This is a mathematical problem that can easily be solved without using any dedicated frameworks. Each line conforms to the ax+by+c = 0 equation. Using coordinates of ends of the lines you can calculate a, b and c and then it is easy to compute the solution by substituting x and y with coordinates of the point you wish to check for intersection. It is similar when talking about intersection of lines. And of course there is QLineF::intersect() to help you.