Intersection between lines (line and geodesic line)

I am currently working on karamba model for winding lines. But for my karamba model I need to get all seperated lines, so between every intersection. In the figure I show my karamba input with the straight lines being lines and the diagonals being geodesics.

But I can only find the intersection between or line-line or geodesic-geodesic. I have checked if the line-geodesic intersection is on the same location with the intersection snap function. In the figures below this can be seen where the yellow circle is between a line and a line and the one without the yellow circle is a line-geodesic intersection.

Now I want to find all intersection points, so geodesic-geodesic, line-line and line-geodesic. I dont know of this is possible. Here an example where it does not work:

Geometrical part + karamaba (81.0 KB)

Hi, you need to develop your geometry in a way so that the lines intersect - for example pulling all the curves onto a surface so that that their are geometric intersections between all curves