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.

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

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

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.

- 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.

- triangle_grid_test.py, calls all the tests.
- triangle_grid_test.sh, runs all the tests.
- triangle_grid_test_output.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.