The higher the exponent, the more accentuated and'unsettled' is the surface because only the weight of the nearest neighbors is integrated in the interpolation (see the followinginteractive animation). Most common form of IDW formula with added distance weighting exponentv ˆ= value to be estimatedv i= known valued p i.,d p n= distances from the n data points to the power of pof the point estimatedThe lower the exponent, the more uniformly all neighbors are incorporated into the calculation (regardless oftheir distance), and therefore, the 'smoother' the estimated surface. The choice of interpolation technique depends on the behavior of data points usually. Newton’s divided difference interpolation. Newton’s backward difference interpolation. Bythe way,they require a linear spatial correlation between the phenomena.Using the so-called ' Inverse Distance Weighting' method or IDW, the weight of any known point is setinversely proportional to its distance from the estimated point. Newton’s forward difference interpolation. The actual distance-based methods use exactly these distances between theestimation points and the known measurement points to weigh their influence in the calculation of the estimated value. A certain number of nearest neighboring pointsHowever, this method is quite fuzzy because of the different distances between the position to be estimated andthe poor integration of knownpoints in the interpolation.
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