pchip interpolates using a piecewise cubic polynomial P(x) with these properties:
- On each subintervalxk≤x≤xk+1, the polynomial P(x) is a cubic Hermite interpolating polynomial for the given data points with specified derivatives (slopes) at the interpolation points.
- P(x)interpolates y, that is, P(xj)=yj, and the first derivative dP/dX is continuous. The second derivative d2P/dX2 is probably not continuous so jumps at the xj are possible.
- The cubic interpolantP(x) is shape preserving. The slopes at the xj are chosen in such a way that P(x) preserves the shape of the data and respects monotonicity. Therefore, on intervals where the data is monotonic, so is P(x), and at points where the data has a local extremum, so does P(x).