MATLAB Function Reference |
Three-dimensional data interpolation (table lookup)
Syntax
VI = interp3(X,Y,Z,V,XI,YI,ZI) VI = interp3(V,XI,YI,ZI) VI = interp3(V,ntimes) VI = interp3(...,method) VI = INTERP3(...,'method',extrapval)
Description
VI = interp3(X,Y,Z,V,XI,YI,ZI)
interpolates to find VI
, the values of the underlying three-dimensional function V
at the points in arrays XI
,YI
and ZI
. XI
,YI
, ZI
must be arrays of the same size, or vectors. Vector arguments that are not the same size, and have mixed orientations (i.e. with both row and column vectors) are passed through meshgrid
to create the Y1
, Y2
, Y3
arrays. Arrays X
, Y
, and Z
specify the points at which the data V
is given. Out of range values are returned as NaN
.
VI = interp3(V,XI,YI,ZI)
assumes X=1:N
, Y=1:M
, Z=1:P
where [M,N,P]=size(V)
.
VI = interp3(V,ntimes)
expands V
by interleaving interpolates between every element, working recursively for ntimes
iterations. The command interp3(V)
is the same as interp3(V,1)
.
VI = interp3(...,method)
specifies alternative methods:
'linear' |
Linear interpolation (default) |
'cubic' |
Cubic interpolation |
'spline' |
Cubic spline interpolation |
'nearest' |
Nearest neighbor interpolation |
VI = INTERP3(...,'method',extrapval)
specifies a method and a value for VI
outside of the domain created by X
,Y
and Z
. Thus, VI
equals extrapval
for any value of XI
, YI
or ZI
that is not spanned by X
, Y
, and Z
, respectively. You must specify a method to use extrapval
. The default method is 'linear'
.
Discussion
All the interpolation methods require that X
,Y
and Z
be monotonic and have the same format ("plaid") as if they were created using meshgrid
. X
, Y
, and Z
can be non-uniformly spaced. For faster interpolation when X
, Y
, and Z
are equally spaced and monotonic, use the methods '*linear
', '*cubic
', or '*nearest
'.
Examples
To generate a coarse approximation of flow
and interpolate over a finer mesh:
[x,y,z,v] = flow(10); [xi,yi,zi] = meshgrid(.1:.25:10, -3:.25:3, -3:.25:3); vi = interp3(x,y,z,v,xi,yi,zi); % vi is 25-by-40-by-25 slice(xi,yi,zi,vi,[6 9.5],2,[-2 .2]), shading flat
See Also
interp1
, interp2
, interpn
, meshgrid
interp2 | interpft |
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