GNGTS 2022 - Atti del 40° Convegno Nazionale

GNGTS 2022 Sessione 3.3 505 The NN (Sibson 1980) method considers the interpolation on a point x* by means of a convex linear function (2) where w i are the weights depending on the relative area of the intersection between Vi and the V* generated by x* (Fig. 2) (3) Fig. 2 - Natural Neighbors (NN) pattern, where x* is the point of interpolation and the red polygon its relative Voronoi. The red area represents the intersection A i ∩ A *. To estimate the local uncertainties of formula (2), we follow a geostatistical approach by assuming a stationarity condition overall and considering the relationship between the covariance and the theoretical semivariogram γ γ(d) = 2 var[ f ( x ) – f ( x +d)] (4) with d being the distances between the points x cov(d) = var( f ) - γ(d) (5) Considering a linear semivariogram model γ(d) = ad + b, we achieved the function (6) With the V i configuration of Fig. 1, we show a preliminary result of function (6) in Fig. 3.