Two equivalent definitions of a convex curve (black): It is a subset of the boundary of a convex set (blue), and it is a curve with at least one supporting line (red) through each of its points.
<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>