# pyramid_grid

pyramid_grid, a FORTRAN90 code which generates a grid of points over the interior of a pyramid in 3D.

The pyramid has a square base. As it rises, the square cross section smoothly shrinks to a point. Thus there are five vertices, of which four are on the square base, and one is the apex. There are 8 edges, consisting of the four edges of the square, and an edge joining each base vertex to the apex vertex.

The unit pyramid is the set of points (X,Y,Z) such that:

```       - ( 1 - Z ) <= X <= 1 - Z
- ( 1 - Z ) <= Y <= 1 - Z
0 <= Z <= 1.
```

### Languages:

pyramid_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 code which computes a grid of points over the interior of a ball in 3D.

CIRCLE_ARC_GRID, a FORTRAN90 code which computes a grid of points over the length of a circular arc in 2D;

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

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

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

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

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

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

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

PYRAMID_EXACTNESS, a FORTRAN90 code which investigates the monomial exactness of a quadrature rule over the interior of the unit pyramid in 3D.

PYRAMID_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

PYRAMID_MONTE_CARLO, a FORTRAN90 code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

PYRAMID_RULE, a FORTRAN90 code which computes a quadrature rule over the interior of the unit pyramid in 3D;

SIMPLEX_GRID, a FORTRAN90 code which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.

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

SPHERE_GRID, a FORTRAN90 code 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 code 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 code which uses longitudes and latitudes to create grids of points, lines, and triangles on the surface of the unit sphere in 3D.

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

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

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

### Source Code:

Last revised on 20 August 2020.