3D Data Interpolation 1.0

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)

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Coinside,  Domain,  Extrapolation,  Inaccurate,  Newtfit,  Points,  Prepare,  Results
Users rating:	0/10