Skip to contents

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")