16-825 Assignment 1

Duc Doan

Q1: Practicing with cameras

Q1.1: 360-degree render

Q1.2: Dolly Zoom

Q2: Practicing with meshes

Q2.1: Tetrahedron

The mesh should have 4 vertices and 4 faces.

Q2.2: Cube

The mesh should have 8 vertices and 12 faces (2 triangles per cube face).

Q3: Re-texturing a mesh

color1 = [0, 0, 1]
color2 = [1, 0, 0]

Q4: Camera transformations

Original image:

Transformations:

a) R_relative rotates the object by 90deg about z, T_relative does nothing:

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b) R_relative does nothing, T_relative moves the object forward:

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c) R_relative does nothing, T_relative moves the object to the left and downward w.r.t. the camera:

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d) R_relative rotates the object -90deg about the camera y, T_relative moves the object forward (+z) then to the left (+x) to bring it back into the camera's FoV:

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Q5: Rendering 3D representations

Q5.1: Rendering point clouds from RGB-D images

PC from first image	PC from second image	Combined PC

Q5.2: Parametric functions

Torus:

Klein bottle (https://en.wikipedia.org/wiki/Klein_bottle#Bottle_shape):

Q5.3: Implicit surfaces

Torus:

Heart (https://mathworld.wolfram.com/HeartSurface.html):

Tradeoffs between rendering as a mesh vs a point cloud:

• rendering speed: rendering a point cloud is probably simpler because we only need to draw points, while for mesh we need to take care of the connectivity.
• rendering quality: thanks to connectivity, rendering a mesh usually provides higher quality. For a high-quality render using point cloud, we need a large number of points.
• ease of use: it depends on the use case, but meshes are easier to render and can be water-tight, while point clouds can be constructed/obtained more easily.
• memory usage: for a high quality shape, point cloud might take more space for the dense cloud.

Q6: Do something fun

A cube being morphed over time:

Q7: Stratified sampling

Mesh	10 pts	100 pts	1000 pts	10000 pts