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Weighted torus surface helpers

Source: R/export_examples.R, R/graph_helpers.R
torus_surface_helpers.Rd

Convenience helpers that embed a toroidal grid graph into \(\mathbb{R}^3\) and use the induced Euclidean edge lengths as positive graph weights. These helpers are intended for benchmark families where the graph topology is toroidal but the intended metric comes from a curved or spatially varying 3D realization.

Usage

torus.surface.graph(
  h,
  w = h,
  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

h

Number of wrapped rows. Must be at least 3.

w

Number of wrapped columns. Defaults to h; must be at least 3.

surface

Torus surface 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. The local tube radius must remain strictly smaller than major.radius everywhere.

amplitude

Finite numeric 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

The coords_surface component is an n x 3 numeric matrix with columns x, y, and z.

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

  • edges: the undirected toroidal-grid edges,

  • n: number of vertices,

  • edge_weights: induced positive edge lengths,

  • coords_surface: the 3D surface embedding,

  • coords_param: the 2D unwrapped parameter coordinates,

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

  • family: always "torus",

  • surface: the chosen surface name,

  • label: a human-readable family label.

Details

The coords.surface component contains the 3D coordinates of the embedded toroidal grid. torus.surface.graph() returns a reusable weighted-graph bundle containing the torus edges, induced edge weights, the 3D surface coordinates, and a 2D unwrapped parameterization.

Examples

torus <- torus.surface.graph(4, 6, surface = "pinched")