PWL_INTERP_2D_SCATTERED
Piecewise Linear Interpolant to 2D Scattered Data

PWL_INTERP_2D_SCATTERED is a C++ library which produces a piecewise linear interpolant to 2D scattered data, that is, data that is not guaranteed to lie on a regular grid.

This program computes a Delaunay triangulation of the data points, and then constructs an interpolant triangle by triangle. Over a given triangle, the interpolant is the linear function which matches the data already given at the vertices of the triangle.

PWL_INTERP_2D requires the R8LIB library. The test code requires the TEST_INTERP_2D library.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

PWL_INTERP_2D_SCATTERED is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_INTERP_2D, a C++ library which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).

PWL_INTERP_2D, a C++ library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

RBF_INTERP_2D, a C++ library which defines and evaluates radial basis function (RBF) interpolants to scattered 2D data.

SHEPARD_INTERP_2D, a C++ library which defines and evaluates Shepard interpolants to scattered 2D data, based on inverse distance weighting.

TEST_INTERP_2D, a C++ library which defines test problems for interpolation of regular or scattered data z(x,y), depending on a 2D argument.

TRIANGULATION, a C++ library which performs various operations on order 3 (linear) or order 6 (quadratic) triangulations.

TRIANGULATION_ORDER3_CONTOUR, a MATLAB program which makes contour plot of scattered data, or of data defined on an order 3 triangulation.

VANDERMONDE_INTERP_2D, a C++ library which finds a polynomial interpolant to data z(x,y) of a 2D argument by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.

Reference:

1. William Press, Brian Flannery, Saul Teukolsky, William Vetterling,
   Numerical Recipes in FORTRAN: The Art of Scientific Computing,
   Third Edition,
   Cambridge University Press, 2007,
   ISBN13: 978-0-521-88068-8,
   LC: QA297.N866.

Source Code:

• pwl_interp_2d_scattered.cpp, the source code.
• pwl_interp_2d_scattered.hpp, the include file.
• pwl_interp_2d_scattered.sh, BASH commands to compile the source code.

Examples and Tests:

• pwl_interp_2d_scattered_prb.cpp, a sample calling program.
• pwl_interp_2d_scattered_prb.sh, BASH commands to compile and run the sample program.
• pwl_interp_2d_scattered_prb_output.txt, the output file.

List of Routines:

• DIAEDG chooses a diagonal edge.
• I4_SIGN evaluates the sign of an I4.
• I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4VEC_HEAP_D reorders an I4VEC into a descending heap.
• I4VEC_MIN computes the minimum element of an I4VEC.
• I4VEC_SORT_HEAP_A ascending sorts an I4VEC using heap sort.
• I4VEC_SORTED_UNIQUE gets the unique elements in a sorted I4VEC.
• LRLINE determines if a point is left of, right or, or on a directed line.
• PERM_CHECK2 checks that a vector represents a permutation.
• PERM_INVERSE inverts a permutation "in place".
• PWL_INTERP_2D_SCATTERED_VALUE evaluates a 2d interpolant of scattered data
• R8TRIS2 constructs a Delaunay triangulation of 2D vertices.
• SWAPEC swaps diagonal edges until all triangles are Delaunay.
• TRIANGULATION_ORDER3_PRINT prints information about a triangulation.
• TRIANGULATION_SEARCH_DELAUNAY searches a Delaunay triangulation for a point.
• VBEDG determines which boundary edges are visible to a point.

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