Geodesic (Class)

In: Geodesic.rb
Parent: Object

Represents a Geodesic dome/sphere; the object is comprised of an array of Face instances, each specified in counter-clockwise order.

Methods

new  

Constants

SQRT2 = Math.sqrt(2)
SQRT3 = Math.sqrt(3)
TETRA_Q = SQRT2 / 3
TETRA_R = 1.0 / 3
TETRA_S = SQRT2 / SQRT3
TETRA_T = 2 * SQRT2 / 3
GOLDEN_MEAN = (Math.sqrt(5)+1)/2
PRIMITIVES = { :tetrahedron => { :points => { :a => Vector[ -TETRA_S, -TETRA_Q, -TETRA_R ], :b => Vector[ TETRA_S, -TETRA_Q, -TETRA_R ], :c => Vector[ 0, TETRA_T, -TETRA_R ], :d => Vector[ 0, 0, 1 ]

Attributes

faces  [R]  Returns the array of Face instances representing the Geodesic.
radius  [RW]  Gets/sets the radius of the Geodesic, scaling the vertices on every face.

Classes and Modules

Class Geodesic::Face

Public Class methods

new( frequency = 1, primitive = :octahedron, radius = 1 )

Creates a new Geodesic dome/sphere of specified radius about the origin.

frequency:The number of times to subdivide each face of the primitive; a frequency of 0 yields the primitive itself. Defaults to 1.
primitive:The type of primitive to use as a basis for the geodesic. May be one of :tetrahedron, :octahedron, or :icosahedron. Defaults to :octahedron.
radius:An initial radius for the geodesic. Defaults to 1.

The number of faces in the Geodesic is (faces in primitive) * (frequency+1)^2: 

 freq  tetra  octa  icosa
    0      4     8     20
    1     16    32     80
    2     36    72    180
    3     64   128    320
    4    100   200    500
    5    144   288    720
    6    196   392    980
    7    256   512   1280
    8    324   648   1620
    9    400   800   2000
   10    484   968   2420
   11    576  1152   2880
   12    676  1352   3380
   13    784  1568   3920
   14    900  1800   4500
   15   1024  2048   5120
   16   1156  2312   5780
   17   1296  2592   6480
   18   1444  2888   7220
   19   1600  3200   8000
    :     :     :     :

For this reason, you should take care not to specify an overly-large frequency value. The following graphic gives a visual depiction of the frequency value:

.

[Validate]