Instersect Bezier with existing form

Hi, I’ve already done some pretty basic “straight” models but this time I need curves… I’ve seen many post regarding the Bezier plug-in but I can’t figure out how to “insert” those curves to an existing form.

In my example I draw a rectangle and I’d like to add/remove some curves to it but I can’t “intersect” the middle point of the curves with the rectangle.
Thanks for your help.
test.skp (12.3 KB)

If you zoom in very close, you can draw a line segment from the point where the curve crosses the vertical edge. That will split things.
If I was drawing this, I would start with a rectangle that is larger than I need so I could draw the entire curve laying on the face. The ends of the curve will automatically split the top and bottom edges and they will be easily deleted.

Another benefit of doing this is that Bezier curves can be 3D. Giving yourself a flat surface to draw them on helps to ensure they remain 2D.

So easy, so clean, so simple! thanks