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Weighted irregular double-torus surface helpers

Source: R/graph_helpers.R
irregular_double_torus_surface_helpers.Rd

Convenience helpers that build a closed genus-2 surface from a deterministically irregular slice family whose cyclic cross-sections follow a `1 -> 3 -> 1` loop transition between two poles. This gives a non-lattice, point-sampled double-torus graph together with either the canonical 3D embedding or simple bulged, twisted, and wavy deformations of that geometry.

Usage

irregular.double.torus.surface.embedding(
  slices = 11,
  tube_count = 14,
  branch_length = 0.85,
  branch_offset = 0.72,
  tube_radius = 0.28,
  transition_width = 0.42,
  count_irregularity = 0.2,
  axial_irregularity = 0.3,
  phase_twist = 0.35,
  surface = c("standard", "bulged", "twisted", "wavy"),
  amplitude = 0.25,
  freq_x = 2,
  freq_theta = 2,
  twist = 0.6
)

irregular.double.torus.surface.graph(
  slices = 11,
  tube_count = 14,
  branch_length = 0.85,
  branch_offset = 0.72,
  tube_radius = 0.28,
  transition_width = 0.42,
  count_irregularity = 0.2,
  axial_irregularity = 0.3,
  phase_twist = 0.35,
  surface = c("standard", "bulged", "twisted", "wavy"),
  amplitude = 0.25,
  freq_x = 2,
  freq_theta = 2,
  twist = 0.6,
  normalize = c("median", "mean", "none")
)

Arguments

slices

Number of non-pole slices through the double torus.

tube_count

Approximate number of vertices around each tube-like loop.

branch_length

Half-length of the three-loop central region.

branch_offset

Offset of the outer loop centers from the central loop.

tube_radius

Baseline radius of each tube-like loop.

transition_width

Width of the left and right transition regions between the single-loop and three-loop slices.

count_irregularity

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

axial_irregularity

Irregularity level for the slice spacing. Must lie in [0, 1].

phase_twist

Finite phase offset used to desynchronize neighboring cyclic slices.

surface

Double-torus geometry family. One of "standard", "bulged", "twisted", or "wavy".

amplitude

Finite deformation amplitude.

freq_x

Positive modulation frequency along the axial direction. Used only when surface = "wavy".

freq_theta

Positive angular modulation frequency around the local tube direction. Used only when surface = "wavy".

twist

Finite twist strength used only when surface = "twisted".

normalize

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

Value

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

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

  • edges: the irregular double-torus edges,

  • n: number of vertices,

  • edge_weights: induced positive edge lengths,

  • coords_surface: the 3D embedding,

  • coords_param: the canonical 3D double-torus coordinates,

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

  • family: always "irregular.double.torus",

  • surface: the chosen surface name,

  • slices: number of non-pole slices,

  • slice_sizes: vertex counts in each slice,

  • slice_components: number of cyclic components in each slice,

  • label: a human-readable family label.