## Fitting cubic Bézier curves

Cubic Béziers are by far the most common curve representation, used both for design and rendering. One of the fundamental problems when working with curves is curve fitting, or determining the Bézier that’s closest to some source curve. Applications include simplifying existing paths, efficiently representing the parallel curve, and rendering other spline representations such as Euler spiral or hyperbezier. A specific feature where curve fitting will be used in Runebender is deleting a smooth on-curve point. The intent is to merge two Béziers into one, which is another way of saying to find a Bézier which best approximates the curve formed from the two existing Bézier segments.

Source: Fitting cubic Bézier curves, an article by Raph Levien.