PWL_INTERP_2D_SCATTERED
Piecewise Linear Interpolant to 2D Scattered Data

PWL_INTERP_2D_SCATTERED, a MATLAB 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 FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_INTERP_2D, a MATLAB 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 MATLAB library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

pwl_interp_2d_scattered_test

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

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

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

TRIANGULATION, a MATLAB 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 MATLAB 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:

• diaedg.m, chooses a diagonal edge.
• i4_sign.m, returns the sign of an integer.
• i4mat_transpose_print.m, prints the transpose of an I4MAT.
• i4mat_transpose_print_some.m, prints some of the transpose of an I4MAT.
• i4vec_heap_d.m, rearranges an I4VEC into a descending heap.
• i4vec_sort_heap_a.m, ascending heap sorts an I4VEC.
• i4vec_sorted_unique.m, returns the unique elements of a sorted I4VEC.
• lrline.m, determines if a point lies to the left or right of a directed line.
• perm_check2.m, checks a permutation.
• perm_inverse.m, finds the inverse of a permutation.
• pwl_interp_2d_scattered_value.m, evaluates a piecewise linear interpolant to scattered 2D data.
• r8tris2.m, returns the Delaunay triangulation of a set of points in 2D.
• swapec.m, determines which of two diagonals of a quadrilateral should to use in a mesh.
• triangulation_order3_print.m, prints information about an order 3 triangulation;
• triangulation_search_delaunay.m, finds the triangle containing a point, using a Delaunay search;
• vbedg.m, determines which edges are visible to a point.