The four types of intersection of a line with a <a href="https://en.wikipedia.org/wiki/Convex_curve" class="extiw" title="en:Convex curve">convex curve</a>, here a regular pentagon. The intersections of the four blue lines with the curve, shown in red, are (from top to bottom) the empty set, a single point, two points, and an interval.
<a href="//commons.wikimedia.org/wiki/User:David_Eppstein" class="mw-redirect" title="User:David Eppstein">David Eppstein</a>
<span class="int-own-work" lang="en">Own work</span>