Interpolate N-D scattered data
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Syntax
vq = griddatan(x,v,xq)
vq = griddatan(x,v,xq,method)
vq = griddatan(x,v,xq,method,options)
Description
example
vq = griddatan(x,v,xq) fitsa hypersurface of the form v = f(x) tothe sample points x with values v.The griddatan function interpolates the surfaceat the query points specified by xq and returnsthe interpolated values, vq. The surface alwayspasses through the data points defined by x and v.
example
vq = griddatan(x,v,xq,method) specifies the interpolation method used to compute vq. Options are "linear" or "nearest".
vq = griddatan(x,v,xq,method,options) specifiesa cell array of character vectors, options, tobe used in Qhull via delaunayn.
Examples
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Fit Hypersurface
Open Live Script
Interpolate a 4-D scattered data set and visualize a 3-D isosurface of the interpolated data.
Create a scattered set of sample points.
rng defaultX = 2*rand([5000 3])-1;Y = sum(X.^2,2);Create x, y, and z grids to use as the 3-D set of query points, and interpolate the scattered data at these points.
d = -0.8:0.05:0.8;[y0,x0,z0] = ndgrid(d,d,d);XI = [x0(:) y0(:) z0(:)];YI = griddatan(X,Y,XI);
Since it is difficult to visualize 4-D data sets, use isosurface at 0.8 to visualize the interpolation result.
YI = reshape(YI, size(x0));p = patch(isosurface(x0,y0,z0,YI,0.8));isonormals(x0,y0,z0,YI,p)p.FaceColor = "blue";p.EdgeColor = "none";view(3)axis equalcamlightlighting phong
Nearest Neighbor Interpolation
Open Live Script
Use nearest neighbor interpolation on a 3-D scattered data set.
Create a sample 3-D data set. The matrix X contains the xyz locations of the observed data, and v contains the (randomly generated) observed data. This type of data set could represent, for example, oxygen levels in ocean water at these locations.
rng defaultX = [rand(100,1) rand(100,1) rand(100,1)];v = rand(100,1);Use nearest neighbor interpolation to approximate the value of the underlying function at some query points.
[xx,yy,zz] = meshgrid(0:0.05:1);xq = [xx(:) yy(:) zz(:)];vq = griddatan(X,v,xq,"nearest");Plot slices of the result on top of the sample point locations.
vq = reshape(vq,size(xx));plot3(X(:,1),X(:,2),X(:,3),"r*")hold onslice(xx,yy,zz,vq,[0.3 0.6],0.5,0.5)hold off
Input Arguments
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x — Sample point coordinates
matrix
Sample point coordinates, specified as a matrix. Specify x asan m-by-n matrix to represent m pointsin n-dimensional space. The sample points mustbe unique.
Data Types: double
v — Sample values
vector
Sample values, specified as a vector. Specify v asa vector of length m, with one value for each samplepoint (row) specified in x.
If v contains complex numbers, then griddatan interpolatesthe real and imaginary parts separately.
Data Types: single | double
Complex Number Support: Yes
xq — Query points
matrix
Query points, specified as a matrix. Specify xq asa p-by-n matrix to represent p pointsin n-dimensional space. xq isusually created from a uniform grid produced by ndgrid.
Data Types: double
method — Interpolation method
"linear" (default) | "nearest" | []
Interpolation method, specified as one of the values in thistable. These methods are both based on a Delaunay triangulation ofthe input data.
| Option | Description | Continuity |
|---|---|---|
"linear" (default) | Triangulation-based linear interpolation. | C0 |
"nearest" | Nearest neighbor interpolation. | Discontinuous |
If method is [], then griddatan uses the default "linear" method.
Data Types: char | string
options — Qhull-specific options
cell array | [] | {''}
Qhull-specific options, specified as a cell array. For a list of supported options, see Qhull Quick Reference.
If options is [], then griddatan usesthe default options:
{'Qt' 'Qbb' 'Qc'}for 2-D and 3-Dinterpolations.{'Qt' 'Qbb' 'Qc' 'Qx'}for interpolationsin 4+ dimensions.
If options is {''}, then griddatan doesnot use any options, not even the defaults.
Data Types: cell
Output Arguments
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vq — Interpolated values
vector
Interpolated values, returned as a vector of length p.The interpolated values in vq correspond to thequery points (rows) in xq.
Tips
It is not practical to use
griddatanforinterpolation in dimensions higher than about 6-D, because the memoryrequired by the underlying triangulation grows exponentially withthe number of dimensions.Scattered data interpolation with
griddatanuses a Delaunay triangulation of the data, so can be sensitive to scaling issues in x. When this occurs, you can use normalize to rescale the data and improve the results. See Normalize Data with Differing Magnitudes for more information.
Extended Capabilities
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
Version History
Introduced before R2006a
See Also
delaunayn | griddata | meshgrid
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