grip (version 0.2.0)

triangulated_annulus_surface_helpers: Weighted triangulated annulus surface helpers

Description

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.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")
)

Value

The coords_surface component is 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.

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".

Details

The coords_surface component is the 3D coordinates of the clipped lattice vertices in the same vertex order as edges. 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.

Examples

annulus <- triangulated.annulus.surface.graph(resolution = 6)