16-889 Assignment 1: Rendering Basics with PyTorch3D

1.1: 360 rotation gif for Cow.mesh

1.2: Dolly Zoom effect

2.1: Tetrahedron 360 view, and how many mesh and vertices should it have

The tetrahedron should have 4 meshes with 4 vertices,

vertices_tara = np.array([[0,0,0],[-0.3,0.3,0],[0.3,0.3,0],[0,0.3,0.3]])

faces_tara = np.array([[1,0,2],[2,0,3],[3,0,1],[1,2,3]])

2.2: Cube 360 view, and how many mesh and vertices should it have

The cube have 8 vertices with 12 meshes

vertices_cube = np.array([[-1,-1,-1],[1,-1,-1],[1,-1,1],[-1,-1,1],

                                               [1,1,1],[-1,1,1],[-1,1,-1],[1,1,-1]])

faces_cube = np.array([[6,0,1],[6,7,1],[7,1,4],[1,2,4],

                                        [4,2,5],[2,3,5],[5,3,0],[6,0,5],

                                          [5,6,7],[5,4,7],[3,0,1],[3,2,1]])

3: Describe your choice of color1 and color 2 with 360 view

Color 1 is [0,0,1] with is pure blue, and color 2 is [1,0,0] which is pure red

4: Describe in words what R_relative and T_relative should be doing and include rendering produced by chosen R_relative and T_relative

R_relative will adjust the viewing rotational angle based on the original camera angle matrix on world coordinate

T_relative will adjust the viewing transitional position of the camera based on the original camera position with respect to the world coordinate

This only requires R_relative provide 90 degree (a=pi/2) rotation on z axis which is

R_relative =([[1, 0, 0],

                    [0, cos(a), -sin(a)],

                    [0, sin(a), sin(a)])

This requires the camera move further away in z axis, with the T_relative is [0.0, 0, 2] based on original T [0.0,0,3]and it won't require any value for R_matrix_

This requires the camera move away in x axis, so the cow is off center, which the T_relative is [0.5, 0, 0] based on original T [0.0,0,3] and it won't require any value for R_matrix_

This requries the camera rotate in y axis for 90 degrees (a=pi/2)only, so the R_relative is

R_relative =([[cos(a), 0, -sin(a)],

                        [0,1 ,0 ],

                        [sin(a),0 ,cos(a) ]])

5.1: Include a gif of each of 3 point clouds side-by-side

For pointcloud 1

For pointcloud 2

For pointcloud 1+ pointcloud 2

5.2: 360 view of the torus parametric render

5.3:Implict surface 360 view and Discuss tradeoff between redering as mesh vs pointcloud (speed, rendering quality, ease of use etc)

For rendering with pointcloud, it easier to use becasue x,y,z can be defined seperatly, but with number of points increase, the rendering time will increase with it. Using parametric surface, it can only show surface information, and only use point to roughly represent the mesh surface location.

For render with mesh, it can render mush faster for simple geometry, and it can create smoother and continuous surface, but it will have issue when the mesh geometry is complicated. When rendering it with implict surface, it will have too many parameters in the equations to solve if the geometry is complicated.

6: Something funny for rendering 3D repsrentation

Complex Implict surface revolution testing

Bonus: Smapling points from meshes

original

sample number:10

sample number:100

sample number:1000

sample number:10000