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.
TRIANGLE_INTERPOLATE is available in a FORTRAN90 version and a MATLAB version and a Python version.
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.
You can go up one level to the FORTRAN90 source codes.