Weighted irregular torus surface helpers

Convenience helpers that build a torus from deterministically irregular major-cycle rings with varying sample counts, stitch adjacent rings into a locally triangulated toroidal graph, and then realize that graph in \(\mathbb{R}^3\) using either a standard, pinched, or wavy tube geometry.

Usage

irregular.torus.surface.embedding(
  major_rings = 8,
  tube_count = 16,
  count_irregularity = 0.2,
  major_irregularity = 0.25,
  phase_twist = 0.35,
  surface = c("standard", "pinched", "wavy"),
  major_radius = 2,
  minor_radius = 0.75,
  amplitude = 0.2,
  freq_major = 2,
  freq_minor = 1,
  twist = 0.25
)

irregular.torus.surface.graph(
  major_rings = 8,
  tube_count = 16,
  count_irregularity = 0.2,
  major_irregularity = 0.25,
  phase_twist = 0.35,
  surface = c("standard", "pinched", "wavy"),
  major_radius = 2,
  minor_radius = 0.75,
  amplitude = 0.2,
  freq_major = 2,
  freq_minor = 1,
  twist = 0.25,
  normalize = c("median", "mean", "none")
)

Arguments

major_rings

Number of cyclic major rings around the torus.

tube_count

Approximate number of vertices around each minor cycle.

count_irregularity

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

major_irregularity

Irregularity level for the major-angle ring spacing. Must lie in [0, 1].

phase_twist

Finite phase offset used to desynchronize neighboring minor cycles.

surface

Torus geometry family. One of "standard", "pinched", or "wavy".

major_radius

Positive distance from the torus center to the center of the tube.

minor_radius

Positive baseline radius of the torus tube.

amplitude

Finite deformation amplitude.

freq_major

Positive angular frequency around the major cycle, used by "wavy" and the periodic twist.

freq_minor

Positive angular frequency around the minor cycle, used by "wavy".

twist

Finite phase twist applied periodically to the minor angle as a function of the major angle.

normalize

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

Value

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

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

• edges: the irregular torus 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.torus",

• surface: the chosen surface name,

• major_rings: number of major-cycle rings,

• ring_sizes: sample counts around each ring,

• label: a human-readable family label.