GNU Octave Manual Version 3by John W. Eaton, David Bateman, Søren Hauberg Paperback (6"x9"), 568 pages ISBN 095461206X RRP £24.95 ($39.95) |

## 28.4 Interpolation on Scattered Data

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`

, `delaunay3`

or `delaunayn`

. Then the
simplices in 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`

.

__Function File:__`zi`=**griddata***(*`x`,`y`,`z`,`xi`,`yi`,`method`)__Function File:__[`xi`,`yi`,`zi`] =**griddata***(*`x`,`y`,`z`,`xi`,`yi`,`method`)-
Generate a regular mesh from irregular data using interpolation. The function is defined by

. The interpolation points are all`z`= f (`x`,`y`)`(`

. If`xi`,`yi`)`xi`,`yi`are vectors then they are made into a 2D mesh.The interpolation method can be

`"nearest"`

,`"cubic"`

or`"linear"`

. If method is omitted it defaults to`"linear"`

.See also delaunay

__Function File:__`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

. The interpolation points are all`y`= f (`x`,`y`,`z`)`xi`.The interpolation method can be

`"nearest"`

or`"linear"`

. If method is omitted it defaults to`"linear"`

.See also griddata, delaunayn

__Function File:__`yi`=**griddatan***(*`x`,`y`,`xi`,`method`,`options`)-
Generate a regular mesh from irregular data using interpolation. The function is defined by

. The interpolation points are all`y`= f (`x`)`xi`.The interpolation method can be

`"nearest"`

or`"linear"`

. If method is omitted it defaults to`"linear"`

.See also griddata, delaunayn

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)); griddata(x,y,z,xx,yy);

that interpolates from a random scattering of points, to a uniform grid.

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