AN INTERPOLATION CURVE USING A SPLINE IN TENSION

The use of a linearized mathematical spline for interpolation between given points occasionally yields extraneous inflection points which for some applications, notably the fairing of ship lines, are not acceptable. To avoid this difficulty, a spline in tension is considered and the value of tension which is sufficient to remove all the extraneous inflection points is determined. The slopes of the interpolating curve at each of the given stations are considered as the unknowns and can be calculated without the necessity of numerical matrix inversion.