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
Cylindrical lens Cylindrical lens A cylindrical lens is a lens which focuses light into a line instead of a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it into a line parallel to the intersection of the surface of the lens and a plane tangent to it. The lens compresses the image in the direction perpendicular to this line, and leaves it unaltered in the direction parallel to it (in the tangent plane). In a light sheet microscope, a cylindrical lens is placed in