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
V can be interpolated to produce a function
of the form
This function can then be used to evaluate a query point
This is a single-valued function; for any query
the domain of
X it will produce a unique value
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
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: