PYRAMID_GRID
Grid of Points Inside a Pyramid in 3D

PYRAMID_GRID is a Python 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 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 grid 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_INTEGRALS, a Python 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 Python library which applies a Monte Carlo method to estimate integrals of a function 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_GRID, a Python library which computes a grid of points over the interior of a triangle in 2D.

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

Source Code:

• pyramid_grid_count.m, count grid points over the interior of an pyramid in 3D.
• pyramid_grid_display.m, display points over the interior of an pyramid in 3D.
• pyramid_grid_points.m, grid points over the interior of an pyramid in 3D.
• r83col_print_part.py, prints part of an R83COL.
• r8mat_write.py, writes an R8MAT to a file.
• timestamp.py, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• pyramid_grid_test.py, calls all the tests.
• pyramid_grid_test.sh, runs all the tests.
• pyramid_grid_test.txt, the output file.
• pyramid_grid_points.xyz, a sample set of grid points written to a file.
• pyramid_grid_points.png, a plot of a sample set of points.
• pyramid_grid_display.png, a demonstration of the output of pyramid_grid_display().

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