recursive_tetrahedron_mask_surface_helpers: Weighted recursive tetrahedron-mask surface helpers

Description

Convenience helpers that recursively subdivide a tetrahedron into four corner subtetrahedra according to a four-corner keep-mask, retain the selected subtetrahedra at each recursion step, and deform the resulting simplicial graph inside \(\mathbb{R}^3\). This provides a generic tetrahedral gasket family that includes the classic Sierpinski tetrahedron together with corner-omission variants.

Usage

recursive.tetrahedron.mask.surface.embedding(
  mask = mask.tetrahedron.classic(),
  level = 2,
  surface = c("standard", "squashed", "twisted", "wavy"),
  amplitude = 0.3,
  freq = 2,
  twist = 0.6
)
recursive.tetrahedron.mask.surface.graph(
  mask = mask.tetrahedron.classic(),
  level = 2,
  surface = c("standard", "squashed", "twisted", "wavy"),
  amplitude = 0.3,
  freq = 2,
  twist = 0.6,
  normalize = c("median", "mean", "none")
)

Value

recursive.tetrahedron.mask.surface.embedding() returns an n x 3

numeric matrix with columns x, y, and z.

recursive.tetrahedron.mask.surface.graph() returns a list with components:

edges: the retained recursive tetrahedron-mask edges,
n: number of vertices,
edge_weights: induced positive edge lengths,
coords_surface: the 3D surface embedding,
coords_param: the canonical 3D tetrahedron coordinates,
weight_scale: the normalization constant applied to the raw edge lengths,
family: always "recursive.tetrahedron.mask",
surface: the chosen surface name,
level: the recursion depth,
mask: the logical keep-mask,
label: a human-readable family label.

Arguments

mask: Four-entry logical or numeric keep-mask. Non-zero entries are retained at each recursive step.
level: Recursion depth. May be 0 or larger.
surface: Tetrahedron surface family. One of "standard", "squashed", "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".
normalize: Normalization applied to the induced edge lengths. One of "median", "mean", or "none".

Details

The mask entries are interpreted in the order base_left, base_right, base_back, and apex. Named masks are reordered automatically to match that convention.