Cubic Spline Interpolation

A trader with a handful of pivot points, a volume profile sampled at uneven price levels, or any other small, irregularly spaced series often needs a value between the points that were actually recorded, not just the nearest one. Linear interpolation gives a value but a visibly kinked curve; this library gives a smooth one, in two variants that trade off differently. BuildNaturalSpline fits the classic cubic spline: the curve is twice continuously differentiable everywhere, built by solving a tridiagonal system for the second derivative at each knot with the Thomas algorithm in a single O(n) pass. It is the smoothest possible curve through the points in a least-curvature sense, but "smoothest" does not mean "safest" - between two points where the trend changes sharply, a natural spline can swing above or below the surrounding data. That overshoot is fine for a cosmetic curve and wrong for anything that must stay monotone by definition. BuildMonotoneSpline implements the Fritsch-Carlson method for exactly that case. Each segment's tangent is derived from its immediate neighbours and then limited so the coefficients satisfy alpha^2 + beta^2 <= 9 - the precise condition that guarantees the resulting cubic never overshoots the data on that segment. It gives up being twice differentiable at every knot in exchange for a curve that can be trusted never to say something the data itself did not say. Both evaluators clamp any x value outside the fitted range to the nearest endpoint rather than extrapolating - a cubic projected past the data it was fit to is unreliable and can diverge sharply within a short distance, so holding flat at the edge is the safer default. Notes and limitations - x[] must be strictly increasing for both spline kinds; both Build functions print why and return false rather than producing a curve from bad input. - At least 3 points are required - two points define only a straight line, which neither spline kind adds anything to. - Both evaluators use a linear scan to find the segment containing xValue, which is intentional: the knot counts this library is meant for (pivot points, a handful of curve control points) are small enough that a binary search would not meaningfully outperform it, and the linear scan is easier to verify at a glance. - Neither spline is monotone-guaranteed to reproduce the input data's true underlying shape between sparse points - both are interpolation, not measurement, and a large gap between two knots is still a guess about what happens in between. - Out-of-range x values are clamped to the nearest endpoint's exact y value, not extrapolated along the edge segment's curve.

Script · MT5 · v1.0 · Free

Tags: Pivot Points · Volume · MT5 Script · MQL5 Source Code

MQL4 & MQL5 scripts · PolyMaria