![]() ![]() Akima noticed this property in his 1974 paper. Generalization to n-D gridsĪkima's formula and our modified 'makima' formula have another desirable property: they generalize to higher dimensional n-D gridded data. Therefore, 'makima' still preserves Akima's desirable properties of being a nice middle ground between 'spline' and 'pchip' in terms of the resulting undulations. In fact, the results are so similar that it is hard to tell them apart on the plot. Notice that 'makima' closely follows the result obtained with Akima's formula. Indeed, 'makima' does not produce an overshoot if the data is constant for more than two nodes ($v_5=v_6=v_7=1$ above).īut what does this mean for the undulations we saw in our first example? compareCubicPlots(x1,v1,xq1,true, 'NE') Let's try the 'makima' formula on the above overshoot example: compareCubicPlots(x2,v2,xq2,true, 'SE') For this special case of constant data, we set $d_i =0$. Modified Akima interpolation - 'makima'Īkima piecewise cubic Hermite interpolationįor each interval $[x_i~x_$.Akima piecewise cubic Hermite interpolation.Select Cubic B-spline interpolate method. Now the Input branch have filled with proper data range, click the drop-down list beside X Values to Interpolate edit box, and select Col(C).Ĥ. Highlight column B and click Analysis: Mathematics: Interpolate/Extrapolate Y from X on the menu to bring up the dialog.ģ. Import Interpolation.dat on \ Samples\ Mathematics folder.Ģ. Spline coefficients when using spline or B-spline method.ġ. The factor helps user control the balance between the smoothness and fidelity to actual data. Use the Y value of the closest input X value for all values in the extrapolated range.īoundary condition only available in cubic spline methodģrd derivatives are continuous on the second and last-second pointĪ non-negative parameter that specifies the smoothness of the interpolated curve in Cubic B-Spline interpolation. Set all Y values in the extrapolated range to be missing values. This option can then be used to specify how to extrapolate the corresponding Y values. When parts of the data range specified by ix is outside that of the X range specified by iy, these range parts will be considered as the extrapolated range, because the resulted Y values for these parts will be computed from extrapolation. You could refer to the algorithm of each interpolation methods. The akima interpolation is stable to outliers. Method:=3, This method is based on a piecewise function composed of a set of polynomials. ![]() Method:=2, This method also splits the input data into pieces, each segment is fitted with discrete Bezier splines. ![]() ![]() With these boundary conditions met, an entire function can be constructed in a piece-wise manner. The second derivative of each cubic function is set equal to zero. Method:=1, This method splits the input data into a given number of pieces, and fits each segment with a cubic polynomial. The resulting point may not be an accurate estimation of the missing data. Method:=0, Linear interpolation is a fast method of estimating a data point by constructing a line between two neighboring data points. Please refer to the page for additional option switches when accessing the x-function from script Variables Display interp1 ix:=Col(3) iy:=Col(2) method:=spline ox:= coef:= Interpolate or extrapolate XY data at a given set of X valuesġ. Analysis: Mathematics: Interpolate/Extrapolate Y from X ![]()
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