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.
Screenshot%20-%206_25_2018%20%2C%208_16_30%20AM
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.
Screenshot%20-%206_25_2018%20%2C%208_18_04%20AM

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