Interpolation (interp2 help) (2024)

scatteredInterpolant Scattered data interpolation scatteredInterpolant performs interpolation on scattered data that resides in 2-D or 3-D space. A scattered data set is defined by sample points X and corresponding values v. A scatteredInterpolant object F represents a surface of the form v = F(X). Interpolated values vq at query points Xq are obtained by evaluating the interpolant, vq = F(Xq). F = scatteredInterpolant creates an empty scattered data interpolant. F = scatteredInterpolant(X,v) creates an interpolant that fits a surface of the form v = F(X) to the sample data set (X,v). The sample points X must have size NPTS-by-2 in 2-D or NPTS-by-3 in 3-D, where NPTS is the number of points. Each row of X contains the coordinates of one sample point. The values v must be a column vector of length NPTS. F = scatteredInterpolant(x,y,v) and F = scatteredInterpolant(x,y,z,v) also allow the sample point locations to be specified in alternative column vector format when working in 2-D and 3-D. F = scatteredInterpolant(...,METHOD) specifies the method used to interpolate the data. METHOD must be one of the following: 'linear' - (default) Linear interpolation 'nearest' - Nearest neighbor interpolation 'natural' - Natural neighbor interpolation The 'natural' method is C1 continuous except at the sample points. The 'linear' method is C0 continuous. The 'nearest' method is discontinuous. F = scatteredInterpolant(...,METHOD,EXTRAPOLATIONMETHOD) also specifies the extrapolation method used for query points outside the convex hull. EXTRAPOLATIONMETHOD must be one of the following: 'linear' - (default if METHOD is 'linear' or 'natural') Linear extrapolation based on boundary gradients 'nearest' - (default if METHOD is 'nearest') Evaluates to the value of the nearest neighbor on the convex hull boundary 'none' - Queries outside the convex hull return NaN Example: % Construct a scatteredInterpolant F from locations x,y and values v t = linspace(3/4*pi,2*pi,50)'; x = [3*cos(t); 2*cos(t); 0.7*cos(t)]; y = [3*sin(t); 2*sin(t); 0.7*sin(t)]; v = repelem([-0.5; 1.5; 2],length(t)); F = scatteredInterpolant(x,y,v) % Evaluate F at query locations xq,yq to obtain interpolated values vq tq = linspace(3/4*pi+0.2,2*pi-0.2,40)'; xq = [2.8*cos(tq); 1.7*cos(tq); cos(tq)]; yq = [2.8*sin(tq); 1.7*sin(tq); sin(tq)]; vq = F(xq,yq); % Plot the sample data (x,y,v) and interpolated query data (xq,yq,vq) plot3(x,y,v,'.',xq,yq,vq,'.'), grid on title('Linear Interpolation') xlabel('x'), ylabel('y'), zlabel('Values') legend('sample data','interpolated query data','Location','best') % Change the interpolation method from 'linear' to 'nearest' F.Method = 'nearest' % Perform nearest neighbor interpolation and plot the result vq = F(xq,yq); figure plot3(x,y,v,'.',xq,yq,vq,'.'), grid on title('Nearest Interpolation') xlabel('x'), ylabel('y'), zlabel('Values') legend('sample data','interpolated query data','Location','best') scatteredInterpolant properties: Points - Locations of the scattered sample points Values - Values associated with each sample point Method - Method used to interpolate at query points ExtrapolationMethod - Extrapolation method used outside the convex hull scatteredInterpolant methods: vq = F(Xq) evaluates the scatteredInterpolant F at scattered query points Xq and returns a column vector of interpolated values vq. Each row of Xq contains the coordinates of one query point. vq = F(xq,yq) and vq = F(xq,yq,zq) also allow the scattered query points to be specified as column vectors of coordinates. Vq = F(Xq,Yq) and Vq = F(Xq,Yq,Zq) evaluates F at gridded query points specified in full grid format as 2-D and 3-D arrays created from grid vectors using [Xq,Yq,Zq] = NDGRID(xqg,yqg,zqg). Vq = F({xqg,yqg}) and Vq = F({xqg,yqg,zqg}) also allow a grid of query points to be specified in compact form as grid vectors. Use this syntax to conserve memory when the query points form a large grid. Vq has the same size as the grid: LENGTH(xqg)-by-LENGTH(yqg) or LENGTH(xqg)-by-LENGTH(yqg)-by-LENGTH(zqg). See also griddedInterpolant, griddata, delaunayTriangulation Documentation for scatteredInterpolant doc scatteredInterpolant

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