# Distance Weighted Interpolation: Gradient Plane Nodal Functions

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Hello everyone, I implemented shepard's method for a distance weighted interpolation. Basically the resource that helped me most was: http://www.ems-i.com/gmshelp/Interpolation/Interpolation_Schemes/Inverse_Distance_Weighted/Shepards_Method.htm To sum it up: f_i are my values I want to interpolate (my scatter points). w_i are the interpolation coefficients. (how much of a scatter point is used to compute the currentInterpolationPoint?) The sum of w_i is 1. Now there seems to be a way which ameliorates this method. The formula can be extended using Gradient Plane Nodal Functions Q_i(x, y, z) in the original formula: f(x, y, z): sum i = 1 to n (w_i * f_i) It is extended to: f(x, y, z): sum i = 1 to n (w_i * Q_i(x, y, z)) where: Q_i(x, y, z) = f_x(x - x_i) + f_y(y - y_i) + f_z(z - z_i) + f_i f_x, f_y and f_z are the partial derivatives at the scatter point. How could I get these? The surrounding scatter points in my data structure are easily to access. x_i and y_i and z_i are the positional values of each scatter point. x, y, z seems to be the positional values of the currentInterpolationPoint, am I right? f_i is simple, this is like before. So basically I am searching for a way the get the partial derivatives. Anyone?

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