Data gridding
Syntax
ZI = griddata(x,y,z,XI,YI)
[XI,YI,ZI] = griddata(x,y,z,xi,yi)
[...] = griddata(...,method
)
Description
ZI = griddata(x,y,z,XI,YI)
fits a surface of the form z = f(x,y)
to the data in the (usually) nonuniformly spaced vectors (x,y,z)
. griddata
interpolates this surface at the points specified by (XI,YI)
to produce ZI
. The surface always passes through the data points. XI
and YI
usually form a uniform grid (as produced by meshgrid
).
XI
can be a row vector, in which case it specifies a matrix with constant columns. Similarly, YI
can be a column vector, and it specifies a matrix with constant rows.
[XI,YI,ZI] = griddata(x,y,z,xi,yi)
returns the interpolated matrix ZI
as above, and also returns the matrices XI
and YI
formed from row vector xi
and column vector yi
. These latter are the same as the matrices returned by meshgrid
.
[...] = griddata(...,method
)
uses the specified interpolation method:
'linear'
|
Triangle-based linear interpolation (default)
|
'cubic'
|
Triangle-based cubic interpolation
|
'nearest'
|
Nearest neighbor interpolation
|
'v4'
|
MATLAB 4 griddata method
|
The method
defines the type of surface fit to the data. The 'cubic'
and 'v4'
methods produce smooth surfaces while 'linear'
and 'nearest'
have discontinuities in the first and zero'th derivatives, respectively. All the methods except 'v4'
are based on a Delaunay triangulation of the data.
Remarks
XI
and YI
can be matrices, in which case griddata
returns the values for the corresponding points (XI(i,j),YI(i,j))
. Alternatively, you can pass in the row and column vectors xi
and yi
, respectively. In this case, griddata
interprets these vectors as if they were matrices produced by the command
meshgrid(xi,yi)
.
Algorithm
The griddata(...,'v4')
command uses the method documented in [1]. The other methods are based on Delaunay triangulation (see delaunay
).
Examples
Sample a function at 100 random points between ±2.0
:
rand('seed',0)
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 grid the data to it:
ti
=
-2:.25:2;
[XI,YI]
=
meshgrid(ti,ti);
ZI
=
griddata(x,y,z,XI,YI);
Plot the gridded data along with the nonuniform data points used to generate it:
mesh(XI,YI,ZI), hold
plot3(x,y,z,'o'), hold
off
See Also
delaunay
, interp2
, meshgrid
References
[1] Sandwell, David T., "Biharmonic Spline Interpolation of GEOS-3 and SEASAT Altimeter Data", Geophysical Research Letters, 2, 139-142,1987.
[2] Watson, David E., Contouring: A Guide to the Analysis and Display of Spatial Data, Tarrytown, NY: Pergamon (Elsevier Science, Inc.): 1992.
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