Multiple Support of Obstacle type

[MaazAhmadDeveloper]

Currently, the library supports only rectangular obstacles.

I’d like to extend this by adding support for:

• Circle obstacles in 2D
• Ellipsoid obstacles in 3D

This would also include visualization support in the plotting utilities.

Tagging @SZanlongo @tahsinkose for feedback

[SZanlongo]

The current approach uses r-Trees which have some nice properties (scale well to higher dimensions), but are for rectangular objects. For an ellipsoid, we could either:

• Convert the ellipsoid to an r-Tree representation with some desired error margin
• Switch from using r-Trees to a more generic alternative such as Bounding Volume Hierarchy

For the r-Tree approach, something like this might work:

• Define the Ellipsoid: define the center and its semi-axes lengths.
• Determine the Bounding Box: Create an axis-aligned bounding box that contains the ellipsoid.
• Define the Error Margin (maybe as a percentage of the semi-axes lengths or as a fixed distance).
• Create Subdivisions: subdivide the bounding box into smaller regions. This can be done using a grid or by recursively dividing the bounding box into smaller boxes. The size of these subdivisions can be determined based on the desired error margin.
• Generate Bounding Boxes for Subdivisions: For each subdivision, check if it intersects with the ellipsoid. If it does, create a bounding box for that subdivision. The bounding boxes will then be used as the entries in the R-tree.