16889-Assignment1

Jinkun Cao (jinkunc@andrew.cmu.edu)

1. Practicing with Cameras

1.1. 360-degree Renders (5 points)

360degree_1_1

1.2 Re-creating the Dolly Zoom (10 points)

dolly

2. Practicing with Meshes

2.1 Constructing a Tetrahedron (5 points)

tetrahedron_2_1

To construct such a tetrahedron, we need 4 verticles and 4 faces:


verticles = [[-1, -1, -1],[1, 1, -1],[-1, 1, 1],[1, -1, 1],]
faces = [[0, 1, 2], [0, 2, 3], [0, 1, 3], [1, 2, 3]]

2.2 Constructing a Cube (5 points)

cube

To construct such a standard sube, we need 8 verticles and 12 faces.


vertices = [    [0,0,1], [0,1,1], [1,1,1], [1,0,1],
                [0,0,0], [0,1,0], [1,1,0], [1,0,0]]
faces = [   [0,1,3], [1,2,3], # surface1
            [0,1,5], [0,4,5], # surface2
            [0,3,7], [0,4,7], # surface3
            [1,2,6], [1,5,6], # surface4
            [2,3,6], [3,6,7], # surface5
            [4,5,7], [5,6,7]] # surface6

3. Re-texturing a mesh (10 points)

color_cow_3_1

To re-texture the cow mesh with two colors, I see the color with gradient:


color1 = torch.Tensor([0, 0, 1])
color2 = torch.Tensor([1, 0, 0])

4. Camera Transformations (20 points)

To get the results below, we need the relative rotation and relative translation matrices indicated under each image.

relative_cow_p4_1


R1_relative = [[ 0,  1,  0],
                [-1,  0,  0],
                [ 0,  0,  1],]
T1_relative = [0, 0, 0]

relative_cow_p4_2


R2_relative = [[1., 0., 0.],
            [0., 1., 0.],
            [0., 0., 1.]]
T2_relative = [0, 0, 2]

relative_cow_p4_3


R3_relative = [[1., 0., 0.],
            [0., 1., 0.],
            [0., 0., 1.]]
T3_relative = [0.5, -0.5, 0]

relative_cow_p4_4


R4_relative = [[0., 0., 1.],
            [0., 1., 0.],
            [-1., 0., 0.]]
T4_relative = [-3, 0, 3]

5. Rendering Generic 3D Representations

5.1 Rendering Point Clouds from RGB-D Images (10 points)

3plants

For the three images shown above, the first the from the first point cloud extracted from the given file and the second image is from the second point cloud. The first image is from the union of the previous two point clouds.

5.2 Parametric Functions (10 points)

torus


# To describe the torus, we need the parametric function:
# where u and v are angles span in [0, 2*pi]
x = (R1 + R2 cos(v)) * cos(u) 
y = (R1 + R2 cos(v)) * sin(u) 
z = R2 * sin(v)
# Here we set R1=3 and R2=2

5.3 Implicit Surfaces (15 points)

torus_mesh

For the implicit function version, the torus can be described by

\begin{array}{r} (R 1 - \sqrt{(X^{2} + Y^{2})})^{2} + Z^{2} - R_{2}^{2} \end{array}

Here we still set R1=2 and R2=3 to align with the previous version. Also, besides the mesh version as shown above, we can also render the point cloud version which uses the verticles of mesh directly.

torus_from_mesh

Compare with the tradeoffs between these two versions, through my implementation, I find that the mesh rendering surprisingly takes shorter time (3.25s) than the point cloud version (5.46s). But the mesh version requires more memory than point cloud because it needs faces as well. I would say mesh has the better rendering quality as it provides the semantic information as well, which is lost in point cloud. For different tasks, it may vary w.r.t the ease of use when comparing them. For example, for 3D perception, point cloud is more popular for easy to process structure. But for animation, the mesh is obviously a better choice to provide more correspondance or even physical references.

6. Do Something Fun (10 points)

I get a .obj file from Free3D and render it with the gaussian-sampled color ditribution.

canon

(Extra Credit) 7. Sampling Points on Meshes (10 points)

I render the mesh version at the very left and four point clouds. From left to right, the four point clouds contain 10, 100, 1000, and 10000 points respectively.

combined_cow_ex7