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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")
)

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".

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.

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.