Curves are the primary source of differentiation on the image plane. They may ultimately be represented by a resolution dependant set of straight line segments. The curve is where the contrast lies and allows our vision to discern independant objects. The kinks in a curve can indicate the presense of human fabricated objects. Curves can also be used to signal directionality, working as paths in space. While an arrowhead can signal orientation, the curve of the path leading from the arrow head indicates whether the arrow is a direction, loop, rough squiggle, etc.
For my undergraduate thesis project, I studied the problem of finding interesting curves from geometric surfaces, such as silhouettes. Extracting Curves from Subdivision Surfaces.
Scribble.js is a tool that processes and intersects sets of curves on an image plane to segment the plane into regions.
Crane.js is a tool that finds important curves in 3D space on pieces of geometry and then projects them onto an image plane.
Here is what I have learned about curves.