TRIANGLE_INTERPOLATE
Interpolation on a Triangle

TRIANGLE_INTERPOLATE is a FORTRAN90 library which demonstrates some simple techniques for interpolating data on a triangle.

In the most common case, the value of a quantity is known at the vertices of a triangle, and a reasonable interpolated value is desired at some point p in the interior of that triangle. This can be done by linear interpolation.

Licensing:

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

Languages:

TRIANGLE_INTERPOLATE 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:

FEM_BASIS, a FORTRAN90 library which can define basis functions for the finite element method (FEM) for any degree in an M-dimensional simplex (1D interval, 2D triangle, 3D tetrahedron, and higher dimensional generalizations.)

GEOMETRY, a FORTRAN90 library which performs geometric calculations in 2, 3 and N dimensional space.

TOMS886, a FORTRAN90 library which defines the Padua points for interpolation in a 2D region, including the rectangle, triangle, and ellipse, by Marco Caliari, Stefano de Marchi, Marco Vianello. This is a version of ACM TOMS algorithm 886.

TRIANGLE_ANALYZE, a FORTRAN90 program which reads a triangle defined in a file, and uses the triangle_properties() library to compute angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.

TRIANGLE_FEKETE_RULE, a FORTRAN90 library which defines Fekete rules for quadrature or interpolation over the interior of a triangle in 2D.

TRIANGLE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a triangle in 2D.

TRIANGLE_HISTOGRAM, a FORTRAN90 program which computes histograms of data on the unit triangle in 2D.

TRIANGLE_PROPERTIES, a FORTRAN90 library which can compute properties, including angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality, of a triangle in 2D.

Source Code:

• triangle_interpolate.f90, the source code.

Examples and Tests:

• triangle_interpolate_test.f90, a sample calling program.
• triangle_interpolate_test.txt, the output file.

List of Routines:

• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_AREA computes the area of a triangle in 2D.
• TRIANGLE_INTERPOLATE_LINEAR interpolates data given on a triangle's vertices.
• UNIFORM_IN_TRIANGLE_MAP1 maps uniform points into a triangle.

You can go up one level to the FORTRAN90 source codes.