Forming field
The field could not be drawn in this browser.
The samples exhibit needs a canvas for the three interpolants.Same samples. Different assumptions.
One frozen set of nine equally spaced samples on the unit interval, spacing 1/8. Abscissae 0, 1/8, 2/8, …, 1. Ordinates 0.20, 0.72, 0.95, 0.55, 0.10, −0.40, −0.05, 0.50, 0.88. Global is the unique degree-8 interpolant, evaluated with barycentric Lagrange weights for equal abscissae. Local is the natural cubic spline: C2 piecewise cubics with y-double-prime equal to zero at both ends. Periodic is the unique real trigonometric polynomial of order 4 with period 9/8 that meets the same nine samples; the period is one spacing longer than the plotted window so the two endpoints remain independent measurements. All three reconstructions interpolate the nodes. None is ground truth implied by the samples alone. Field transitions between claims are presentation crossfades, not members of any interpolant family.