irregular_annulus_surface_helpers: Weighted irregular annulus surface helpers

Description

Convenience helpers that build an annulus from deterministically irregular concentric rings with varying sample counts, stitch adjacent rings into a locally triangulated graph, and then optionally lift the resulting irregular planar parameterization into \(\mathbb{R}^3\). This provides a non-lattice annulus family with boundary and nonuniform local valence.

Usage

irregular.annulus.surface.embedding(
  rings = 6,
  outer_count = 28,
  outer_radius = 1,
  inner_radius = 0.45,
  count_irregularity = 0.2,
  radial_irregularity = 0.35,
  phase_twist = 0.35,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.6,
  freq_u = 1,
  freq_v = 1
)
irregular.annulus.surface.graph(
  rings = 6,
  outer_count = 28,
  outer_radius = 1,
  inner_radius = 0.45,
  count_irregularity = 0.2,
  radial_irregularity = 0.35,
  phase_twist = 0.35,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.6,
  freq_u = 1,
  freq_v = 1,
  normalize = c("median", "mean", "none")
)

Value

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

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

edges: the irregular annulus edges,
n: number of vertices,
edge_weights: induced positive edge lengths,
coords_surface: the 3D embedding,
coords_param: the irregular planar annulus coordinates,
weight_scale: the normalization constant applied to the raw edge lengths,
family: always "irregular.annulus",
surface: the chosen surface name,
rings: number of concentric rings,
ring_sizes: sample counts on each ring,
label: a human-readable family label.

Arguments

rings: Number of concentric sample rings, including the inner and outer boundary cycles.
outer_count: Approximate number of vertices on the outer boundary.
outer_radius: Positive outer annulus radius.
inner_radius: Positive inner annulus radius.
count_irregularity: Irregularity level for the per-ring sample counts. Must lie in [0, 1).
radial_irregularity: Irregularity level for within-ring radial perturbations. Must lie in [0, 1].
phase_twist: Finite angular phase offset used to desynchronize neighboring rings.
surface: Geometry family used for the 3D lift. One of "flat", "saddle", "paraboloid", "ripple", or "folded".
amplitude: Finite deformation amplitude.
freq_u: Positive ripple frequency in the first planar coordinate. Used only when surface = "ripple".
freq_v: Positive ripple frequency in the second planar coordinate. Used only when surface = "ripple".
normalize: Normalization applied to the induced edge lengths. One of "median", "mean", or "none".