Cubic Splines

Cubic splines are used to smoothly connect the dots. Write implementation of the class Curve that:

• Accepts a list or set of tuples (x, y).
• Builds n-1 splines for n unique knots.
• Computes y for given x.
• Finds min and max of the curve.
• Supports knot addition and removal.
• Supports overloaded operators +, -.

More detailed description of the class with names of methods is in the docstrings in the Code window.

Examples

For the given 6 lists of knots in Tests, the following curves are constructed:

Notes

• In practical usage of the splines x is inside the knots range, but in this challenge x can be anywhere to compute y.
• The minimum or maximum can lie either on a knot or somewhere inside if a spline bends. The search range is restricted to the range of knots; outside the curve goes to infinity.
• The algorithm for building splines is pretty straightforward and well explained in the wiki page: Spline (mathematics).