3D Data Interpolation

3D interpolation using modified 4-point vector Newton interpolation

Syntax: ui=NewtFit(x,y,z,u,xi,yi,zi)

3D interpolation. It may be used where griddata3 fails to find a triangularization of the datagrid (x,y,z). The function uses a modified 4 point Newton interpolation formula for vector arguments in 3D instread of scalars used in 1D. The interpolation is performed for the 4 nearest neighbors for each point in the (xi,yi,zi).

u=u(x,y,z) is the data from which ui(xi,yi,zi) is interpolated x,y,z,u are vectors of same size and xi,yi,zi are also vectors. The fit is exact (u=ui) for points (xi,yi,zi) that coinside with data points (x,y,z). Note: NewtFit also delivers result for points outside the domain (i.e., extrapolation), but results may be inaccurate then.

%Example: Prepare data in random non-uniform grid
xyz=rand(10003,3);
x=xyz(:,1);y=xyz(:,2);z=xyz(:,3);
u=x.^3+sin(pi*y).^2.*z.^2;

%Gridpoints to fit:
xyz=rand(8007,3);
xi=xyz(:,1);yi=xyz(:,2);zi=xyz(:,3);

%Interpolate
ui=NewtFit(x,y,z,u,xi,yi,zi);

%compare and plot
uui=xi.^3+sin(pi*yi).^2.*zi.^2;%exact
plot(uui,ui,'.');pause(4)
hist(uui-ui,60);
standard_deviation=std(uui-ui)