TRIANGULATION_ORDER6_CONTOUR
Color Contour of Triangulated Data

TRIANGULATION_ORDER6_CONTOUR is a MATLAB function which reads datafiles describing a set of nodes, a triangulation of the nodes into six-node triangles, and a scalar evaluated at the nodes. It produces a plot of the triangulation, and several styles of color contour plots of the scalar

This program has a flaw - MATLAB can easily display linear data, so the program essentially divides each quadratic 6-node triangle into smaller 3-node triangles, and lets MATLAB compute and display a surface which is planar over each triangle. This is only an approximation, and if the "fine scale" quadratic behavior of the solution is of interest, it will not show up using this program! To do so well requires computing the underlying quadratic function at numerous sampling points before constructing and displaying the (now much smaller) planar surfaces that approximate the quadratic surface.

The program reads three data files that form a "finite element model" of a scalar quantity defined over a 2D region:

• nodes.txt, a node file, containing X, Y coordinates of points;
• elements.txt, an element file, containing a list of sets of six points making up each triangular element;
• solution.txt, a solution file, containing the value of a scalar function U(X,Y) evaluated at each node.

The program automatically displays five plots:

1. An image of the 3-node triangles created by discarding the midside nodes of the input triangulation;
2. A color contour plot, using the crude 3-node triangulation, with color constant over a triangle.
3. An image of the finer 3-node triangles created by breaking the 6-node triangles into 4 3-node triangles.
4. A color contour plot, using the finer 3-node triangulation, with color constant over a triangle.
5. A color contour plot, using the finer 3-node triangulation, with color linearly interpolated to make a very nice picture.

Usage:

triangulation_order6_contour

runs the program.

Related Data and Programs:

FEM is a data directory which contains a description and examples of the FEM format.

FEM_BASIS_T6_DISPLAY is a MATLAB program which reads a quadratic triangle mesh and displays any associated basis function.

FEM2D_POISSON generates data that may be plotted by this program. FEM2D_POISSON is available in a FORTRAN90 version, a C++ version and a MATLAB version.

TABLE is a format used for each of the three input data files.

TRIANGULATION is a MATLAB library of routines for carrying out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_MASK is an executable MATLAB program, which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.

TRIANGULATION_ORDER3_CONTOUR is a similar program which handles the case where the triangulation is of order 3.

TRIANGULATION_ORDER6 is a directory which describes the format for the node and element files describing an order 6 triangulation.

TRIANGULATION_ORIENT is an executable MATLAB program that reads data defining a triangulation, makes sure that every triangle has positive orientation, and if not, writes a corrected triangle file.

TRIANGULATION_REFINE is an executable MATLAB program that reads data defining a triangulation, replaces each triangle by four congruent smaller ones, and writes the new triangulation information to a file.

VECTOR_MAGNITUDE_GRID is a MATLAB program which reads node and vector data from a file, computes an interpolatory function, evaluates on a uniform grid of points specified by the user, and displays a contour plot of the vector magnitude.

Source Code:

• triangulation_order6_contour.m, the routine for creating the contour plot;
• timestamp.m, prints the current YMDHMS date as a timestamp;
• triangulation_order6_to_order3.m, converts a 6-node triangulation to a 3-node triangulation.

Examples and Tests:

• triangulation_order6_contour.out, the printed output from a run of the program;
• nodes.txt, a node file created by FEM2D_POISSON;
• elements.txt, an element file created by FEM2D_POISSON;
• solution.txt, a solution file created by FEM2D_POISSON;
• contours.png, a PNG image of the nicest contour plot;

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