Assignment 1

Paritosh Mittal (paritosm)

1.1 360-degree Renderers

1.2 Re-creating the Dolly Zoom

2.1 Constructing a Tetrahedron

Each (Triangular) Mesh has 1 face and three edges. Hence for a tetrahedron, we have 4 vertices and 4 (triangular) faces.

2.2 Constructing a Cube

Each (Triangular) Mesh has 1 face and three edges. Hence for a cube, we have 8 vertices and 12 (triangular) faces.

3 Re-texturing a Mesh

For the above .gif, we interpolate between two colors: (a) Green (Color_a: [0, 1, 0]), and (b) Blue (Color_b: [0, 0, 1])

4 Camera Transformations

---->

R_rel

0.	1.	0.
-1.	0.	0.
0.	0.	1.

T_rel

0.

0.

0.

For this transform we need to rotate by 90 degree clockwise along Z axis.

---->

R_rel

1.	0.	0.
0.	1.	0.
0.	0.	1.

T_rel

0.

0.

2.

For this transform we need to Translate along -Z axis by some units (2 here). As we go back the distance from camera to origin increases and hence the +2 transform.

---->

R_rel

1.	0.	0.
0.	1.	0.
0.	0.	1.

T_rel

0.7

-0.5

0.

For this transform we need to move up (+Y axis) and right (-X axis). Hence the distance from origin to camera will change by positive offset for X (+.7 here) and by negative offset for Y (-.5 here).

---->

R_rel

0.	0.	1.
0.	1.	0.
-1.	0.	0.

T_rel

-3.

0

3.

For this transform we need to both translate and rotate. For camera rotation, we need to rotate the camera along Y axis by 90 degrees counter-clockwise. Once rotated, we move along -X axis (original) or -Z axis (in Rotated frame), thereby adding a positive offset along Z (+3 here). Since we were originally 3 units behind the origin along Z axis (original), we undo that. To do so, be move by 3 units along original Z axis or rotated -X axis (offset of -3. here).

5.1 Rendering Point Cloud from RGB-D Images

5.2 Parametric Functions

5.3 Implicit Surfaces

Discussion on tradeoffs between rendering mesh and point cloud:

• For large scenes, it might be easier to render point clouds vs creating and rendering meshes
• Meshes might take less memory and still represent details faithfully (better quality) while dense point clouds (more memory) is required to capture fine local details.
• Points in point cloud can be manipulated and used independently while meshes are difficult to manipulate or transform

6 Do Something Fun

Here I try to create a scene inspired by Penguins of Madagascar. A group of spy penguins (from Free3D) trying to save a sea-lion from wild animals

Key things to observe include, 10 penguins are aligned in a circle with view aligned by corresponding normals at their location. The code is designed to create symmetric rendering with different possible number of animals

7. Sampling Points on Meshes