1. Practicing with Cameras

1.1. 360-degree Renders

Here is a 360-degree gif of the provided cow mesh. The camera rotates around the azimuth in 12 degree increments.

1.2. Re-creating the Dolly Zoom

Here is a gif with my dolly zoom effect. I tried to reproduce what was provided in the assignemnt page as much as possible. It is almost identical except that I had to use fewer frames due to rendering speed.

2. Practicing with Meshes

2.1. Constructing a Tetrahedron

Here is a 360-degree gif of my tetraheron. I textured the faces and rotated it such that all four sides could be seen. In the mesh there are 4 vertices, one for each corner, and four faces, one for each triangular face.

2.2. Constructing a Cube

Here is a 360-degree gif of my cube. I textured the faces and rotated it such that all four sides could be seen. In the mesh there are 8 vertices, one for each corner. However, for the faces, there are 12. This is because we are using triangular meshes. Since there are 6 square sides to a cube and two triangles make a square, this requires 12 triangular faces.

3. Re-texturing a mesh

Here is a 360-degree gif of my textured cow. I ran this twice: once with colour1 = [0, 0, 1] and colour2 = [1, 0, 0] to reproduce the example provided in the assignment; and once with colour1 = [1,0.64705882,0] and colour2 = [0,1,1] because they are a nice tropical orange and cyan, and I was feeling very tropical while working on this assignment.

4. Camera Transformations

Please find below my relative transformations, rendered images, and and the explanations of what each relative transformation should be doing.

Transform 0

R_relative is [[1, 0, 0], [0, 1, 0], [0, 0, 1]] and T_relative is [0, 0, 0]. Here, the relative transformation is doing nothing, they are the identity transformation.

Transform 1

R_relative is [[0, 1, 0], [-1, 0, 0], [0, 0, 1]] and T_relative is [0, 0, 0]. Here, the relative transformation is rotating the camera about the z axis. This has the effect of the cow appearing rotated around the z axis. Another 90 degrees and it would appear to be upside-down!

Transform 2

R_relative is [[1, 0, 0], [0, 1, 0], [0, 0, 1]] and T_relative is [0, 0, 2]. Here, the relative transformation is moving the camera along the z-axis, making the cow look smaller / further away.

Transform 3

R_relative is [[1, 0, 0], [0, 1, 0], [0, 0, 1]] and T_relative is [0.5, -0.5, 0]. Here, the relative transformation is moving the camera along the x and and y axes. This has the effect of making the cow appear further down and towards the left in the image. The cow head now looks slightly rotated but that is only because more of the side of the cow is visible as a result of the translation. There is no rotation going on here.

Transform 4

R_relative is [[0, 0, 1], [0, 1, 0], [-1, 0, 0]] and T_relative is [-3, 0, 3]. Here, the relative transformation is first rotating around the y-axis. After doing so, the camera facing in the direction that points towards the side of the cow. However, for the cow to be in view, the camera be translated, otherwise the cow would no longer be in the frame. This requires a translation about the x and z axis since the camera was roated about the y axis.

5. Rendering Generic 3D Representations

5.1 Rendering Point Clouds from RGB-D Images

Here is a 360-degree gif of the first point cloud, second point cloud, and combined point clouds. Because I am running this on a CPU, I was limited by the number of frames I could process. These images are spaced 60 degrees around the azimuth.

5.2 Parametric Functions

Here is a 360-degree gif of my torus. I chose a rainbow texture. Because I am running this on a CPU, I was limited by the number of frames I could process. These images are spaced 60 degrees around the azimuth.

5.3 Implicit Functions

Here is a 360-degree gif of my torus. I chose a rainbow texture. Because I am running this on a CPU, I was limited by the number of frames I could process. These images are spaced 60 degrees around the azimuth.

Mesh vs Point Cloud Render Tradeoffs:

There are a few tradeoffs between rendering a mesh and a point cloud. The advantage for point clouds is that they are much faster to render (assuming not too many points). This is because there is no connectivity information and as a result no need to render any faces; it is only composed of points. As a result, rendering a point cloud also uses less memory and cpu usage. Point clouds are also generally easier and faster to work with. For example, to downsample a point cloud, one can just sample the vertices. However, downsampling a mesh is more complicated. One cannot just sample faces as that would lead to gaps, and one cannot only simply sample vertices as that affects the face connectivity. It is also easier to texture a point cloud as only the vertices need colour, as opposed to a mesh where one must define how the area within each face should be textured.

Yet, meshes do have their advantages. A mesh generally has better quality than a point cloud. Looking at the toruses (or tori), the rendered mesh looks a lot more real because you cannot see the spaces between the tube rings. To get a point cloud on the same calibre, there would be far too many points to render. As well, meshes contain more information. One can always go from a mesh to a point cloud by sampling points, but the inverse is not as trivial. There are several methods that approximate a mesh from a point cloud (alpha shapes, ball pivoting, poisson surface reconstruction, and more) but they each have their own advantages and disadvantages.

6. Do Something Fun

For my something fun, I decided to make a cow walk down a road. I decided to do this becuase it utilized several of the skills I learned throughout the assignment, and I thought it would be exiting to bring something to life.

This required creating, texturing, and manipulating meshes. The cow mesh used the cow.obj file provided to us, but several rotations and translation on the vertices were applied to create the walking animation. The road was constructed from scratch using vertices and faces similar to question 2. Lastly, the tree from https://free3d.com/3d-model/realistic-tree-01-435242.html was used. However, due to the size of the mesh, I had to crop it down a bit otherwise it would take forever to render. The cow, road, and trees were all rotated and shifted to give the illusion of the cow walking.

7. Sampling Points on Meshes

Please see the renderings for a sample using 10, 100, 1000, and 10000 points. As expected, the rendering looks much better as the number of points increase, but at the cost of cpu resources and the time it takes to render.