Weighted irregular sphere surface helpers

Convenience helpers that build a sphere from deterministically irregular latitude bands with varying sample counts, stitch adjacent bands into a locally triangulated graph, and then realize that graph in \(\mathbb{R}^3\) using either a standard sphere, an ellipsoid, or a wavy radial modulation.

Usage

irregular.sphere.surface.embedding(
  bands = 6,
  equator_count = 28,
  count_irregularity = 0.2,
  lat_irregularity = 0.35,
  phase_twist = 0.35,
  surface = c("standard", "ellipsoid", "wavy"),
  radius = 1,
  amplitude = 0.2,
  freq_theta = 3,
  freq_lat = 2,
  twist = 0.25
)

irregular.sphere.surface.graph(
  bands = 6,
  equator_count = 28,
  count_irregularity = 0.2,
  lat_irregularity = 0.35,
  phase_twist = 0.35,
  surface = c("standard", "ellipsoid", "wavy"),
  radius = 1,
  amplitude = 0.2,
  freq_theta = 3,
  freq_lat = 2,
  twist = 0.25,
  normalize = c("median", "mean", "none")
)

Arguments

bands

Number of non-pole latitude bands.

equator_count

Approximate number of vertices near the equator.

count_irregularity

Irregularity level for per-band sample counts. Must lie in [0, 1).

lat_irregularity

Irregularity level for latitude-band spacing. Must lie in [0, 1].

phase_twist

Finite angular phase offset used to desynchronize neighboring latitude bands.

surface

Sphere geometry family. One of "standard", "ellipsoid", or "wavy".

radius

Positive baseline radius.

amplitude

Finite deformation amplitude. For "ellipsoid", positive values make the shape oblate and negative values make it prolate.

freq_theta

Positive longitudinal frequency used only when surface = "wavy".

freq_lat

Positive latitudinal frequency used only when surface = "wavy".

twist

Finite longitude twist applied smoothly by latitude.

normalize

Normalization applied to the induced edge lengths. One of "median", "mean", or "none".

Value

irregular.sphere.surface.embedding() returns an n x 3 numeric matrix with columns x, y, and z.

irregular.sphere.surface.graph() returns a list with components:

• edges: the irregular sphere edges,

• n: number of vertices,

• edge_weights: induced positive edge lengths,

• coords_surface: the 3D embedding,

• coords_param: the irregular angular parameter coordinates,

• weight_scale: the normalization constant applied to the raw edge lengths,

• family: always "irregular.sphere",

• surface: the chosen surface name,

• bands: number of non-pole latitude bands,

• band_sizes: sample counts in each latitude band,

• label: a human-readable family label.