recursive_triangle_mask_surface_helpers: Weighted recursive triangle-mask surface helpers

Description

Convenience helpers that recursively subdivide an equilateral triangle into three corner subtriangles plus one central inverted subtriangle according to a four-slot keep-mask, retain the selected subtriangles at each recursion step, and lift the resulting vertex graph into \(\mathbb{R}^3\). This provides a generic gasket-style triangular family that includes the classic Sierpinski triangle together with bridge and asymmetric variants.

Usage

recursive.triangle.mask.surface.embedding(
  mask = mask.triangle.classic(),
  level = 2,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.75,
  freq_u = 1,
  freq_v = 1,
  x_scale = 1,
  y_scale = 1
)
recursive.triangle.mask.surface.graph(
  mask = mask.triangle.classic(),
  level = 2,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.75,
  freq_u = 1,
  freq_v = 1,
  x_scale = 1,
  y_scale = 1,
  normalize = c("median", "mean", "none")
)

Value

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

numeric matrix with columns x, y, and z.

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

edges: the retained recursive triangle-mask edges,
n: number of vertices,
edge_weights: induced positive edge lengths,
coords_surface: the 3D surface embedding,
coords_param: the canonical 2D triangle coordinates,
weight_scale: the normalization constant applied to the raw edge lengths,
family: always "recursive.triangle.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: Triangle surface family. One of "flat", "saddle", "paraboloid", "ripple", or "folded".
amplitude: Finite deformation amplitude.
freq_u: Positive ripple frequency in the first canonical triangle coordinate. Used only when surface = "ripple".
freq_v: Positive ripple frequency in the second canonical triangle coordinate. Used only when surface = "ripple".
x_scale: Positive horizontal scaling applied to the canonical triangle coordinates.
y_scale: Positive vertical scaling applied to the canonical triangle coordinates.
normalize: Normalization applied to the induced edge lengths. One of "median", "mean", or "none".

Details

The mask entries are interpreted in the order left, right, top, and center. Named masks are reordered automatically to match that convention.