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TriScatteredInterp - Class: TriScatteredInterp

Interpolate scattered data

Syntax

F = TriScatteredInterp() F = TriScatteredInterp(X, V) F = TriScatteredInterp(X, Y, V) F = TriScatteredInterp(X, Y, Z, V) F = TriScatteredInterp(DT, V) F = TriScatteredInterp(..., method)

Description

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 >= 2. 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. 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.

Inputs

`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.
`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

Outputs

`F`	Creates an interpolant that fits a surface of the form `V = F(X)` to the scattered data.

Evaluation

To evaluate the interpolant, express the statement in Monge's form V=F(x), V=F(x,y), or V=F(x,y,z).

Definitions

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.

Examples

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');