Class I Icosahedron Geodesic Sphere

The c1icosa directory contains

• GNU Public License.
• lib.mak: compiles a library of subroutines to calculate Class I icosahedron geodesic spheres.
• genc1.pl: a perl script to generate a C source program to calculate vertices and strut lengths for an icosacap triangle.
• gensph.pl: a perl script for generating a C source program to calculate vertices and strut lengths for a half dome. Below the icosacap triangle, the C program generates two half triangles extending to the equator.
• genmak.pl: a perl script for generating a make file to compile each C program.
• bldvtx.pl: a perl script for reading the output report from the C program to produce a file of strut locations. This perl script feeds the vtx2ppm and cap2ppm programs. See below.
• bldsph.pl: a perl script for reading the output report from the C program to produce a file of strut locations. This perl script feeds the dom2ppm and sph2ppm programs. See below.
• vtx2ppm: a C program to produce a PPM image of the icosacap triangle, edge view.
• cap2ppm: a C program to produce a PPM image of the icosacap dome, front view.
• sph2ppm: a C program to produce a PPM image of a half dome, edge view. In this view one pentagon appears in the front of the half dome, and one pentagon appears on each side.
• sph2ico: a C program to produce a PPM image of a half dome, edge view. In this view one pentagon appears in the front of the half dome, and one pentagon appears on each side. The size of the image is 64 x 64 for creating an icon.
• sph2bg: a C program to produce a PPM background image of a half dome, edge view. In this view one pentagon appears in the front of the half dome, and one pentagon appears on each side. The size of the image is small enough to fit on an HTML page. The color is determined by 3 RGB input parameters. See Wallpaper below.
• dom2ppm: a C program to produce a PPM image of a half dome, front view. In this view two pentagons appear in the front of the dome.
• dom2ico: a C program to produce a PPM image of a half dome, front view. In this view two pentagons appear in the front of the dome. The size of the image is 64 x 64 for creating an icon.
• dom2bg: a C program to produce a PPM background image of a half dome, front view. In this view two pentagons appear in the front of the dome. The size of the image is small enough to fit on an HTML page. The color is determined by 3 RGB input parameters. See Wallpaper below.
• tr2ppm: a C program to produce a PPM image of a truncated half dome, front view. In this view two pentagons appear in the front of the dome. The dome looks like a bucky ball, or a football/soccer ball.
• gcview: an X Windows program to view a compressed PPM file.

Purpose of using perl scripts.

They do not use the most efficient method for calculating a sphere.

You can learn best about geodesic math by studying the C source programs that the perl scripts generate.

Once you understand the structure of the C programs, you will understand the perl scripts more easily.

Scope and limitations

The programs generate spheres with frequencies from 1 to 32. You may generate higher frequency domes by modifying the perl script that generates the C program.

Spheres larger than frequency 8 use trusses or diamond shells for reinforcing their struts and vertices. The programs in this directory do not calculate trusses or diamond shells.

Calculating a sphere

Example:

    calc 3

This example calculates the vertices and strut lengths for a 3 frequency sphere.

Vertex location is based on row and column in a triangle.

First digit is row.
Second digit is column.

The diagram below shows vertex locations on a 2v triangle.

 

                             0,0
                             /\
                           /   \
                         /      \
                       /         \
                 1,0  ------------  1,1
                    / \          / \
                  /    \       /    \
                /       \    /       \
              /          \ /          \
             --------------------------
          2,0            2,1          2,2

 

Vertices in a sphere are defined as phi and theta angles from the center of the sphere (the point of origin). The angle phi is the number of degrees south from the north pole. The angle theta is the number of degrees east of the 0 degree meridian.

The strut length in the calc program is calculated from a radius of 1. In an 3 frequency dome, the calculated strut length ranges around 30% or 40% of the radius length. If the diameter of the dome is 40 feet, the radius is 20 feet (40 / 2). Multiply the original strut length times the calculated radius to give the actual strut length. If the original strut length is 30% of the radius, the actual strut length is 6 feet when the radius is 20 feet.

    D = 40     (Diameter)

    S = .3     (Strut length when R = 1)

    R = D / 2     (Radius)

    L = R * S     (Actual Strut Length)

Calculating a half dome geodesic sphere

Example:

    calcdome 6

This example calculates the vertices and strut lengths for a 6 frequency half dome from the north pole to the equator.

Generating a PPM image of a triangle.

Example:

    c1ppm 3

This example generates a PPM image file for a 3 frequency icosacap triangle.

Generating an icosacap PPM file

Example:

    c1cap 3

This example generates a PPM image file for a 3 frequency icosacap dome.

Half dome PPM front view

Example:

    c1dome 6

This example generates 2 PPM image files for a 6 frequency half dome, front view.

Half dome PPM edge view

Example:

    c1sph 6

This example generates 2 PPM image files for a 6 frequency half dome.

Output Files

The following output files are created for a 6 frequency dome.

• c1 in the file name refers to class 1.
• v6 in the file name refers to frequency 6.

• c1v6.c is the C program generated by Perl.
• c1v6.mak is the make file generated by Perl.
• c1v6 is the executable from the C program.
• c1v6.txt is the output report from the C program.
• c1v6 creates c1v6.txt as standard output.
• The output report contains phi/theta vertex coordinates and strut lengths based on a radius of 1.
• c1v6.vtx is the input to a PPM program.
• 6.ppm.gz is the PPM image file in compressed format.
• 6i.ppm.gz is the PPM image file in compressed format. The size is 64 x 64 pixels for creating an icon.

Truncated Half dome, front view

Example:

    tr2ppm 3 <trunc.3v

The input file is trunc.6v for a 6 frequency truncated dome.

Example:

    tr2ppm 6 <trunc.6v

Truncated Half dome, edge view

Example:

    sph2ppm 3 <trunc.3v

The input file is trunc.6v for a 6 frequency truncated dome.

Example:

    sph2ppm 6 <trunc.6v

Class I Octahedron     Class II Method 3 Icosaahedron

Class II Method 3 Octahedron