DIST_PLOT
Contour Plots of Distance Function

DIST_PLOT is a MATLAB program which creates a color contour plot of the distance function, as used in Strang and Persson's DISTMESH program.

Usage:

dist_plot ( p, t, @fd )

• p, a list of node coordinates;
• t, a list of node indices forming a triangulation of the nodes;
• @fd, points to a distance function d = fd ( p ) which computes the distance d from the region to any point p.

Related Data and Programs:

DISTMESH, a MATLAB program which is Strang and Persson's code for generating meshes over regions with an associated distance function.

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

TABLE_IO, a MATLAB library which reads and writes files using the TABLE format; these routines are used by DIST_PLOT_DEMO when reading the input files.

TEST_TRIANGULATION, a MATLAB library which defines some test regions for triangulation.

TRIANGULATION_ORDER3, a data directory which discusses order 3 triangulations; The node and triangle files input to DIST_PLOT are an example of such triangulations.

TRIANGULATION_PLOT, a MATLAB program which can make a plot of a triangulation.

TRIANGLE, a C program which can triangulate a region.

Reference:

1. http://math.mit.edu/~persson/mesh Per-Olof Persson's web site.
2. Per-Olof Persson, Gilbert Strang,
   A Simple Mesh Generator in MATLAB,
   SIAM Review,
   Volume 46, Number 2, June 2004, pages 329-345.

Source Code:

• dist_plot.m displays a plot of the distance function over the region.

Examples and Tests:

DIST_PLOT_DEMO displays plots for all the standard problems used in DISTMESH:

• dist_plot_demo.m reads the node and triangle data for each of a set of standard problems for DISTMESH, and displays a plot of the distance function.
• dcircle.m returns the signed distance of one or more points to a circle.
• ddiff.m returns the signed distance of one or more points to a region defined as the set difference of two regions.
• dintersect.m returns the signed distance to a region that is the intersection of two regions.
• dpoly.m returns the signed distance of one or more points to a polygon.
• drectangle.m returns the signed distance of one or more points to a rectangle.
• dsegment.m returns the signed distance of one or more points to a set of line segments.
• dsegment.dll (binary file), a Windows DLL file, returns the signed distance of one or more points to a set of line segments. This version is faster than the M-file.
• dunion.m returns the signed distance to a region that is the union of two regions.
• file_column_count.m counts the number of columns in a table file.
• file_row_count.m counts the number of rows in a table file.
• i4mat_data_read.m reads the data of an I4MAT file.
• i4mat_header_read.m reads the header of an I4MAT file.
• i4mat_read.m reads an I4MAT file.
• i4mat_write.m writes an I4MAT file.
• protate.m rotates a set of points by a given angle.
• pshift.m shifts a set of points by a given increment.
• r8mat_data_read.m reads the data of an R8MAT file.
• r8mat_header_read.m reads the header of an R8MAT file.
• r8mat_write.m writes an R8MAT file.
• s_len_trim.m returns the length of a string to the last nonblank.
• s_word_count.m counts the number of "words" in a string.
• timestamp.m prints the current YMDHMS date as a timestamp.

P01 is the circle:

• p01_nodes.txt the mesh nodes of the problem.
• p01_triangles.txt the mesh triangles of the problem.
• p01_dist.png, a PNG image of a contour plot of the distance function.

P02 is the circle with a hole:

• p02_nodes.txt the mesh nodes of the problem.
• p02_triangles.txt the mesh triangles of the problem.
• p02_dist.png, a PNG image of a contour plot of the distance function.

P03 is the square with a hole:

• p03_nodes.txt the mesh nodes of the problem.
• p03_triangles.txt the mesh triangles of the problem.
• p03_dist.png, a PNG image of a contour plot of the distance function.

P04 is the hexagon with hexagonal hole:

• p04_nodes.txt the mesh nodes of the problem.
• p04_triangles.txt the mesh triangles of the problem.
• p04_dist.png a PNG image of a contour plot of the distance function.

P05 is the horn:

• p05_nodes.txt the mesh nodes of the problem.
• p05_triangles.txt the mesh triangles of the problem.
• p05_dist.png, a PNG image of a contour plot of the distance function.

P06 is the superellipse:

• p06_nodes.txt the mesh nodes of the problem.
• p06_triangles.txt the mesh triangles of the problem.
• p06_dist.png, a PNG image of a contour plot of the distance function.

P07 is the bicycle seat:

• p07_nodes.txt the mesh nodes of the problem.
• p07_triangles.txt the mesh triangles of the problem.
• p07_dist.png, a PNG image of a contour plot of the distance function.

P08 is the holey pie slice:

• p08_nodes.txt the mesh nodes of the problem.
• p08_triangles.txt the mesh triangles of the problem.
• p08_dist.png, a PNG image of a contour plot of the distance function.

P09 is Jeff Borggaard's square with two hexagonal holes:

• p09_nodes.txt the mesh nodes of the problem.
• p09_triangles.txt the mesh triangles of the problem.
• p09_dist.png a PNG image of a contour plot of the distance function.

P10 is the unit square:

• p10_nodes.txt the mesh nodes of the problem.
• p10_triangles.txt the mesh triangles of the problem.
• p10_dist.png a PNG image of a contour plot of the distance function.

P11 is the L-shaped region:

• p11_nodes.txt the mesh nodes of the problem.
• p11_triangles.txt the mesh triangles of the problem.
• p11_dist.png, a PNG image of a contour plot of the distance function.

P12 is the John Shadid's H-shaped region:

• p12_nodes.txt the mesh nodes of the problem.
• p12_triangles.txt the mesh triangles of the problem.
• p12_dist.png a PNG image of a contour plot of the distance function.

P13 is the Sandia fork:

• p13_nodes.txt the mesh nodes of the problem.
• p13_triangles.txt the mesh triangles of the problem.
• p13_dist.png a PNG image of a contour plot of the distance function.

P14 is Marcus Garvie's Lake Alpha, with Beta Island:

• p14_nodes.txt the mesh nodes of the problem.
• p14_triangles.txt the mesh triangles of the problem.
• p14_dist.png, a PNG image of a contour plot of the distance function.

P15 is Sangbum Kim's forward step region:

• p15_nodes.txt the mesh nodes of the problem.
• p15_triangles.txt the mesh triangles of the problem.
• p15_dist.png, a PNG image of a contour plot of the distance function.

P16 is Kevin Pond's elbow:

• p16_nodes.txt the mesh nodes of the problem.
• p16_triangles.txt the mesh triangles of the problem.
• p16_dist.png, a PNG image of a contour plot of the distance function.

P17 is the channel with a Reuleaux triangle obstruction:

• p17_nodes.txt the mesh nodes of the problem.
• p17_triangles.txt the mesh triangles of the problem.
• p17_dist.png, a PNG image of a contour plot of the distance function.

P18 is the dumbbell region:

• p18_nodes.txt the mesh nodes of the problem.
• p18_triangles.txt the mesh triangles of the problem.
• p18_dist.png, a PNG image of a contour plot of the distance function.

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