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I am trying to build an application which the user can use to draw clothoids with the mouse, i.e. to set the start point and the end point of the spiral and then by dragging these points with the mouse he could also set the shape of the clothoid by modifying the start and end curvature. Probably for changing the curvature I will need to use the tangents though I am not sure of that.
How can one implement that in Qt? Do you know of any example codes that I could run in Qt?
The best approach would probably be to use the Graphics View Framework.
There are a few examples that should help you getting started in the Graphics View Examples page. The Diagram scene one looks like a good starting point for what you want to achieve.