as3geometry – Parabolas

The as3geometry library has been neglected of late, but I have managed to push out a couple of important updates this week: the invalidation manager and parabola handling. I will discuss the invalidation manager later in the week since it is quite a technical and complex update. The implementation of parabolas is rather more straightforward.

Parabola defined by a line and vertex

Parabola segment defined by a line segment and vertex:

Usefully, a parabola (which, precisely, is “the locus of points equidistant from a point and a line”) can be expressed as a quadratic bezier curve. The implementation ‘simply’ finds the three control points of a quadratic bezier curve and then uses the Flash Player’s Graphics.curveTo method to draw.