Monotone Spline

Dependencies

This node requires SciPy library to function.

Functionality

A monotone spline is a smooth curve, which interpolates input set of X and Y values, with additional property: interpolated values of Y are strictly increasing when X is increasing.

As a consequence, Y values of whole curve lie within the span between the first and last values of Y provided.

One of possible applications of monotone splines is reparametrization of curves. In original curve, you have some dependency of the point on the curve from curve T parameter; when T is increasing, the point on the curve goes in one direction along the curve. When you do reparametrization, you change this dependency in such a way that the speed at which the point travels along the curve when T is changing, becomes different from original curve. But you still want the point to travel always in one direction.

This node takes two sets of numbers, for X (independent variable) and Y (dependent variable). Both sets are sorted. The node builds a monotone spline, which is a curve third degree. First derivative is continuous, but the second derivative can have discontinuities. This curve is “NURBS-like”, i.e. can be automatically converted to NURBS by nodes which work with NURBS curves.

Curve parametrization: according to provided set of X values.

Inputs

This node has the following inputs:

• X. Set of independent variable values. This input is mandatory.

• Y. Set of dependent variable values. This input is mandatory.

The inputs are automatically renamed according to selected value of the Plane parameter.

Parameters

This node has the following parameter:

• Plane. The coordinate plane in which the spline will be drawn. The available options are:

  • XY. It is assumed that Y depends on X.

  • XZ. It is assumed that Z depends on X.

  • YZ. It is assumed that Z depends on Y.

  The default option is XY.

Outputs

This node has the following output:

• Curve. The generated monotone spline curve.

Examples of Usage

In the following example, green line is a cubic spline, and you can see that for these points the cubic spline is decreasing in the beginning and in the end of curve; and it also goes outside of the range between first and last Y values.