SHORELINE2
Identify and Triangulate the Domain where F(X,Y) = C

SHORELINE2 is a MATLAB library which tries to identify and triangulate the approximate 2D domain over which F(X,Y) = C for some user specified function F.

The program begins with a given rectangular domain, within which all the investigation is confined. A set of points is generated within the domain and triangulated. Then the function is evaluated at the points. Triangles are dropped from the triangulation if all 3 vertices have the same sign for F(X,Y)-C. Triangles whose vertices have conflicting sign are saved for further study.

Each triangle is now divided into four subtriangles, using the natural splitting involving the midpoints. The function is evalluated at these midpoints, and all subtriangles with vertices of matching sign are again discarded.

This process may be repeated several times. In general, each step of the process is expected to produce a refined estimate of the region where f(x,y)=0, using about twice as many triangles, each of 1/4 the area of the previous triangulation.

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:

CONTOUR_GRADIENT, a MATLAB program which displays contours and gradient vectors for a function f(x,y).

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

SHORELINE, a MATLAB program which tries to identify and triangulate the 2D domain over which some function f(x,y) is nonnegative.

TOMS626, a FORTRAN77 library which creates a contour plot of data associated with a triangulated set of points; this is ACM TOMS algorithm 626.

TRIANGULATION_ORDER3_CONTOUR, a MATLAB program which makes contour plot of scattered data, or of data defined on an order 3 triangulation.

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

Source Code:

• cull_pure_triangles.m, removes from the triangulation those triangles for which all vertices have the same sign.
• i4col_compare.m, compares two columns of an I4COL;
• i4col_sort_a.m, ascending sorts the columns of an I4COL;
• i4col_swap.m, swaps two columns of an I4COL;
• product_grid.m, samples a rectangle with a product grid.
• refine_size.m, determines the "size" of the refinement of a triangulation.
• refine_triangles.m, computes the refinement of a triangulation.
• shoreline2.m, identifies and triangulates a region for which F(X,Y) is approximately zero.
• sort_heap_external.m, external sorts a list of values into ascending order;
• timestamp.m, prints the current YMDHMS date as a time stamp.
• triangulation_area.m, returns the area of a triangulation.

Examples and Tests:

MYLINE_TEST applies the program to a case in which the function is a straight line.

• myline.m, defines the function f(x,y) = x-3y-2.1.
• myline_test.m, the test code.
• myline_test_output.txt, the output file.
• myline.png, a PNG image.

CAMEL_TEST applies the program to a case in which the function defines a blobby closed curve.

• camel.m, defines the "camel" function.
• camel_test.m, the test code.
• camel_test_output.txt, the output file.
• camel.png, a PNG image.

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