Extending lines to their Bounding Box in QGIS

Question

How to extend lines to Bounding Box in QGIS as in the following image:

Figure 1: Lines

Figure 2: Lines extended to Bounding Box

Link to Shapefile of Bounding Box: https://drive.google.com/drive/folders/1jsJ8m2dG0DNwF1jepxpWzwfUVI5sVJJe?usp=sharing

Link to shapefile of lines: https://drive.google.com/drive/folders/1BQvrMiPillL5ubYsDHfEyoV9st12z0E9?usp=sharing

Answer 1

Use this expression with Geometry generator or Geometry by expression (see here for details and differences between these two options) - the expression is adapted to the data you provided (layer name: 'Bounding Box', distance to extend the line: 65):

intersection (
    extend (
        $geometry,65,65
    ),
    geometry (
        get_feature_by_id(
            'Bounding Box',0
        )
    )
)

Answer 2

It may not be the most elegant way. However, you use "Extend line" to extend lines by the distance of the longest edge of the polygon.

The output looks like this and you can clip by Polygon with the "Intersection" tool.

And the output looks like this