Irregular rectangle surface helpers — irregular_rectangle_surface

Convenience helpers that keep ordinary rectangular-mesh adjacency but replace the regular parameter grid by a deterministic irregular rectangle. The resulting family stays simply connected and rectangular in topology while breaking the strongest row/column symmetries of the lattice.

Usage

irregular.rectangle.param.coords(
  h,
  w = h,
  x_scale = 1,
  y_scale = 1,
  row_irregularity = 0.2,
  col_irregularity = 0.2,
  row_phase = 0.35,
  col_phase = 0.65,
  interior_warp = 0.08,
  shear = 0,
  min_step_ratio = 0.3
)

irregular.rectangle.surface.embedding(
  h,
  w = h,
  surface = c("flat", "saddle", "paraboloid", "ripple"),
  amplitude = 0.75,
  freq_u = 1,
  freq_v = 1,
  x_scale = 1,
  y_scale = 1,
  row_irregularity = 0.2,
  col_irregularity = 0.2,
  row_phase = 0.35,
  col_phase = 0.65,
  interior_warp = 0.08,
  shear = 0,
  min_step_ratio = 0.3
)

irregular.rectangle.surface.graph(
  h,
  w = h,
  surface = c("flat", "saddle", "paraboloid", "ripple"),
  amplitude = 0.75,
  freq_u = 1,
  freq_v = 1,
  x_scale = 1,
  y_scale = 1,
  row_irregularity = 0.2,
  col_irregularity = 0.2,
  row_phase = 0.35,
  col_phase = 0.65,
  interior_warp = 0.08,
  shear = 0,
  min_step_ratio = 0.3,
  connectivity = c("orthogonal", "diagonal"),
  normalize = c("median", "mean", "none")
)

Arguments

h: Number of rows.
w: Number of columns. Defaults to h.
x_scale: Positive horizontal scaling of the parameter domain.
y_scale: Positive vertical scaling of the parameter domain.
row_irregularity: Irregularity level for the row spacing. Must lie in [0, 1].
col_irregularity: Irregularity level for the column spacing. Must lie in [0, 1].
row_phase: Finite phase shift for the deterministic row-spacing perturbation.
col_phase: Finite phase shift for the deterministic column-spacing perturbation.
interior_warp: Non-negative interior warp strength. Must lie in [0, 1]. The warp vanishes on the boundary.
shear: Finite affine shear applied after the boundary-vanishing warp. Larger values can force a validation error if the mesh cells invert.
min_step_ratio: Positive lower bound for the perturbed row and column interval lengths, expressed relative to the unperturbed interval scale. Must lie in (0, 1].
surface: Surface family used for the lift. One of "flat", "saddle", "paraboloid", or "ripple".
amplitude: Finite numeric amplitude controlling the non-flat displacement.
freq_u: Positive ripple frequency in the horizontal parameter direction. Used only when surface = "ripple".
freq_v: Positive ripple frequency in the vertical parameter direction. Used only when surface = "ripple".
connectivity: Mesh neighborhood rule passed to edges.mesh().
normalize: Normalization applied to the induced edge lengths. One of "median", "mean", or "none".

Value

irregular.rectangle.param.coords() returns an n x 2 numeric matrix with columns u and v.

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

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

edges: the undirected rectangular-mesh edges,
n: number of vertices,
edge_weights: induced positive edge lengths,
coords_surface: the 3D surface embedding,
coords_param: the irregular 2D parameter coordinates,
coords_regular_param: the underlying regular 2D parameter coordinates used to define the boundary-vanishing warp,
row_breaks: per-row parameter coordinates in row order,
col_breaks: per-column parameter coordinates in column order,
weight_scale: the normalization constant applied to the raw edge lengths,
family: always "irregular.rectangle",
surface: the chosen surface name,
connectivity: the chosen mesh connectivity rule,
label: a human-readable family label.

Details

`irregular.rectangle.param.coords()` returns the irregular planar parameter coordinates. `irregular.rectangle.surface.embedding()` lifts those coordinates into \(\mathbb{R}^3\). `irregular.rectangle.surface.graph()` returns a reusable weighted-graph bundle with the induced Euclidean edge lengths.