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Note: TriScatteredInterp will be removed in a future release. Use scatteredInterpolant instead. |
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-by-ndim, 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 2-D and 3-D.
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-by-ndim, 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-by-ndim, 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 | Nearest-neighbor 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)*4-2; y = rand(100,1)*4-2; z = x.*exp(-x.^2-y.^2);
Construct the interpolant:
F = TriScatteredInterp(x,y,z);
Evaluate the interpolant at the locations (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