Notice the smaller undulations (or wiggles) generated by 'makima'. Here's how 2-D 'makima' interpolation compares with 2-D 'spline' interpolation on gridded data generated with the peaks function: = peaks(5) Therefore, 'makima' is supported not only in interp1, but also in interp2, interp3, interpn, and griddedInterpolant. The same procedure applies to higher dimensional n-D grids with $n\ge 2$ and requires computing cross-derivatives along all possible cross-directions. The derivatives and cross-derivatives are then plugged in as coefficients of a two-variable cubic Hermite polynomial representing the 2-D interpolant. The cross-derivative formula first computes the 2-D divided differences corresponding to the 2-D grid data and applies the 'makima' derivative formula along $x$ on these differences then, it takes the result and applies the derivative formula along $y$. Then, we also compute the cross-derivative along $xy$ for each grid node. 17-1, p.18-20, 1974.įor example, to interpolate on a 2-D grid $\left(x,y\right)$, we first apply the 'makima' derivative formula separately along $x$ and $y$ to obtain two directional derivatives for each grid node. Akima, "A Method of Bivariate Interpolation and Smooth Surface Fitting Based on Local Procedures", Communications of the ACM, v. 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 $d_i =0$. ![]() extrapolating will be (c1+c2)/100values less than 30, find the percentage value of extrapolation, add the (percentage value to the value of extrapolation:c3). you will need to find the value of c from the linear discriminant model. Modified Akima interpolation - 'makima'Īkima piecewise cubic Hermite interpolationįor each interval $[x_i~x_$. yes, its is possible to set a lower bound. ![]()
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