Linear interpolation graph

This app computes piecewise linear interpolation from your (x, y) points. It shows f(x), the formula of the affine segment in use, and a graph of the interpolated curve.

Built for numerical analysis and lab work, it makes the method visible: between two knots you get a straight line, not a black box. Outside the data range, extrapolation is constant (first or last point).

Input
Enter the x_data abscissas and y_data ordinates, separated by commas or semicolons, then the x value to interpolate. At least two points are required; the x values must be strictly increasing. Three ready-made examples illustrate a saturating curve, an irregular signal, and a sampled parabola.

Result
After Calculate, you get f(x) to six decimal places and the active-segment formula, of the form f(x) = m·x + b on [xi ; xi+1]. If x lies left or right of the data cloud, the text states constant extrapolation. The numeric result always follows piecewise linear interpolation, including at the edges.

With exactly three or four points, the app also shows the unique polynomial (expanded form, degree 2 or 3) that passes through all knots. The displayed value follows the polyline, not that global polynomial: this is intentional, so you can compare the broken line with the polynomial.

Graph and export
The chart draws the interpolated polyline, known points in red, and the evaluated point as a black square. You can share the image (messaging, email) or save it to the gallery for a report or slides.

Audience
Students, teachers, and anyone who wants to see linear interpolation on a phone: piecewise affine functions, undergraduate numerical analysis, a sketch or a live demo in class.

Created by Tamandro.