PYRAMID_GRID
Grid of Points Inside a Pyramid in 3D

PYRAMID_GRID is a C++ library 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.
       

Licensing:

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

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 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 grid 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.

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

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

PYRAMID_EXACTNESS, a C++ program which investigates the monomial exactness of a quadrature rule for the pyramid.

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

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

PYRAMID_RULE, a C++ program which computes a quadrature rule over the interior of the unit pyramid in 3D;

SIMPLEX_GRID, a C++ library which generates a regular grid of points over the interior of an arbitrary 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.

Source Code:

• pyramid_grid.cpp, the source code.
• pyramid_grid.hpp, the include file.

Examples and Tests:

• pyramid_grid_test.cpp, a sample calling program.
• pyramid_grid_test.txt, the output file.

PYRAMID_UNIT is a set of data defining a GNUPLOT image of a grid on a unit pyramid.

• pyramid_unit_commands.txt, a file of commands to be input to gnuplot.
• pyramid_unit_nodes.txt, a file containing the coordinates of the grid points.
• pyramid_unit_vertices.txt, a file containing the coordinates of the pyramid vertices.
• pyramid_unit.png, an image of the grid.

List of Routines:

• PYRAMID_GRID_SIZE sizes a pyramid grid.
• PYRAMID_UNIT_GRID computes grid points in the unit pyramid.
• PYRAMID_UNIT_GRID_PLOT sets up a GNUPLOT plot of a unit pyramid grid.
• PYRAMID_UNIT_VERTICES returns the vertices of the unit pyramid.
• R8_PRINT prints an R8.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.