test_interp
test_interp,
a C++ code which
defines data that may be used to test interpolation algorithms.
The following sets of data are available:

p01_plot.png,
18 data points, 2 dimensions.
This example is due to HansJoerg Wenz.
It is an example of good data, which is dense enough in areas
where the expected curvature of the interpolant is large.
Good results can be expected with almost any reasonable
interpolation method.

p02_plot.png,
18 data points, 2 dimensions. This example is due to ETY Lee of Boeing.
Data near the corners is more dense than in regions of small curvature.
A local interpolation method will produce a more plausible
interpolant than a nonlocal interpolation method, such as
cubic splines.

p03_plot.png,
11 data points, 2 dimensions. This example is due to Fred Fritsch and Ralph Carlson.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparselyplaced data. This can cause an interpolant to overshoot
the data in a way that seems implausible.

p04_plot.png,
8 data points, 2 dimensions. This example is due to Larry Irvine, Samuel Marin and Philip Smith.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparselyplaced data. This can cause an interpolant to overshoot
the data in a way that seems implausible.

p05_plot.png,
9 data points, 2 dimensions. This example is due to Larry Irvine, Samuel Marin and Philip Smith.
This data can cause problems for interpolation methods.
There are sudden changes in direction, and at the same time,
sparselyplaced data. This can cause an interpolant to overshoot
the data in a way that seems implausible.

p06_plot.png,
49 data points, 2 dimensions. The data is due to deBoor and Rice.
The data represents a temperature dependent property of titanium.
The data has been used extensively as an example in spline
approximation with variablyspaced knots.
DeBoor considers two sets of knots:
(595,675,755,835,915,995,1075)
and
(595,725,850,910,975,1040,1075).

p07_plot.png,
4 data points, 2 dimensions. The data is a simple symmetric set of 4 points,
for which it is interesting to develop the Shepard interpolants
for varying values of the exponent p.

p08_plot.png,
12 data points, 2 dimensions. This is equally spaced data for y = x^2,
except for one extra point whose x value is close to another, but whose
y value is not so close. A small disagreement in nearby data can
become a disaster.
The code requires access to a compiled copy of the R8LIB library.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
test_interp is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
DIVDIF,
a C++ code which
includes many routines to construct and evaluate divided difference
interpolants.
hermite_interpolant,
a C++ code which
computes the Hermite interpolant, a polynomial that matches function values
and derivatives.
LAGRANGE_INTERP_1D,
a C++ code which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data, so that p(x(i)) = y(i).
NEAREST_INTERP_1D,
a C++ code which
interpolates a set of data using a piecewise constant interpolant
defined by the nearest neighbor criterion.
NEWTON_INTERP_1D,
a C++ code which
finds a polynomial interpolant to data using Newton divided differences.
PWL_INTERP_1D,
a C++ code which
interpolates a set of data using a piecewise linear function.
R8LIB,
a C++ code which
contains many utility routines using double precision real (R8) arithmetic.
rbf_interp_1d,
a C++ code which
defines and evaluates radial basis function (RBF) interpolants
to 1D data.
SPLINE,
a C++ code which
includes many routines to construct and evaluate spline
interpolants and approximants.
TEST_APPROX,
a C++ code which
defines test problems for approximation,
provided as a set of (x,y) data.
test_interp_test
test_interp_nd,
a C++ code which
defines test problems for interpolation of data z(x),
depending on an Mdimensional argument.
Reference:

Carl DeBoor, John Rice,
Leastsquares cubic spline approximation II  variable knots.
Technical Report CSD TR 21,
Purdue University, Lafayette, Indiana, 1968.

Carl DeBoor,
A Practical Guide to Splines,
Springer, 2001,
ISBN: 0387953663,
LC: QA1.A647.v27.

Fred Fritsch, Ralph Carlson,
Monotone Piecewise Cubic Interpolation,
SIAM Journal on Numerical Analysis,
Volume 17, Number 2, April 1980, pages 238246.

Larry Irvine, Samuel Marin, Philip Smith,
Constrained Interpolation and Smoothing,
Constructive Approximation,
Volume 2, Number 1, December 1986, pages 129151.

ETY Lee,
Choosing Nodes in Parametric Curve Interpolation,
ComputerAided Design,
Volume 21, Number 6, July/August 1989, pages 363370.

HansJoerg Wenz,
Interpolation of Curve Data by Blended Generalized Circles,
Computer Aided Geometric Design,
Volume 13, Number 8, November 1996, pages 673680.
Source Code:
Last revised on 22 April 2020.