16825-Learning For 3D HW1 Answers

Andrew ID: abhinavm

1. Practicing with Cameras

1.1 360-degree Renders

A 360-degree gif of the cow mesh.

Figure: 360-degree cow mesh rotation

1.2 Dolly Zoom

A gif demonstrating the dolly zoom effect.

Figure: Dolly zoom

2. Practicing with Meshes

2.1 Tetrahedron

Rendered tetrahedron with 4 vertices and 4 triangle faces.

Figure: Tetrahedron

2.2 Cube

Rendered cube with 8 vertices and 12 triangle faces.

Figure: Cube

3. Re-texturing a Mesh

Cow Mesh Re-texturing

Color smoothly interpolated from purple (front) to cyan (back) based on Z-coordinate.

Figure: Cow re-textured by Z-coordinate

4. Camera Transformations

Camera Transformations

Images showing cow mesh rendered with different camera transformations.

Flipping around Z-axis R_rel = [[0, -1, 0], [-1, 0, 0], [0, 0, 1]] T_rel = [0, 0, 0]	Moving camera back in Z R_rel = [[1, 0, 0], [0, 1, 0], [0, 0, 1]] T_rel = [0, 0, 3]
Camera moved to the right and up R_rel = [[1, 0, 0], [0, 1, 0], [0, 0, 1]] T_rel = [0.4, -0.6, 0]	Flipping around Y-axis Important: T = T_0 + T_relative and not R_0 @ T_0 + T_relative R_rel = [[0, 0, -1], [0, 1, 0], [-1, 0, 0]] T_rel = [0, 0, 0]

5. Rendering Generic 3D Representations

5.1 Point Clouds from RGB-D Images

Rendered point clouds from two RGB-D images and their union.

Point cloud 1

Point cloud 2

Union of point clouds

5.2 Parametric Torus

Torus point cloud rendered with varying sample densities.

Torus 50 samples

Torus 100 samples

Torus 250 samples

Torus 500 samples

5.2 Parametric Ellipsoid

Ellipsoid point cloud rendered with varying sample densities.

Ellipsoid 50 samples

Ellipsoid 100 samples

Ellipsoid 250 samples

Ellipsoid 500 samples

5.3 Implicit Surfaces

Torus and ellipsoid rendered as implicit surfaces using marching cubes.

Torus implicit surface

Ellipsoid implicit surface

Mesh vs Point Cloud tradeoffs

Sources: (https://mindkosh.com/blog/point-cloud-vs-mesh-in-3d-modeling-and-computer-graphics/, https://imerit.net/resources/blog/3d-point-cloud-vs-mesh/)

• Rendering speed: raw point draws can be fastest for huge unstructured scans, but meshes scale better with GPU rasterization, indexed draws, and LOD. In my CPU experimentation, meshes rendering was much faster
• Visual quality: meshes give continuous silhouettes, correct shadows, and texture mapping; point clouds need high density to match.
• Memory: good meshes often use fewer vertices with connectivity. High-quality point clouds may require many more points.
• Ease of use: point clouds are easier to acquire; meshes require are harder to acquire.
• Lighting & effects: meshes integrate with PBR and shadow maps; point clouds require extra work to achieve similar effects.
• Use cases: prefer point clouds for fast capture and analysis, meshes for final rendering, animation, and production.

6. Do Something Fun

Traffic Cone

Custom traffic cone rendered with striped texture.

Traffic cone rotating