TRIANGLE_GRID
Triangular Grid of Points

TRIANGLE_GRID is a MATLAB library which generates a triangular grid of points.

Starting with any 3 points A, B, and C that define a triangle, we can divide each side of the triangle into N subintervals, and create a triangular grid. This defines ((N+1)*(N+2))/2 points that lie on the intersections of grid lines. The arrangement is suggested by this diagram:

              X
             9 X
            8 9 X
           7 8 9 X
          6 7 8 9 X
         5 6 7 8 9 X
        4 5 6 7 8 9 X
       3 4 5 6 7 8 9 X
      2 3 4 5 6 7 8 9 X
     1 2 3 4 5 6 7 8 9 X
    0 1 2 3 4 5 6 7 8 9 X
      

The library includes a routine which allows the user to pick an arbitrary triangle and an arbitrary number of subdivisions. It then returns the triangular gridpoints defined by that choice.

Licensing:

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

Languages:

TRIANGLE_GRID is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BALL_GRID, a MATLAB library which computes grid points that lie inside a 3D ball.

CIRCLE_ARC_GRID, a MATLAB program which computes points equally spaced along a circular arc;

CIRCLE_GRID, a MATLAB library which computes grid points that lie inside a circle.

ELLIPSE_GRID, a MATLAB library which computes grid points that lie inside an ellipse.

ELLIPSOID_GRID, a MATLAB library which computes grid points that lie inside a 3D ellipsoid.

TETRAHEDRON_GRID, a MATLAB library which computes a tetrahedral grid of points.

Source Code:

• r82vec_print_part.m, prints part of an R82VEC.
• r8mat_write.m, writes an R8MAT to a file.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• triangle_grid.m, computes points on a triangular grid.
• triangle_grid_count.m, counts grid points inside a triangle.
• triangle_grid_display.m, displays grid points inside a triangle.

Examples and Tests:

• triangle_grid_test.m, calls all the tests.
• triangle_grid_test_output.txt, the output file.
• triangle_grid_test01.m, sets up a grid of 66 points, generated by subdividing by 10 each side of the (0,0), (1,0), (1/2,sqrt(3)/2) triangle.
• triangle_grid_test01.xy, a grid of 66 points, generated by subdividing by 10 each side of the (0,0), (1,0), (1/2,sqrt(3)/2) triangle.
• triangle_grid_test01.png, an image of the points.
• triangle_grid_test02.m, sets up a grid of 66 points, generated by subdividing by 10 each side of the (0,0), (1,0), (1/2,sqrt(3)/2) triangle.
• triangle_grid_test02.xy, a grid of 5151 points, generated by subdividing by 100 each side of the (0,0), (1,0), (1/2,sqrt(3)/2) triangle.
• triangle_grid_test02.png, a closeup of an image of the points.

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