TRIANGULATION_ORDER3_CONTOUR
Contour Plots of Triangulated Data

TRIANGULATION_ORDER3_CONTOUR is a MATLAB program which reads datafiles describing a set of nodes, their triangulation, and the value of a scalar quantity at each node, and creates a color contour plot of the scalar.

The program reads three data files:

• a node file, containing X, Y coordinates of points;
• an element file, containing a list of sets of three points making up each triangular element; (if this file does not exist, the program will generate the element data automatically).
• a values file, containing the values of a scalar function U(X,Y) evaluated at each node.

The program automatically displays three plots:

1. An line drawing of the triangulation;
2. A color contour plot with color constant over a triangle.
3. A color contour plot with color linearly interpolated to make a very nice picture.

Usage:

triangulation_order3_contour ( 'prefix' )

• 'prefix'_nodes.txt, lists the node coordinates;
• 'prefix'_elements.txt lists the indices of nodes that form elements (this file is optional, and if not supplied, the information will be generated internally);
• 'prefix'_values.txt contains the value assigned to each node.

Licensing:

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

Related Data and Programs:

DIST_PLOT, a MATLAB program which makes contour plots of the distance function, as defined and used in Persson and Strang's distmesh code;

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

FEM_BASIS_T3_DISPLAY, a MATLAB program which displays a basis function associated with a linear triangle ("T3") mesh.

LEVELS, a MATLAB library which makes a contour plot, choosing the contour levels using random sampling.

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

TRIANGULATION, a MATLAB library which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_CORNER, a MATLAB program which patches triangulations so that no triangle has two sides on the boundary.

TRIANGULATION_DELAUNAY_DISCREPANCY, a MATLAB program which measures the amount by which a triangulation fails the local Delaunay test;

TRIANGULATION_HISTOGRAM, a MATLAB program which computes histograms of data over a triangulation.

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

TRIANGULATION_ORDER3, a directory which describes the format for the node and element files describing an order 3 triangulation.

TRIANGULATION_ORDER6_CONTOUR, a MATLAB program which can display a contour plot of scalar data defined on a triangulation of order 6.

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

TRIANGULATION_QUAD, a MATLAB program which estimates the integral of a function over a triangulated region.

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

TWOD_PLOTC, a MATLAB program which makes a color contour plot of scalar data defined on a 2D finite element mesh.

VECTOR_MAGNITUDE_GRID, 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_order3_contour.m, the routine for creating the contour plot;

Examples and Tests:

CHANNEL is a channel region 3 units wide and 1 unit high. The Stokes flow solver FREE_FEM_STOKES computes the fluid velocity and pressure in the channel. The pressure is a scalar and can be plotted by this routine. Data files you can copy include:

• channel_nodes.txt, a node file;
• channel_elements.txt, an element file;
• channel_values.txt, a value file;
• channel_contours.png, a PNG image of the interpolated contour plot of the data;

ELL is an L-shaped region. Data files you can copy include:

• ell_nodes.txt, a node file;
• ell_elements.txt, an element file;
• ell_values.txt, a value file;
• ell_triangulation.png, a PNG image of the triangulation;
• ell_contours.png, a PNG image of the interpolated contour plot of the data;

ELL2 is the same as ELL, except we do not supply the elements. The program will work just the same, except it will compute triangular elements internally, and write a copy out as a file.

• ell2_nodes.txt, a node file;
• ell2_values.txt, a value file;

LAKE is a simulated lake with an island region. Data files you can copy include:

• lake_nodes.txt, a node file;
• lake_elements.txt, an element file;
• lake_values.txt, a value file;
• lake_triangulation.png, a PNG image of the triangulation;
• lake_contours.png, a PNG image of the interpolated contour plot of the data;

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