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Format Field Descriptions

P and Q
Determines the [P,Q] symmetry group. For a regular {P,Q} tiling, this means we have P-gons, with Q meeting at each vertex.

The choice of this will determine the geometry, depending on the value of (P-2)*(Q-2).

Centering
Controls how the tiling is centered.
  • General (controlled by the Mobius property)
  • Fundamental_Triangle_Vertex1
  • Fundamental_Triangle_Vertex2
  • Fundamental_Triangle_Vertex3
  • Vertex (centers on the generating vertex)
ColoringOption
An integer, which determines some main approaches for coloring.
  • 0: Coloring assigned to polygon types.
  • 1: Edges colored according to where vertex lies in fundamental triangle.
  • 2: Color assigned to tiling and intensity of edges fade.
  • 3: Coloring altered by number of reflections.
  • 4: Used for importing pictures as the background. Not user friendly at all.
Colors
An array of colors. The meaning of these depends on the ColoringOption setting.

The format of a color comes from the DataContractSerializer for the C# System.Drawing.Color class. The easiest way to configure will be with known colors

SphericalModel
For spherical tilings, the following options are possible:
  • Sterographic
  • Gnomonic
  • Azimuthal_Equidistant
  • Azimuthal_EqualArea
  • Equirectangular
  • Mercator
  • Orthographic
  • Sinusoidal
  • PeirceQuincuncial
EuclideanModel
For euclidean tilings, the following options are possible:
  • Isometric
  • Conformal
  • Disk
  • UpperHalfPlane
  • Spiral
  • Loxodromic
HyperbolicModel
For hyperbolic tilings, the following options are possible:
  • Poincare
  • Klein
  • Pseudosphere
  • Hyperboloid
  • Band
  • UpperHalfPlane
  • Orthographic
  • Square
  • InvertedPoincare
  • Joukowsky
  • Ring
  • Azimuthal_Equidistant
  • Azimuthal_EqualArea
  • Schwarz_Christoffel
GeodesicLevels
If > 1, can be used to denote the number of recusive divisions for a "geodesic sphere" or "geodesic saddle".

NOTES!

  • This setting will only apply if P = 3.
  • Not currently supported for Euclidean tilings.