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Weighted Sierpinski triangle surface helpers

Source: R/graph_helpers.R
sierpinski_triangle_surface_helpers.Rd

Convenience helpers that take the canonical recursive embedding of the Sierpinski triangle graph and lift it into \(\mathbb{R}^3\). These helpers are intended for benchmark families where the topology is the usual triangular gasket but the intended metric comes from a curved or folded geometry rather than the flat equilateral reference drawing.

Usage

sierpinski.triangle.surface.embedding(
  level = 2,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.75,
  freq_u = 1,
  freq_v = 1,
  x_scale = 1,
  y_scale = 1
)

sierpinski.triangle.surface.graph(
  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")
)

Arguments

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".

Value

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

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

  • edges: the Sierpinski triangle 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 "sierpinski.triangle",

  • surface: the chosen surface name,

  • level: the recursion depth,

  • label: a human-readable family label.