irregular_sphere_surface_helpers: Weighted irregular sphere surface helpers

Description

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")
)

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.

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".