griddata - Interpolate scattered data

Note   Qhull-specific options are no longer supported. Remove the OPTIONS argument from all instances in your code that pass it to griddata. In a future release, the following syntaxes will be removed: [Xq,Yq,Vq] = griddata(x,y,v,xq,yq) [Xq,Yq,Vq] = griddata(x,y,v,xq,yq, method) In addition, griddata will not accept any input vectors of mixed orientation in a future release. To specify a grid of query points, construct a full grid with ndgrid or meshgrid before calling griddata.

Syntax

Description

vq = griddata(x,y,v,xq,yq) fits a surface of the form v = f(x,y) to the scattered data in the vectors (x,y,v). The griddata function interpolates the surface at the query points specified by (xq,yq) and returns the interpolated values, vq. The surface always passes through the data points defined by x and y.

vq = griddata(x,y,z,v,xq,yq,zq) fits a hypersurface of the form v = f(x,y,z).

vq = griddata(..., method) uses a specified interpolation method to compute vq.

Input Arguments

x	Vector specifying the x- coordinates of the sample points.
y	Vector specifying the y- coordinates of the sample points.
z	Vector specifying the z- coordinates of the sample points.
v	Vector of sample values that correspond to the sample coordinates x, y (and z for 3-D interpolation).
xq	Vector or array that specifies x- coordinates of the query points to be evaluated. xq must be the same size as yq (and zq for 3-D interpolation). Specify an array if you want to pass a grid of query points. Use ndgrid or meshgrid to construct the array. Specify a vector if you want to pass a collection of scattered points.
yq	Vector or array that specifies y- coordinates of the query points to be evaluated. yq must be the same size as xq (and zq for 3-D interpolation). Specify an array if you want to pass a grid of query points. Use ndgrid or meshgrid to construct the array. Specify a vector if you want to pass a collection of scattered points.
zq	Vector or array that specifies z- coordinates of the query points to be evaluated. zq must be the same size as xq and yq. Specify an array if you want to pass a grid of query points. Use ndgrid or meshgrid to construct the array. Specify a vector if you want to pass a collection of scattered points.
method	Keyword that specifies the interpolation method. Use one of the following: 'linear' Linear interpolation (default) 'cubic' Cubic interpolation 'natural' Natural neighbor interpolation 'nearest' Nearest neighbor interpolation 'v4' MATLAB 4 griddata method

Output Arguments

vq

The interpolated values at the query points. For 2-D interpolation, where xq and yq specify an m-by-n grid of query points, vq is an m-by-n array. For 3-D interpolation, where xq, yq, and zq specify an m-by-n-by-p grid of query points, vq is an m-by-n-by-p array. If xq, yq, (and zq for 3-D interpolation) are vectors that specify scattered points, vq is a vector of the same length.

Examples

Interpolate Scattered Data Over a Uniform Grid

Sample a function at 100 random points between -2.0 and 2.0.

rng(0,'twister')
x = rand(100,1)*4-2;  
y = rand(100,1)*4-2;
z = x.*exp(-x.^2-y.^2);

x, y, and z are now vectors containing nonuniformly sampled data. Define a regular grid and interpolate the scattered data over the grid.

ti = -2:.25:2; 
[xq,yq] = meshgrid(ti,ti);
zq = griddata(x,y,z,xq,yq);

Plot the gridded data along with the scattered data.

mesh(xq,yq,zq), hold
plot3(x,y,z,'o'), hold off
set(gca,'XTick',[-2 -1 0 1 2]);
set(gca,'YTick',[-2 -1 0 1 2]);

Interpolate 3-D Data Set Over a Grid in the x-y Plane

Sample a function at 5000 random points between -1 and 1.

rng(0,'twister')
x = 2*rand(5000,1)-1; 
y = 2*rand(5000,1)-1; 
z = 2*rand(5000,1)-1;
v = x.^2 + y.^2 + z.^2;

x, y, and z are now vectors containing nonuniformly sampled data. Define a regular grid with points in the range [-0.8, 0.8].

d = -0.8:0.05:0.8;
[xq,yq,zq] = meshgrid(d,d,0);

Interpolate the scattered data over a rectangular region at z=0. Then, plot the results.

vq = griddata(x,y,z,v,xq,yq,zq);
surf(xq,yq,vq);
set(gca,'XTick',[-1 -0.5 0 0.5 1]);
set(gca,'YTick',[-1 -0.5 0 0.5 1]);

See Also

delaunay | griddatan | interpn | meshgrid | ndgrid | TriScatteredInterp

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