octave: Interpolation on Scattered Data
30.4 Interpolation on Scattered Data
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An important use of the Delaunay tessellation is that it can be used to
interpolate from scattered data to an arbitrary set of points. To do
this the N-simplex of the known set of points is calculated with
‘delaunay’ or ‘delaunayn’. Then the simplices in to which the desired
points are found are identified. Finally the vertices of the simplices
are used to interpolate to the desired points. The functions that
perform this interpolation are ‘griddata’, ‘griddata3’ and ‘griddatan’.
-- : ZI = griddata (X, Y, Z, XI, YI)
-- : ZI = griddata (X, Y, Z, XI, YI, METHOD)
-- : [XI, YI, ZI] = griddata (...)
Generate a regular mesh from irregular data using interpolation.
The function is defined by ‘Z = f (X, Y)’. Inputs ‘X, Y, Z’ are
vectors of the same length or ‘X, Y’ are vectors and ‘Z’ is matrix.
The interpolation points are all ‘(XI, YI)’. If XI, YI are vectors
then they are made into a 2-D mesh.
The interpolation method can be "nearest", "cubic" or "linear". If
method is omitted it defaults to "linear".
DONTPRINTYET See also: 
griddata3 XREFgriddata3, *notegriddatan:
DONTPRINTYET See also: griddata3 XREFgriddata3, griddatan
XREFgriddatan, delaunay XREFdelaunay.
-- : VI = griddata3 (X, Y, Z, V, XI, YI, ZI)
-- : VI = griddata3 (X, Y, Z, V, XI, YI, ZI, METHOD)
-- : VI = griddata3 (X, Y, Z, V, XI, YI, ZI, METHOD, OPTIONS)
Generate a regular mesh from irregular data using interpolation.
The function is defined by ‘V = f (X, Y, Z)’. The interpolation
points are specified by XI, YI, ZI.
The interpolation method can be "nearest" or "linear". If method
is omitted it defaults to "linear".
The optional argument OPTIONS is passed directly to Qhull when
computing the Delaunay triangulation used for interpolation. See
‘delaunayn’ for information on the defaults and how to pass
different values.
DONTPRINTYET See also: griddata XREFgriddata, *notegriddatan:
DONTPRINTYET See also: griddata XREFgriddata, griddatan
XREFgriddatan, delaunayn XREFdelaunayn.
-- : YI = griddatan (X, Y, XI)
-- : YI = griddatan (X, Y, XI, METHOD)
-- : YI = griddatan (X, Y, XI, METHOD, OPTIONS)
Generate a regular mesh from irregular data using interpolation.
The function is defined by ‘Y = f (X)’. The interpolation points
are all XI.
The interpolation method can be "nearest" or "linear". If method
is omitted it defaults to "linear".
The optional argument OPTIONS is passed directly to Qhull when
computing the Delaunay triangulation used for interpolation. See
‘delaunayn’ for information on the defaults and how to pass
different values.
DONTPRINTYET See also: griddata XREFgriddata, *notegriddata3:
DONTPRINTYET See also: griddata XREFgriddata, griddata3
XREFgriddata3, delaunayn XREFdelaunayn.
An example of the use of the ‘griddata’ function is
rand ("state", 1);
x = 2*rand (1000,1) - 1;
y = 2*rand (size (x)) - 1;
z = sin (2*(x.^2+y.^2));
[xx,yy] = meshgrid (linspace (-1,1,32));
zz = griddata (x, y, z, xx, yy);
mesh (xx, yy, zz);
that interpolates from a random scattering of points, to a uniform grid.
Info Catalog
octave: Convex Hull
octave: Geometry