menger_sponge_surface_helpers: Weighted Menger sponge surface helpers

Description

Convenience wrappers around recursive.cube.mask.surface.*() using the classic \(3 \times 3 \times 3\) Menger-sponge keep-mask. These helpers provide a named cubical 3D benchmark family whose vertices are occupied subcubes and whose edges connect face-adjacent occupied cells.

Usage

menger.sponge.surface.embedding(
  level = 2,
  surface = c("standard", "bulged", "twisted", "wavy"),
  amplitude = 0.2,
  freq = 2,
  twist = 0.6,
  x_scale = 1,
  y_scale = 1,
  z_scale = 1
)
menger.sponge.surface.graph(
  level = 2,
  surface = c("standard", "bulged", "twisted", "wavy"),
  amplitude = 0.2,
  freq = 2,
  twist = 0.6,
  x_scale = 1,
  y_scale = 1,
  z_scale = 1,
  normalize = c("median", "mean", "none")
)

Value

menger.sponge.surface.embedding() returns an n x 3 numeric matrix with columns x, y, and z, where n = 20^level.

menger.sponge.surface.graph() returns the same components as recursive.cube.mask.surface.graph(), with family set to "menger.sponge" and a family-specific class and label.

Arguments

level: Recursion depth. Must be at least 1.
surface: Cube-mask geometry family. One of "standard", "bulged", "twisted", or "wavy".
amplitude: Finite deformation amplitude.
freq: Positive modulation frequency used only when surface = "wavy".
twist: Finite twist strength used only when surface = "twisted".
x_scale: Positive horizontal scaling applied to the canonical cube coordinates.
y_scale: Positive vertical scaling applied to the canonical cube coordinates.
z_scale: Positive depth scaling applied to the canonical cube coordinates.
normalize: Normalization applied to the induced edge lengths. One of "median", "mean", or "none".