1, 0, 0], [0, np.cos(theta), -np.sin(theta)], [0, np.sin(theta), np.cos(theta)]])
R_relative = R_relative_2 @ R_relative
T_relative = [0, 0, -0.5]
image = render_textured_cow(R_relative=R_relative, T_relative=T_relative)
media.show_image(image, border=True)

# fourth transformation, rotate along y for 90 degree 
theta = np.deg2rad(-90)
R_relative = np.array([[np.cos(theta), 0, -np.sin(theta)], [0, 1, 0], [np.sin(theta), 0, np.cos(theta)]])
T_relative = [-3, 0, 3]
image = render_textured_cow(R_relative=R_relative, T_relative=T_relative)
media.show_image(image, border=True)

5. Rendering Generic 3D Representations

5.1 Rendering Point Clouds from RGB-D Images

5.2 Parametric Functions

5.3 Implicit Surfaces

Comparison with rendering with mesh and point cloud

Obivously, rendering with mesh with marching cube is much slower than rendering with point cloud, even with a not very large voxel size (32). In addition, as shown, when rendering using mesh, the obtained torus surface is not very smooth due to the voxelization. The advantage of rendering with mesh is that it gives continuous surface, while rendering with point cloud is inheriantly discrete.

6. Do Something Fun

I rendered a sealion mesh downloaded from free3d.