POLYGON_GRID
Grid Points in a Polygon

POLYGON_GRID is a FORTRAN90 library which generates a grid of points over the interior of a polygon in 2D.

The program relies on a simple idea in which the "vertex centroid" (average of the vertices) is computed, allowing the polygon to be triangulated. Each triangle can then easily be gridded. The collection of triangular grids joins up to form a grid over the polygon, although the spacing of the the grid points will vary from triangle to triangle.

The program really only works properly for convex polygons. If the polygon is not convex, then the vertex centroid need not lie inside the polygon, consequently the grid points may also seem misaligned.

Licensing:

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

Languages:

POLYGON_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 FORTRAN90 library which computes a grid of points over the interior of a ball in 3D.

CIRCLE_ARC_GRID, a FORTRAN90 program which computes points equally spaced along a circular arc;

CUBE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a cube in 3D.

DISK_GRID, a FORTRAN90 library which computes a grid of points over the interior of a disk in 2D.

ELLIPSE_GRID, a FORTRAN90 library which computes a grid of points over the interior of an ellipse in 2D.

ELLIPSOID_GRID, a FORTRAN90 library which computes a grid of points over the interior of an ellipsoid in 3D.

HYPERCUBE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a hypercube in M dimensions.

LINE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a line segment in 1D.

PYRAMID_GRID, a FORTRAN90 library which computes a grid of points over the interior of the unit pyramid in 3D;

SIMPLEX_GRID, a FORTRAN90 library which generates a grid of points over the interior of a simplex in M dimensions.

SPHERE_CUBED_GRID, a FORTRAN90 library which uses the projection of a cube to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3D.

SPHERE_FIBONACCI_GRID, a FORTRAN90 library which uses a Fibonacci spiral to create a grid of points on the surface of the unit sphere in 3D.

SPHERE_GRID, a FORTRAN90 library which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, on the surface of the unit sphere in 3D.

SPHERE_LLQ_GRID, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 library which computes a grid of points over the interior of a square in 2D.

TETRAHEDRON_GRID, a FORTRAN90 library which computes a grid of points over the interior of a tetrahedron in 3D.

TRIANGLE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a triangle in 2D.

WEDGE_GRID, a FORTRAN90 library which computes a grid of points over the interior of the unit wedge in 3D.

Source Code:

• polygon_grid.f90, the source code.

Examples and Tests:

• polygon_grid_test.f90, a sample calling program.
• polygon_grid_test.txt, the output file.

ELL is an L-shaped (non-convex!) polygon for which the program output doesn't look too bad, although the grid is degenerate.

• ell_commands.txt, the gnuplot command file.
• ell_grid.txt, the grid point coordinates.
• ell_vertex.txt information about the polygon vertices and centroid that are used to draw boundary lines.
• ell.png a plot of the grid.
• ell.xy the grid points.

QUAD is a quadrilateral polygon.

• quad_commands.txt, the gnuplot command file.
• quad_grid.txt, the grid point coordinates.
• quad_vertex.txt information about the polygon vertices and centroid that are used to draw boundary lines.
• quad.png a plot of the grid.
• quad.xy the grid points.

TRIANGLE is a triangular polygon.

• triangle_commands.txt, the gnuplot command file.
• triangle_grid.txt, the grid point coordinates.
• triangle_vertex.txt information about the polygon vertices and centroid that are used to draw boundary lines.
• triangle.png a plot of the grid.
• triangle.xy the grid points.

List of Routines:

• GET_UNIT returns a free FORTRAN unit number.
• POLYGON_GRID_COUNT counts the grid points inside a polygon.
• POLYGON_GRID_DISPLAY displays grid points inside a polygon.
• POLYGON_GRID_POINTS computes points on a polygonal grid.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8MAT_WRITE writes an R8MAT file.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.