Geodesic Dome Design
September 22, 1996
What is DOME?
DOME is a program which calculates the properties of a geodesic dome symmetry
triangle. DOME calculates spherical vertex coordinates, symmetry triangle topological
abundance, and chord factors. DOME supports class I (alternate) and class II (triacon)
breakdowns for Icosahedron, Octahedron and Tetrahedron polyhedron types. DOME also
supports "Buckyball" formations as well as elliptical geodesics.
DOME began as a set of geodesic math test algorithims for use in investigating
properties of generalized geodesic structures. This continues to be the main purpose
of my development of the DOME code. DOME should serve as a basic tool for those interested
in geodesic dome design and modeling. All source code is also included in this package
and is freely modifiable under the conditions of the GNU General Public License.
DOME has been complied using Borland C++ 4.52 and should run on any PC class system.
Dome frequency is limited by the amount of memory available. Full spheres use more
memory so the frequency should be reduced accordingly.
Changes From Previous Release Version 4.2
-Full support for class II spheres!
-Split the POV output into two files. The .POV file contains the scene description
while the dome.inc file contains the geometry. This provides better flexability in
rendering scene changes.
-Defined a wire-frame type for VRML & DXF output.
-Added wire-frame vrml support for buckyballs.
-Placed comments in output files specifying the polyface associated with the data.
This makes editing out certain faces easy.
-DAT file output now displays Axial & Face angles for spherical symmetry triangles.
DOME is run from the DOS command line. The program will terminate with an error
message if there is not enough memory to allocate array space for the coordinate matrix.
If this occurs, re-run DOME and request a smaller subdivision frequency. Only even
frequencies are allowed when using class II.
Usage: dome [-fnnn] [-cn] [-px] [-s or -sb] [-en] [-v] [-w] [-h] [filename.xxx]<BR>
Where: -fnnn is geodesic frequency (default nnn=2)
-cn is class type (n=1 or 2; default n=1)
-px sets the polyhedron type
where x is: i for icosahedron (default)
o for octahedron
t for tetrahedron
-s generate full sphere data (default: symmetry triangle)
-sb generate a buckyball. Must use class I with frequency equal
to a multiple of three.
-en enable elliptical formation (default: n=1 circle)
n=elliptical eccentricity (n > 0.0 and n < 2.0)
-v verbose data display at run-time
-w enable wire-frame VRML or DXF output (default: face data)
-h displays a help screen
filename.xxx is a standard DOS filename
where xxx is: DXF, DAT, WRL, POV or PRN
Examples of Usage
-A 5 frequency, class I, icosahedron sphere in DXF format
(note class I & icosa are the defaults): dome -f5 myfile.dxf
-A 3 frequency buckyball in POV format: dome -f3 -sb myfile.pov
-A 10 frequency, class II, octahedron symmetry triangle in DXF
format: dome -f10 -c2 -po myfile.dxf
DOME currently supports five file formats:
1.) DXF - DXF face data which can be input into most computer aided design packages.
Each polyhedron face is saved on a seperate level if spherical data generation is
requested. DXF data for Buckyballs are saved as LINE data. The default DXF data for
all other structures is 3D POLYFACE data. This can be changed to LINE data with
the -w option. Note that not all applications support DXF line data. In these cases,
use polyface instead. There are also applications that do not like DXF comment groups.
Use and ASCII test editor to remove the lines containing only a "999" and the following
line which indicates which polyface the data references.
2.) DAT - An ASCII report format. Shows only symmetry triangle parameters. This format
displays chord factors, face angles and axial angles. Not available for Buckyballs.
3.) PRN - An ASCII comma delimited format. Contains vertex coordinate and chord
coordinate data. Suitable for parsing into custom routines and spreadsheets. Only data
for the symmetry triangle is saved. Not available for Buckyballs.
4.) POV - POV-ray script file. Generates spheres for vertexia, cylinders for chords
and triangles for faces. Faces are not saved when using the Buckyball option.
The POV script consists of two files. The .POV file contains the scene description
while the dome.inc file contains the dome geometry. Note that DOME references "up"
as the z-axis while POV references the y-axis. The Sky statement in the camera
definition compensates for this.
5.) WRL - VRML file for use with a VRML browser such as Worldview or Live3D.
Only wire-frame output is available with Buckyball option.
DOME allows the creation of elliptical geodesic structures. The -en switch enables
this feature. The "n" parameter is the elliptical eccentricity. This value is simply
the ratio of the ellipse major axis to ellipse minor axis. A circle has an
eccentricity of 1.0.
