Geodesic Dome Design
DOME
Version 4.80
October 8. 2002
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 & geodesic parabolic dishes.
Why DOME?
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.
System Requirements
Dome frequency is limited by the amount of memory available.
Changes From Previous Release Version 4.6
-Rewrote several functions into modules. -Added Windows GUI front-end
-Upgraded VRML output to the VRML97 specification
Usage
DOME is run as a console application. 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
-dn enables parabolid and specifies focus location
-rn sets Outer radius of paraboloid.
-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
File Formats
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.
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 enabled browser such as the Cortona plugin
from ParallelGraphics. Only wire-frame output is available with Buckyball option. WinDome supports the VRML97 Specification.
Elliptical Structures
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.
Parabolic Structures
DOME now includes functions which allow the design of geodesic parabolic dishes. Two command line switches have been added to enable parabolics:
-dn where n = the distance from the dish center to the focus.
-rn Where n = the radius of the dish. This defaults to 2 x focus.
The parabolic functions work with:
1.) Class I or Class II geodesics
2.) All supported polyhedron types.
The following restrictions apply to the use of parabolics:
1.) A DXF filename must be included with the parabolic switches. 2.) The -w wireframe option should not be used. 3.) The ratio of focal length to dish diameter (f/d) must be greater than or equal 0.25. 4.) No other output file type aside from the 3DFACE DXF file is supported at this time. 5.) Frequency is based on a spherical formation. Large values of f/d will reduce the number of
faces used in the structure. Compensate by further increasing the frequency.
DOME produces a DXF file containing the dish face data and an ASCII text file named parabolic.txt containing the raw data for each face. The following data is output:
1.) Index data for each triangle vertex (A, B, C see map.gif) 2.) Chord lengths for each triangle side (a, b, c) 3.) Face angles (A, B, C).
This data is given for each polyhedron face. In the case of the class I icosahedron 20 faces will be output. The class II structure will use up to 60 triangles. Many of these faces may not contain data as this is dependent on the truncation used.
The enclosed file map.gif contains a graphical representation one polyhedron face as well as the nomenclature used for each triangle.
The units used for the focus location will determine the units of chord length. If -d6 is used where 6 is the focal length in feet, then the chord lengths will be output in feet as well.
The parabolic.txt file is designed to be read by a spreadsheet application such as Microsoft Excel. When importing this file into a spreadsheet, set the field delimiter to 'tab', the text delimiter to '"' and make sure that the first three columns are read as text fields.
Other Goodies
See the Applied Synergetics Homepage for image samples and links to other Synergetics Web sites. The latest DOME info can be found at http://www.applied-synergetics.com/ashp/html/domes.html
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 comments.
UNIX/Linux Install
Open the tarball and type make to build the dome executable. Change directory to dxftopov and type make to build the dxftopov utility.
Other Platforms
Check the DOME web page for versions which support other platforms including 32-bit Windows.
Source Code Comments
Releases of DOME prior to 4.0 had all the source code in one file. DOME 4.80 has the source code split across several files:
dome.txt - this file
Dome.cpp - Source code for main program loop.
Geodesic.h - 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.
Cartesian.cpp - cartesian & spherical coordinate conversion & data structures
Cartesian.h - header for cartesian.cpp
Chords.cpp - class containing chord data structures
Chords.h - header for chord.cpp
Command.cpp - class implementing input parameter data structures
Command.h - header for command.cpp
Faces.cpp - class containing triangle face data structures
Faces.h - header for faces.cpp
Labels.cpp - class containing vertex label data structures
Labels.h - header for labels.cpp
Points.cpp - class containing vertex position data structures
Points.h - header for points.cpp
ThetaTruncation.cpp - class for collecting truncation data
ThetaTruncation.h - header for ThetaTruncation.cpp
dxftopov.cpp - source code for dxf to pov conversion utility
DOME Updates
This is some of the stuff I'd like to see in future versions of DOME & WinDome
-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
-Graphical Display
Feel free to contact me at rjbono@applied-synergetics.com for suggestions, bug reports or questions.
Copyright Information
DOME 4.80, Copyright (C) 1995 - 2002 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 details.
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 02139, USA.
Please direct inquiries, comments and modifications to:
Richard J. Bono
44 Augusta Rd.
Brownsville, TX 78521
email: rjbono@applied-synergetics.com
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 and my daughters 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.