Curvature is a measure of how much a curve curves.

Curvature is measured by fitting a circle into the curve, then taking the reciprocal of the radius of the circle. In the illustration, at point x, the curve is best described by a circle with radius r. At this point, the curvature is 1/r.

(We use the reciprocal, 1/r, instead of just r because a flat line has an infinite radius. Taking the reciprocal gives us 0 instead of infinity.)

Several tools in Alias, such as the Locators > Curve Curvature tool, allow you to display a comb plot of a curve’s curvature. At regular points along the curve, the tool samples the curvature, and draws a line (sometimes called a “quill” because it looks like a spine on the back of a porcupine). The length of the line represents the curvature value at that point.