## Normalizing
In order to normalize, we need to determine the distance of each vertice (x,y,z) from the center or an origin (x
or more general
To normalize we divide each of x, y and z by the distance:
or more general
which adjusts the point to have distance of 1 to the center - a sphere is a form where all points of the surface have the same distance to its center; so by normalizing the point is spherized or spherical projected. There is far more math to cover in geodesic approaches, but for now I leave it at this and may extend it later more. A bit more math comes when calculating details of the required struts to compose a dome, this follows on the next page then. ## References**NASA Contractor Report: Advanced Structural Geometry Studies, Part I: Polyhedral Subdivision Concepts for Structural Applications**by Joseph D. Clinton (1971)**Geodesic Math**by Joseph D. Clinton, rewrite by**Jay Salsburg****Structural Design Concepts for Future Space Missions**or "Geodesic Design Concepts" for NASA in 1968, by various authors incl. B. Fuller, rewrite by Jay Salsburg**Mother Earth News: Where Domes Come From**(1971)
The next pages go into the details of the geodesic domes variants. Page
**Page 1:**Table of Content, Changes**Page 2:**Introduction, Origin of the Geodesic Dome, Geodesize: Triangulate & Normalize, Procedure & Evolution of a Subdividing Triangle ...**Page 3:**Overview of Variants, Numerical Overview, Amount of Struts vs. Strut Variance, Amount of Struts vs. Strut Types ...**Page 4:**The Icosahedron, 1V/L1 2/3 Icosahedron Dome, 2V/L2 Icosahedron Dome, 3V 4/9 Icosahedron Dome ...**Page 5:**5V 7/15 Icosahedron Dome, 5V 8/15 Icosahedron Dome, 6V Icosahedron Dome, 2V.3V Icosahedron Dome ...**Page 6:**7V 10/21 Icosahedron Dome, 7V 11/21 Icosahedron Dome, 8V Icosahedron Dome, L4 Icosahedron Dome ...**Page 7:**The Octahedron, 1V/L1 Octahedron Dome, 2V/L2 Octahedron Dome, 3V Octahedron Dome**Page 8:**4V Octahedron Dome, L3 Octahedron Dome, L3 1/4 Octahedron Dome, L3 5/8 Octahedron Dome**Page 9:**5V Octahedron Dome, 6V Octahedron Dome, 2V.3V Octahedron Dome, 3V.2V Octahedron Dome**Page 10:**7V Octahedron Dome, 8V Octahedron Dome, L4 Octahedron Dome, L4 7/16 Octahedron Dome, L4 9/16 Octahedron Dome ...**Page 11:**9V Octahedron Dome, 3V.3V Octahedron Dome, 10V Octahedron Dome, 2V.5V Octahedron Dome, 2V.5V Octahedron Dome ...**Page 12:**The Cube, Preparing the Cube, 1V/L1 Cube Dome, 2V/L2 Cube Dome, 3V Cube Dome, 4V Cube Dome, L3 Cube Dome ...**Page 13:**5V Cube Dome, 6V Cube Dome, 2V.3V Cube Dome, 3V.2V Cube Dome, 7V Cube Dome**Page 14:**The Cuboctahedron, Preparing the Cuboctahedron, 1V/L1 Cuboctahedron Dome, 2V/L2 Cuboctahedron Dome ...**Page 15:**5V Cuboctahedron Dome, 6V Cuboctahedron Dome, 2V.3V Cuboctahedron Dome, 3V.2V Cuboctahedron Dome ...**Page 16:**The Truncated Octahedron, Preparing the Truncated Octahedron, 1V/L1 Truncated Octahedron Dome ...**Page 17:**The Rhombicuboctahedron, Preparing the Rhombicuboctahedron, 1V/L1 3/8 Rhombicuboctahedron Dome ...**Page 18:**Building Models, 3V 5/9 Icosahedron Model, 2V Icosahedron Model, 4V Icosahedron Model, 2V/L2 Cuboctahedron Model ...**Page 19:**Real Life Application, Options, Connectors, Separate Functions, Cover, 4/8 Sphere Cover Calculator ...
Creative Commons (CC) BY, SA, NC 2005-2017,
developed, designed and written by
René K. Müller,
Graphics & illustrations made with Inkscape, Tgif, Gimp, PovRay, GD.pm Web-Site powered by FreeBSD & Debian/Linux - 100% Open Source |