## Tension Function

This is a hyperbolic function often used in spline interpolations that parameterises the 'tension' of a curve interpolation between points. At low tension it behaves like a cubic polynomial, while at high tension, it tends towards a piecewise smooth series of linear functions.

They are derived from the following constraints on an interval `[x_i, x_i+1]`:

This yields a C2 continuous function with hyperbolic terms (not a polynomial) that ranges from looking like a cubic interpolation at low tensions (`tau -> 0`) and a linearly blended interpolation at high tensions.