CatmullRomCurve class

An animation easing curve that passes smoothly through the given control points using a centripetal Catmull-Rom spline.

When this curve is evaluated with transform, the values will interpolate smoothly from one control point to the next, passing through (0.0, 0.0), the given points, and then (1.0, 1.0).

Unlike most cubic splines, Catmull-Rom splines have the advantage that their curves pass through the control points given to them. They are cubic polynomial representations, and, in fact, Catmull-Rom splines can be converted mathematically into cubic splines. This class implements a "centripetal" Catmull-Rom spline. The term centripetal implies that it won't form loops or self-intersections within a single segment.

This class uses a centripetal Catmull-Rom curve (a CatmullRomSpline) as its internal representation. The term centripetal implies that it won't form loops or self-intersections within a single segment, and corresponds to a Catmull-Rom α (alpha) value of 0.5.

See also:

• CatmullRomSpline, the 2D spline that this curve uses to generate its values.
• A Wikipedia article on centripetal Catmull-Rom splines.
• CatmullRomCurve.new for a description of the constraints put on the input control points.
• This paper on using Catmull-Rom splines.