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3d gaussian splatting: hands-on course

*overview*

3d gaussian splatting is a technique used in computer graphics and visualization to represent point cloud data or to create smooth surfaces from discrete points. this method is particularly useful in rendering and visualizing 3d data, such as volumetric data or point clouds from 3d scans. in this tutorial, we will cover the basics of 3d gaussian splatting, and provide a hands-on coding example using python and popular libraries.

*prerequisites*

before getting started, ensure you have the following installed on your desktop:

python 3.x
numpy
matplotlib
open3d (for point cloud visualization)

you can install the required libraries using pip:

```bash
pip install numpy matplotlib open3d
```

step 1: understanding gaussian splatting

in gaussian splatting, each point in a point cloud is replaced by a 3d gaussian distribution which contributes to the overall surface representation. the properties of gaussians allow for smooth interpolation between points, leading to visually appealing results.

the gaussian function in 3d is defined as:

\[ g(x, y, z) = \frac{1}{(2\pi)^{3/2} \sigma^3} e^{-\frac{x^2 + y^2 + z^2}{2\sigma^2}} \]

where:
\( \sigma \) is the standard deviation, controlling the spread of the gaussian.
\( (x, y, z) \) are the coordinates relative to the gaussian center.

step 2: creating a point cloud

let's create a synthetic 3d point cloud for demonstration. we will generate random points in space.

```python
import numpy as np

generate random 3d points
num_points = 1000
point_cloud = np.random.rand(num_points, 3) * 10 scale to a range [0, 10]
```

step 3: visualizing the point cloud

we will use open3d to visualize the generated point cloud.

```python
import open3d as o3d

create a point cloud object
pcd = o3d.geometry.pointcloud()
pcd.points = o3d.utility.vector3dvector(point_cloud)

visualize the point cloud
o3d.visualization.draw_geometries([pcd])
```

step 4: implementing ...

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3D Gaussian Splatting
Hands-on Course
Desktop Edition
3D Modeling
Computer Graphics
Visual Effects
Interactive Learning
Data Visualization
Animation Techniques
Software Training
Graphics Programming
Digital Art
Splatting Techniques
Rendering Methods
3D Visualization