https://en.wikipedia.org/wiki/Spline_(mathematics)
For the elastic rulers being the model for the spline interpolation, one has that to the left of the left-most "knot" and to the right of the right-most "knot" the ruler can move freely and will therefore take the form of a straight line with q′′ = 0. As q′′ should be a continuous function of x, natural splines in addition to the n − 1 linear equations (15) should have