VECTOR_MAGNITUDE_GRID
Vector Magnitude Contour Plot,
Uniform Grid from Scattered Data

VECTOR_MAGNITUDE_GRID is a MATLAB library which reads vector data defined at possibly scattered points, creates an interpolating function to the data, and evaluates that data on an even grid to produce a contour plot of the vector magnitude.

The program is mainly a preprocessor for MATLAB's contour routine. It reads the (X,Y) coordinates of a set of points from a "node" file, and the corresponding vector values from a "vector" file. It uses MATLAB's griddata facility to create an interpolatory function to the given data. The interpolated function is then sampled on a regular grid, and the data is used to produce a contour plot.

Both the node and vector files are simple "table" files whose format is described online.

This program was written as a quick and convenient way to view finite element data. It can also be used for any situation in which a collection of points and vectors are available.

However, a small "sin" is committed when we use this program on finite element data, since we take only the node locations and vector values, but not the elements. We simply use MATLAB's grid data feature which constructs a cubic spline interpolant to scattered data. This is OK, and probably doesn't distort the data too much, but in fact, we are not actually viewing values of the finite element function, and there is no guarantee that this surrogate function will actually satisfy the boundary conditions or other characteristics of the finite element function.

VECTOR_MAGNITUDE_GRID is based in part on a plotting routine written by Professor Hyung-Chun Lee of Ajou University, Korea.

Usage:

The calling sequence is:

vector_magnitude_grid ( node_file, vector_file, grid_num, contour_num )

where

node_file: the name of the node file, which must be a quoted string;
vector_file: the name of the vector file, which must be a quoted string;
grid_num: the number of grid points to use in one direction. This is actually the number that will be used in the longest dimension of the region. A value of 10 is reasonable to start with, which would result in 100 grid points if your region happens to be a square. The grid points don't show up directly in your plot, but you should use enough so that the function can be properly contoured.
contour_num: the number of contour lines to draw.

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:

DIRECTION_ARROWS, a MATLAB program which plots the velocity direction field.

DIRECTION_ARROWS_SEQUENCE, a MATLAB program which plots the velocity direction fields of many data files with names that are numbered in sequence.

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

VECTOR_PLOT, a FORTRAN90 program which can read an XY file and a UV file and plot the velocity and velocity direction fields.

VECTOR_STREAM_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 streamline plot of the vector field.

VELOCITY_ARROWS, a MATLAB program which plots a velocity vector field.

VELOCITY_ARROWS_GRID, a MATLAB program which reads node and velocity data from a file, and using interpolation is able to display a velocity vector field along any uniform grid of points specified by the user.

VELOCITY_ARROWS_SEQUENCE, a MATLAB program which can process a set of many data files with names that are numbered in sequence.

VELOCITY_ARROWS_SEQUENCE2, a MATLAB program which reads a single XYUV file of nodes and velocities, plots the data and writes it to a PNG file, and then repeats the process for the next file.

Source Code:

vector_magnitude_grid.m, is the program;

Examples and Tests:

BIG_CAVITY is a fluid flow problem involving an irregular mesh of 8,185 nodes in a square region.

nodes.txt, the coordinates of 8185 nodes.
velocity.txt, the velocity at the nodes.
magnitude_10x20.png, a PNG image of the plot of the direction field on a 10x10 grid and 20 contour lines.
magnitude_20x20.png, a PNG image of the plot of the direction field on a 20x20 grid and 20 contour lines.

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