Fig. 5.
This figure explains how the weights are calculated when using the predictions in the irregular z-resampling. For all panels the red diamonds are observed points, the tick-marks are the regular grid-points for which one wants interpolated values and the pentagons are predicted values (which exist for all points on the regular grid). The weight given to any prediction is completely given by its bracketing observations. All distances in the figure are given in points on the regular grid. In the upper left corner is the case where the distance between the bracketing points () is less than one grid-point, in which case the prediction is not used at all. In the upper right corner is the case where and where the bracketing points bracket a single grid-point. In this case the prediction will be given the weight . The lower left corner still shows the case where , but now the points bracket two grid-points. In this case the weights for each prediction are given by the distance to the nearest bracketing observation. Note that this still means that the sum of weights for the two points is . The bottom right panel shows the case where and where the bracketing points bracket three grid-points. The middle prediction is now given the weight 1 and the weights for the other two points are still given by the distance to their nearest bracketing point.