irregular_pair_of_pants_surface_helpers: Weighted irregular pair-of-pants surface helpers

Description

Convenience helpers that build a pair-of-pants domain from deterministically irregular horizontal slices, sample each surviving slice interval with varying point counts, and stitch adjacent slices into a locally triangulated surface-with-boundary graph. The resulting irregular planar parameterization can then be lifted into \(\mathbb{R}^3\) using the same planar surface families as the triangulated annulus and irregular annulus helpers.

Usage

irregular.pair.of.pants.surface.embedding(
  slices = 11,
  outer_count = 28,
  outer_radius = 1.1,
  hole_radius = 0.24,
  hole_offset = 0.38,
  hole_height = 0.18,
  count_irregularity = 0.2,
  vertical_irregularity = 0.35,
  phase_twist = 0.35,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.6,
  freq_u = 1,
  freq_v = 1
)
irregular.pair.of.pants.surface.graph(
  slices = 11,
  outer_count = 28,
  outer_radius = 1.1,
  hole_radius = 0.24,
  hole_offset = 0.38,
  hole_height = 0.18,
  count_irregularity = 0.2,
  vertical_irregularity = 0.35,
  phase_twist = 0.35,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.6,
  freq_u = 1,
  freq_v = 1,
  normalize = c("median", "mean", "none")
)

Value

irregular.pair.of.pants.surface.embedding() returns an n x 3

numeric matrix with columns x, y, and z.

irregular.pair.of.pants.surface.graph() returns a list with components:

edges: the irregular pair-of-pants edges,
n: number of vertices,
edge_weights: induced positive edge lengths,
coords_surface: the 3D embedding,
coords_param: the irregular planar pair-of-pants coordinates,
weight_scale: the normalization constant applied to the raw edge lengths,
family: always "irregular.pair.of.pants",
surface: the chosen surface name,
slices: number of horizontal sample slices,
slice_sizes: vertex counts in each slice,
slice_components: number of connected slice intervals in each slice,
label: a human-readable family label.

Arguments

slices: Number of horizontal sample slices through the pair-of-pants domain.
outer_count: Approximate number of vertices across the widest slices.
outer_radius: Positive outer boundary radius.
hole_radius: Positive radius of each interior hole.
hole_offset: Positive horizontal offset of the two hole centers.
hole_height: Shared vertical coordinate of the two hole centers.
count_irregularity: Irregularity level for the per-slice sample counts. Must lie in [0, 1).
vertical_irregularity: Irregularity level for slice spacing. Must lie in [0, 1].
phase_twist: Finite phase offset used to desynchronize neighboring slice samples.
surface: Geometry family used for the 3D lift. One of "flat", "saddle", "paraboloid", "ripple", or "folded".
amplitude: Finite deformation amplitude.
freq_u: Positive ripple frequency in the first planar coordinate. Used only when surface = "ripple".
freq_v: Positive ripple frequency in the second planar coordinate. Used only when surface = "ripple".
normalize: Normalization applied to the induced edge lengths. One of "median", "mean", or "none".