Interpolate 2-D or 3-D scattered data (2024)

Interpolate 2-D or 3-D scattered data

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Syntax

vq = griddata(x,y,v,xq,yq)

vq = griddata(x,y,z,v,xq,yq,zq)

vq = griddata(___,method)

[Xq,Yq,vq] = griddata(x,y,v,xq,yq)

[Xq,Yq,vq] = griddata(x,y,v,xq,yq,method)

Description

example

vq = griddata(x,y,v,xq,yq) fitsa surface of the form v = f(x,y) tothe scattered data in the vectors (x,y,v). The griddata functioninterpolates the surface at the query points specified by (xq,yq) andreturns the interpolated values, vq. The surfacealways passes through the data points defined by x and y.

example

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

vq = griddata(___,method) specifies the interpolation method used to compute vq using any of the input arguments in the previous syntaxes. method can be "linear", "nearest", "natural", "cubic", or "v4". The default method is "linear".

[Xq,Yq,vq] = griddata(x,y,v,xq,yq) and [Xq,Yq,vq] = griddata(x,y,v,xq,yq,method) additionally return Xq and Yq, which contain the grid coordinates for the query points.

Examples

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Interpolate Scattered Data over Uniform Grid

Open Live Script

Interpolate random scattered data on a uniform grid of query points.

Sample a function at 200 random points between -2.5 and 2.5. The resulting vectors x, y, and v contain scattered sample points and data values at those points.

rng defaultxy = -2.5 + 5*rand([200 2]);x = xy(:,1);y = xy(:,2);v = x.*exp(-x.^2-y.^2);

Define a grid of query points and interpolate the scattered data over the grid.

[xq,yq] = meshgrid(-2:.2:2, -2:.2:2);vq = griddata(x,y,v,xq,yq);

Plot the gridded data as a mesh and the scattered data as dots.

mesh(xq,yq,vq)hold onplot3(x,y,v,"o")xlim([-2.7 2.7])ylim([-2.7 2.7])

Interpolate 4-D Data Set over Grid

Open Live Script

Interpolate a 3-D slice of a 4-D function that is sampled at randomly scattered points.

Sample a 4-D function v(x,y,z) at 2500 random points between -1 and 1. The vectors x, y, and z contain the nonuniform sample points.

x = 2*rand(2500,1) - 1; y = 2*rand(2500,1) - 1; z = 2*rand(2500,1) - 1;v = x.^2 + y.^3 - z.^4;

Create a grid with xy points in the range [-1, 1], and set z=0. Interpolating on this grid of 2-D query points (xq,yq,0) produces a 3-D interpolated slice (xq,yq,0,vq) of the 4-D data set (x,y,z,v).

d = -1:0.05:1;[xq,yq,zq] = meshgrid(d,d,0);

Interpolate the scattered data on the grid. Plot the results.

vq = griddata(x,y,z,v,xq,yq,zq);plot3(x,y,v,"ro")hold onsurf(xq,yq,vq)hold off

Interpolate 2-D or 3-D scattered data (2)

Comparison of Scattered Data Interpolation Methods

Open Live Script

Compare the results of several different interpolation algorithms offered by griddata.

Create a sample data set of 50 scattered points. The number of points is artificially small to highlight the differences between the interpolation methods.

x = -3 + 6*rand(50,1);y = -3 + 6*rand(50,1);v = sin(x).^4 .* cos(y);

Create a grid of query points.

[xq,yq] = meshgrid(-3:0.1:3);

Interpolate the sample data using the "nearest", "linear", "natural", and "cubic" methods. Plot the results for comparison.

z1 = griddata(x,y,v,xq,yq,"nearest");plot3(x,y,v,"mo")hold onmesh(xq,yq,z1)title("Nearest Neighbor")legend("Sample Points","Interpolated Surface","Location","NorthWest")

Interpolate 2-D or 3-D scattered data (3)

z2 = griddata(x,y,v,xq,yq,"linear");figureplot3(x,y,v,"mo")hold onmesh(xq,yq,z2)title("Linear")legend("Sample Points","Interpolated Surface","Location","NorthWest")

