Convex curve itself. A closed regular plane simple curve "C" is convex "if and only if" its curvature is either always non-negative or always non-positive—i.e., if and only if the "turning angle" (the angle of the tangent to the curve) is a weakly monotone function of the parametrization of the curve. Proof: ⇐ If "C" is not convex, then by the parallel tangents lemma there are three points {"p","q1","q2"} such that the tangents at these points are parallel. At least two must have their signed tangents pointing in the same direction. Without loss of generality, assume that these points are "q1" and
Telecentric lens Telecentric lens A telecentric lens is a compound lens that has its entrance or exit pupil at infinity; in the prior case, this produces an orthographic view of the subject. This means that the chief rays (oblique rays that pass through the center of the aperture stop) are parallel to the optical axis in front of or behind the system, respectively. The simplest way to make a lens telecentric is to put the aperture stop at one of the lens's focal points. An entrance pupil at infinity makes the lens object-space telecentric. Such lenses are used in machine vision systems