Weighted irregular torus surface helpers
Source:R/export_examples.R, R/graph_helpers.R
irregular_torus_surface_helpers.RdConvenience 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.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
The coords_surface component is 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.