16-889: Learning for 3D Vision

Assignment-1

Aditya Ghuge aghuge

1. Practicing with Cameras

1.1 360-degree Renders

1.2 Re-creating the Dolly Zoom

2. Practicing with Meshes

2.1 Constructing a Tetrahedron

Number of vertices: 4

Number of faces: 4

2.2 Constructing a Cube

Number of vertices: 8

Number of faces: 12

3. Re-texturing a mesh

Color1 = [0, 1, 0]

Color2 = [1, 0, 1]

4. Camera Transformations

4.1 Rotation of camera frame 

Here we have to rotate the camera axis such that the given y axis becomes -x-axis (minus) and x-axis to be shifted to given y-axis location. There is not translation

R = [ [ 0, 1, 0],

[-1, 0, 0],

[ 0 0, 1]]

T = [ 0, 0, 0]

4.2 Translation of camera frame in Z-axis

Here we have to translate the camera axis such that the given camera center now lies in positive new Z-axis. There is no rotation.

R = [ [ 1, 0, 0],

[ 0, 1, 0],

[ 0 0, 1]]

T = [ 0, 0, 2]

4.3 Translation of camera frame in XY-axes

Here we have to translate the camera axis such that the given camera center now lies in positive new X and negative new Y. There is no rotation.

R = [ [ 1, 0, 0],

[ 0, 1, 0],

[ 0 0, 1]]

T = [ 0.5, -0.5, 0]

4.4 Both Translation and Rotation of camera frame

Here we have to rotate the camera axis such that the new X axis becomes given - Z-axis(minus) and new Z-axis to be shifted to given X-axis location. Here we have to translate the camera such that the given camera center now lies in positive new Z and positive new X.

R = [ [ 0, 0, -1],

[ 0, 1, 0],

[ 1 0, 0]]

T = [ -3, 0, 3]

5. Rendering Generic 3D Representations

5.1 Rendering Point Clouds from RGB-D Images

Construct 3 different point clouds:

1. The point cloud corresponding to the first image
2. The point cloud corresponding to the second image
3. The point cloud formed by the union of the first 2point clouds.

5.2 Parametric Functions

5.3 Implicit Surfaces

Q) Discuss some of the tradeoffs between rendering as a mesh vs a point cloud. Things to consider might include rendering speed, rendering quality, ease of use, memory usage, etc.

Ans) Tradeoffs between rendering as a mesh vs point cloud.

Rendering Speed:

Given similar quality of rendering, mesh structure takes less time to render compared to point clouds as for similar quality we need a lot of 3D points.

Rendering Quality:

Mesh rendering is of better quality than Point cloud rendering due to connectivity of mesh the rendered object looks like closed shape. Point clouds with large number of points sampled can sometimes be sparse along certain areas.

Ease of Use:

Meshes while intuitive for easy shapes can be difficult to use for complex shapes and one can miss connectivity of vertices(face), while Point clouds consisting of only 3D points of objects are a bit easy to use.

Memory Usage:

This depends on the quality of the rendering desired. If poor quality is okay(unlikely) ie. If number of points sampled if around number of vertices, then Point clouds are memory efficient as we do not have to store connectivity information of vertices(faces). For good quality of rendering, higher number of point clouds need to be sampled which makes it more memory intensive than meshes.

6. Do Something Fun

Textured mesh rendering with different colors for Ironman (downloaded from Free3D)

7. Sampling Points on Meshes (Extra credit)

7.1 Sample 10 points from cow mesh

7.2 Sample 100 points from cow mesh

7.3 Sample 1000 points from cow mesh

7.4 Sample 10000 points from cow mesh