Interpolate 2-D or 3-D scattered data (4)

z3 = griddata(x,y,v,xq,yq,"natural");figureplot3(x,y,v,"mo")hold onmesh(xq,yq,z3)title("Natural Neighbor")legend("Sample Points","Interpolated Surface","Location","NorthWest")
z4 = griddata(x,y,v,xq,yq,"cubic");figureplot3(x,y,v,"mo")hold onmesh(xq,yq,z4)title("Cubic")legend("Sample Points","Interpolated Surface","Location","NorthWest")

Interpolate 2-D or 3-D scattered data (6)

Plot the exact solution.

figureplot3(x,y,v,"mo")hold onmesh(xq,yq,sin(xq).^4 .* cos(yq))title("Exact Solution")legend("Sample Points","Exact Surface","Location","NorthWest")

Interpolate 2-D or 3-D scattered data (7)

Input Arguments

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x, y, zSample point coordinates
vectors

Sample point coordinates, specified as vectors. Correspondingelements in x, y, and z specifythe xyz coordinates of points where the samplevalues v are known. The sample points must be unique.

Data Types: double

vSample values
vector

Sample values, specified as a vector. The sample values in v correspondto the sample points in x, y,and z.

If v contains complex numbers, then griddata interpolatesthe real and imaginary parts separately.

Data Types: double
Complex Number Support: Yes

xq, yq, zqQuery points
vector | array

Query points, specified as vectors or arrays. Correspondingelements in the vectors or arrays specify the xyz coordinatesof the query points. The query points are the locations where griddata performsinterpolation.

  • Specify arrays if you want to pass a grid of querypoints. Use ndgrid or meshgrid to construct the arrays.

  • Specify vectors if you want to pass a collection of scattered points.

The specified query points must lie inside the convex hull ofthe sample data points. griddata returns NaN forquery points outside of the convex hull.

Data Types: double

methodInterpolation method
"linear" (default) | "nearest" | "natural" | "cubic" | "v4"

Interpolation method, specified as one of the methods in thistable.

MethodDescriptionContinuity
"linear"Triangulation-based linear interpolation (default) supporting2-D and 3-D interpolation.C0
"nearest"Triangulation-based nearest neighbor interpolation supporting2-D and 3-D interpolation.Discontinuous
"natural"Triangulation-based natural neighbor interpolation supporting2-D and 3-D interpolation. This method is an efficient tradeoff betweenlinear and cubic.C1 except at sample points
"cubic"Triangulation-based cubic interpolation supporting 2-D interpolationonly.C2
"v4"

Biharmonic spline interpolation (MATLAB® 4 griddata method)supporting 2-D interpolation only. Unlike the other methods, thisinterpolation is not based on a triangulation.

C2

Data Types: char | string

Output Arguments

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vq — Interpolated values
vector | array

Interpolated values, returned as a vector or array. The sizeof vq depends on the size of the query point inputs xq, yq,and zq:

  • For 2-D interpolation, where xq and yq specifyan m-by-n grid of query points, vq isan m-by-n array.

  • For 3-D interpolation, where xq, yq,and zq specify an m-by-n-by-p gridof query points, vq is an m-by-n-by-p array.

  • If xq, yq, (and zq for3-D interpolation) are vectors that specify scattered points, then vq isa vector of the same length.

For all interpolation methods other than "v4", the output vq contains NaN values for query points outside the convex hull of the sample data. The "v4" method performs the same calculation for all points regardless of location.

Xq, Yq — Grid coordinates for query points
vectors | matrices

Grid coordinates for query points, returned as vectors or matrices. The shape of Xq and Yq depends on how you specify xq and yq:

  • If you specify xq as a row vector and yq as a column vector, then griddata uses those grid vectors to form a full grid with [Xq,Yq] = meshgrid(xq,yq). In this case, the Xq and Yq outputs are returned as matrices that contain the full grid coordinates for the query points.

  • If xq and yq are both row vectors or both column vectors, then Xq = xq and Yq = yq.

Tips

  • Scattered data interpolation with griddata uses a Delaunay triangulation of the data, so can be sensitive to scaling issues in x, y, and z. 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

Version History

Introduced before R2006a

See Also

scatteredInterpolant | delaunay | griddatan | interpn | meshgrid | ndgrid

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Interpolate 2-D or 3-D scattered data (8)

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Interpolate 2-D or 3-D scattered data (2024)
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