Grid of Points Inside a Line Segment in 1D

**LINE_GRID**,
a C++ library which
generates a grid of points
over the interior of a line segment in 1D.

The 1D line segment is the set of points X such that:

A <= X <= B

The parameters are:

- N, the number of points;
- A, B, the left and right endpoints;
- C, one of 5 choices for centering the grid.

The centering options allow the user to control the centering of the equally spaced points. This is easiest to illustrate if we assume A = 0 and B = 1. Then, using N = 4, the centering options will produce 4 equally spaced points as follows:

- 1: 0, 1/3, 2/3, 1 (include endpoints)
- 2: 1/5, 2/5, 3/5, 4/5 (do not include endpoints)
- 3: 0, 1/4, 2/4, 3/4 (do not include right endpoint)
- 4: 1/4, 2/4, 3/4, 1 (do not include left endpoint)
- 5: 1/8, 3/8, 5/8, 7/8 (half spacing at the ends)

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

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

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

CIRCLE_ARC_GRID, a C++ program which computes a grid of points over the length of a circular arc in 2D;

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

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

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

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

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

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

PYRAMID_GRID, a C++ library which computes a grid of points over the interior of the unit pyramid in 3D.

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

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

SPHERE_GRID, a C++ 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 C++ 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 C++ 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 C++ library which computes a grid of points over the interior of a square in 2D.

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

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

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

- line_grid.cpp, the source code.
- line_grid.sh, compiles the source code.
- line_grid.hpp, the include file.