![]() "NCM", Numerical Computing with MATLAB, has more mathematical details. The v5 cubic is the black curve between spline and pchip.Ī extensive collection of tools for curve and surface fitting, by splines and many other functions, is available in the Curve Fitting Toolbox. Here is our example data, modified slightly to exaggerate behavior, and interpgui modified to include the 'v5cubic' option of interp1. Because the abscissa are equally spaced, the v5 cubic can be evaluated quickly by a convolution operation. Described in table lookup terms, the table is tab x,y. Interpolation is the same operation as table lookup. This is shown below, along with the relationship between vectors x, Y, xi, and yi. It finds values of a one-dimensional function f (x) underlying the data at intermediate points. The resulting piecewise cubic does not have a continuous second derivative and it does not always preserve shape. The interp1 command interpolates between data points. I'll tell you later where the coefficients of the cubics come from. These functions are formed by adding cubic terms that vanish at the end points to the linear interpolatant. This results in 2k-1 interpolated points between sample values. Vq interp3 (V,k) returns the interpolated values on a refined grid formed by repeatedly halving the intervals k times in each dimension. We have the y-values at the knots, so in order to get a particular PCHIP, we have to somehow specify the values of the derivative, y', at the knots.Ĭonsider these two cubic polynomials in $x$ on the interval $1 \le x \le 2$. Vq interp3 (V) returns the interpolated values on a refined grid formed by dividing the interval between sample values once in each dimension. Just as two points determine a linear function, two points and two given slopes determine a cubic. Since we want the function to go through the data points, that is interpolate the data, and since two points determine a line, the plip function is unique.Ī PCHIP, a Piecewise Cubic Hermite Interpolating Polynomial, is any piecewise cubic polynomial that interpolates the given data, AND has specified derivatives at the interpolation points. There is a different linear function between each pair of points. And remember that extrapolated values are always to be taken with a pinch of salt. So I added the title plip because this is a graph of the piecewise linear interpolating polynomial. interp1 (x,y, 6,7,'linear','extrap') ans. ![]() With line type '-o', the MATLAB plot command plots six 'o's at the six data points and draws straight lines between the points. Here is the data that I will use in this post. ![]()
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