Dome allows eccentricity values greater than 0.0 but less than 2.0. An eccentricity
less than 1.0 results in an ellipse having a semimajor axis = 1.0 and aligned along
the x-axis. Likewise, an eccentricity greater than results in an ellipse having a
semiminor axis = 1.0 and major axis aligned along the z-axis.
See the Applied Synergetics Homepage for image samples and links
to other Synergetics Web sites. The latest DOME info can be found
DOME is also available via ftp from Kirby Urner's Synergetics on the Web
site at ftp.teleport.com/pub/users/pdx4d/bin/dome46.zip.
DXFtoPOV is a short utility which converts DXF line entities to POV-ray script.
This is useful when using a CAD program to modify a DXF file. The modified DXF
file can then be rendered using POV-ray. See the source code for more implementation
Visit the following sites for freeware that will come in handy using DOME:
1.) http://www.pov.org/ for POVray 3.0 is now available for several different
platforms. Lots of enhancements on the previous version. A 32-bit windows
version is now available. This is a great program!
2.) Try a copy of WCVT2POV V2.6. It can be found at
http://www.europa.com/~keithr/free.htm</A>. This is a pretty good
windows-based format converter/viewer for VRML, DXF, POV and other formats.
3.) Those interested in Tensegrities should download a copy of Gerald de Jong's
Struck program at http://www.xs4all.nl/~gdj/. It is available
in both a windows and Java version. Also try my Struck Utilities which
will convert Struck's RBF file format to VRML, POVray & DXF.
It's at http://www.cris.com/~rjbono/html/utility.html.
4.) Though not freeware, Paint Shop Pro (http://www.jasc.com/) comes in real handy for
manipulating graphics images created by POVray. A shareware version is available.
Note: I can recommend these programs but I cannot support (with the exception
of the Struck Utilities) them or guarantee their availablity.
Several defines have now been added to the DOME & DXFtoPOV source code to allow
porting to UNIX machines.
A Unix/LINUX makefile developed by Chris Fearnley has now been included
to improve g++ compilation.
Source Code Comments
Releases of DOME prior to 4.0 had all the source code in one file.
DOME 4.60 has the source code split across several files:
dome.cpp - Source code for main program loop.
geodesic.hpp - Header file containing variables, structures and class
member function prototypes.
geodesic.cpp - Source code for geodesic class member functions. Most of
the work is done by these routines.
dxfsave.cpp - Geodesic class DXF save routines.
povsave.cpp - Geodesic class POV save routines.
wrlsave.cpp - Geodesic class WRL (VRML) save routines.
dxftopov.cpp - source code for dxf to pov conversion utility
domegcc.mak - GNU make file for DOME and DXFtoPOV
readme.html - This file in HTML format
The next major release of DOME will include:
-Provide Buckyball topological abundance in reports
-Buckyball face data
-Dihedral Face Angles
-INI file input for customizing POV-ray and other settings.
-Enhanced non-spherical support
-Space frame support
-Enhanced VRML Support
Feel free to contact me at firstname.lastname@example.org for suggestions, bug reports or
DOME 4.60, Copyright (C) 1995, 1996 Richard J. Bono
This program is free software; you can redistribute it
and/or modify it under the terms of the GNU General Public
License as published by the Free Software Foundation; either
version 2 of the License, or any later version.
This program is distributed in the hope that it will be
useful, but WITHOUT ANY WARRANTY; without even the implied
warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the GNU General Public License for more
You should have received a copy of the GNU General Public
License along with this program; if not, write to the Free
Software Foundation, Inc., 675 Mass Ave, Cambridge, MA
Please direct inquiries, comments and modifications to:
Richard J. Bono
44 Augusta Rd.
Brownsville, TX 78521
Acknowledgements & References
The main reference used in the creation of this code was:
"Geodesic Math & How to Use It" by Hugh Kenner, 1976,
University of California Press. ISBN 0-520-02924-0;
Library of Congress Catalog Card Number: 74-27292.
Many thanks to Hugh for putting this data in an accessible format.
Also, many thanks to:
-J. F. (Jym) Nystrom for turning me on to Bucky back in the summer of 1984.
-My wife Sonia and my daughter Kathy for their de-finite patience.
-Chris Fearnley for pushing me to release this code, providing uploading
tips, general comments, GNU POV scripts and UNIX/LINUX make files.
-Kirby Urner for introducing me to POV-ray and for providing DOME
with a home in cyberspace.
-R. Buckminster Fuller for changing the way I view Universe.