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Weighted triangulated annulus surface helpers

Source: R/graph_helpers.R
triangulated_annulus_surface_helpers.Rd

Convenience helpers that triangulate a planar annulus by clipping a regular triangular lattice to the region between two concentric circles. The resulting graph is a triangulated manifold with boundary and a single hole, making it a useful complement to the closed triangulated-polyhedron families.

Usage

triangulated.annulus.surface.embedding(
  resolution = 12,
  outer_radius = 1,
  inner_radius = 0.45,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.6,
  freq_u = 1,
  freq_v = 1
)

triangulated.annulus.surface.graph(
  resolution = 12,
  outer_radius = 1,
  inner_radius = 0.45,
  surface = c("flat", "saddle", "paraboloid", "ripple", "folded"),
  amplitude = 0.6,
  freq_u = 1,
  freq_v = 1,
  normalize = c("median", "mean", "none")
)

Arguments

resolution

Positive lattice-resolution control. Larger values produce finer triangulations.

outer_radius

Positive outer annulus radius.

inner_radius

Positive inner annulus radius. Must be strictly smaller than outer_radius.

surface

Geometry family used for the 3D lift. One of "flat", "saddle", "paraboloid", "ripple", or "folded".

amplitude

Finite deformation amplitude.

freq_u

Positive ripple frequency in the first planar coordinate. Used only when surface = "ripple".

freq_v

Positive ripple frequency in the second planar coordinate. Used only when surface = "ripple".

normalize

Normalization applied to the induced edge lengths. One of "median", "mean", or "none".

Value

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

triangulated.annulus.surface.graph() returns a list with components:

  • edges: the triangulated-annulus edges,

  • n: number of vertices,

  • edge_weights: induced positive edge lengths,

  • coords_surface: the 3D embedding,

  • coords_param: the canonical 2D annulus coordinates,

  • weight_scale: the normalization constant applied to the raw edge lengths,

  • family: always "triangulated.annulus",

  • surface: the chosen surface name,

  • resolution: the lattice-resolution parameter,

  • label: a human-readable family label.

Details

triangulated.annulus.surface.embedding() returns the 3D coordinates of the clipped lattice vertices in the same vertex order as edges.triangulated.annulus(). triangulated.annulus.surface.graph() returns a reusable weighted-graph bundle with the annulus edges, induced edge weights, the 3D embedding, and the 2D annulus parameter coordinates.