Given a circle of radius $r$ located at $(x_c, y_c)$ and a rectangle defined by the points $(x_l, y_l), (x_l+w, y_l+h)$ is there a way to determine whether the the two overlap? The square's edges are parallel to the $x$ and $y$ axes.
I am thinking that overlap will occur if one of the rectangle's corners is contained in the circle or one of the circle's circumference points at ($n\frac{\pi}{2}, n=\{0,1,2,3\}$ radians) is contained in the rectangle. Is this true?
EDIT: One answer has pointed out a case not covered by the above which is resolved by also checking whether the center of the circle is contained.
Is there a method which doesn't involve checking all points on the circle's circumference?