Shape-preserving knot removal

Starting with a shape-preserving C¹ quadratic spline, we show how knots can be removed to produce a new spline which is within a specified tolerance of the original one, and which has the same shape properties. We give specific algorithms and some numerical examples, and also show how the method can be used to compute approximate best free-knot splines. Finally, we discuss how to handle noisy data, and develop an analogous knot removal algorithm for a monotonicity preserving surface method.