Gridded and Scattered Sample Data
Interpolation is a method for estimating the value at a query location that lies
within the domain of a set of sample data points. A sample data set defined by
locations X and corresponding values V can be
interpolated to produce a function of the form V =
F(X). This function can then be used to
evaluate a query point Xq, to give Vq =
F(Xq). This is a single-valued function;
for any query Xq within the domain of X it will
produce a unique value Vq. The sample data is assumed to respect
this property in order to produce a satisfactory interpolation. One other interesting
characteristic is that the interpolating function passes through the data points.
This is an important distinction between interpolation and curve/surface fitting. In
fitting, the function does not necessarily pass through the sample data
points.
The computation of the value Vq is generally based on the data
points in the neighborhood of the query point Xq. There are
numerous approaches to performing interpolation. In MATLAB® interpolation is classified into two categories depending on the
structure of the sample data. The sample data may be ordered in a axis-aligned grid
or they may be scattered. In the case of a gridded distribution of sample points, you
can leverage the organized structure of the data to efficiently find the sample
points in the neighborhood of the query. Interpolation of scattered data on the other
hand requires a triangulation of the data points, and this introduces an additional
level of computation.
The two approaches to interpolation are covered in the following sections:
The Interpolating Gridded Data section covers 1-D interpolation, and the N-D (N ≥ 2) interpolation of sample data in axis-aligned grid format:
The Interpolating Scattered Data section covers the N-D (N ≥ 2) interpolation of scattered data:
