TRIANGLE_GRID
Triangular Grid of Points

TRIANGLE_GRID is a Python library which generates a grid of points over the interior of a triangle in 2D.

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 FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BALL_GRID, a Python library which computes a grid of points over the interior of a ball in 3D.

CIRCLE_ARC_GRID, a Python library which computes a grid of points along a circle or circular arc in 2D.

CUBE_GRID, a Python library which computes a grid of points over the interior of a cube in 3D.

DISK_GRID, a Python library which computes a grid of points over the interior of a disk in 2D.

ELLIPSE_GRID, a Python library which computes a grid of points over the interior of an ellipse in 2D.

ELLIPSOID_GRID, a Python library which computes a grid of points over the interior of an ellipsoid in 3D.

HYPERCUBE_GRID, a Python library which computes a grid of points over the interior of a hypercube in M dimensions.

LINE_GRID, a Python library which computes a grid of points over the interior of a line segment in 1D.

POLYGON_GRID, a Python library which generates a grid of points over the interior of a polygon in 2D.

PYRAMID_GRID, a Python library which computes a grid of points over the interior of the unit pyramid in 3D;

SIMPLEX_GRID, a Python library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.

SPHERE_FIBONACCI_GRID, a Python library which uses a Fibonacci spiral to create a grid of points on the surface of the unit sphere in 3D.

SPHERE_LLQ_GRID, a Python library which uses longitudes and latitudes to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3D.

SPHERE_LLT_GRID, a Python library which uses longitudes and latitudes to create grids of points, lines, and triangles on the surface of the unit sphere in 3D.

SQUARE_GRID, a Python library which computes a grid of points over the interior of a square in 2D.

TETRAHEDRON_GRID, a Python library which computes a grid of points over the interior of a tetrahedron in 3D.

TRIANGLE_INTERPOLATE, a Python library which shows how vertex data can be interpolated at any point in the interior of a triangle.

WEDGE_GRID, a Python library which computes a grid of points over the interior of the unit wedge in 3D.

Source Code:

• r82col_print_part.py, prints part of an R82COL.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8mat_write.py, writes an R8MAT to a file.
• timestamp.py, prints the current YMDHMS date as a time stamp.
• triangle_grid_count.py, counts grid points inside a triangle.
• triangle_grid_display.py, displays grid points inside a triangle.
• triangle_grid_points.py, computes points on a triangular grid.

Examples and Tests:

• triangle_grid_test.py, calls all the tests.
• triangle_grid_test.sh, runs all the tests.
• triangle_grid_test.txt, the output file.
• triangle_grid_points.xy, a grid of points in a triangle.
• triangle_grid_points.png, an image of the points.
• triangle_grid_display.png, a grid of points in a triangle, as a demonstration of triangle_grid_display.

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