Note:

F = TriScatteredInterp()
F = TriScatteredInterp(X, V)
F = TriScatteredInterp(X, Y, V)
F
= TriScatteredInterp(X, Y, Z, V)
F = TriScatteredInterp(DT, V)
F = TriScatteredInterp(..., method)
F = TriScatteredInterp()
creates an empty
scattered data interpolant. This can subsequently be initialized with
sample data points and values (Xdata
, Vdata
)
via F.X = Xdata
and F.V = Vdata
.
F = TriScatteredInterp(X, V)
creates an
interpolant that fits a surface of the form V = F(X)
to
the scattered data in (X
, V
). X
is
a matrix of size mpts
byndim
,
where mpts
is the number of points and ndim
is
the dimension of the space where the points reside (ndim
is
2 or 3). The column vector V
defines the values
at X
, where the length of V
equals mpts
.
F = TriScatteredInterp(X, Y, V)
and F
= TriScatteredInterp(X, Y, Z, V)
allow the data point
locations to be specified in alternative column vector format when
working in 2D and 3D.
F = TriScatteredInterp(DT, V)
uses the
specified DelaunayTri
object DT
as
a basis for computing the interpolant. DT
is a
Delaunay triangulation of the scattered data locations, DT.X
.
The matrix DT.X
is of size mpts
byndim
,
where mpts
is the number of points and ndim
is
the dimension of the space where the points reside, 2 <=
ndim <= 3
. V
is a column vector that
defines the values at DT.X
, where the length of V
equals mpts
.
F = TriScatteredInterp(..., method)
allows
selection of the technique method
used to interpolate
the data.
X  Matrix of size mpts byndim ,
where mpts is the number of points and ndim is
the dimension of the space where the points reside. Input may also
be specified as column vectors (X , Y )
or (X , Y , Z )  
V  Column vector that
defines the values at X , where the length of V equals mpts .  
DT  Delaunay triangulation of the scattered data locations  
method  natural  Natural neighbor interpolation 
linear  Linear interpolation (default)  
nearest  Nearestneighbor interpolation 
F  Creates an interpolant that fits a surface of the form V
= F(X) to the scattered data. 
To evaluate the interpolant, express the statement in Monge's
form Vq = F(Xq)
, Vq = F(Xq,Yq)
,
or Vq = F(Xq,Yq,Zq)
where Vq
is
the value of the interpolant at the query location and Xq
, Yq
,
and Zq
are the vectors of point locations.
The Delaunay triangulation of a set of points is a triangulation such that the unique circle circumscribed about each triangle contains no other points in the set.
Create a data set:
x = rand(100,1)*42; y = rand(100,1)*42; z = x.*exp(x.^2y.^2);
F = TriScatteredInterp(x,y,z);
(qx, qy)
. The
corresponding value at these locations is qz
.ti = 2:.25:2; [qx,qy] = meshgrid(ti,ti); qz = F(qx,qy); mesh(qx,qy,qz); hold on; plot3(x,y,z,'o');
delaunayTriangulation
 interp1
 interp2
 interp3
 meshgrid