occupied_mesh_surface_helpers: Occupied-mesh and perforated-grid helpers

Description

edges.occupied.mesh() builds a finite occupied-grid graph on the retained cells of a rectangular occupancy matrix. The corresponding surface helpers lift those occupied cells into \(\mathbb{R}^3\) using the same "saddle", "paraboloid", and "ripple" families used for regular meshes.

Usage

occupied.mesh.surface.embedding(
  keep,
  surface = c("saddle", "paraboloid", "ripple"),
  amplitude = 0.75,
  freq_u = 1,
  freq_v = 1,
  x_scale = 1,
  y_scale = 1
)
occupied.mesh.surface.graph(
  keep,
  surface = c("saddle", "paraboloid", "ripple"),
  amplitude = 0.75,
  freq_u = 1,
  freq_v = 1,
  x_scale = 1,
  y_scale = 1,
  connectivity = c("orthogonal", "diagonal"),
  normalize = c("median", "mean", "none")
)

Value

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

occupied.mesh.surface.graph() returns a list with components:

edges: the occupied-cell mesh edges,
n: number of vertices,
edge_weights: induced positive edge lengths,
coords_surface: the 3D surface embedding,
coords_param: the 2D parameter coordinates,
weight_scale: the normalization constant applied to the raw edge lengths,
family: always "occupied.mesh",
surface: the chosen surface name,
connectivity: the chosen occupied-mesh connectivity rule,
keep: the logical occupancy matrix,
label: a human-readable family label.

Arguments

keep: Logical or numeric occupancy matrix. Non-zero entries are kept.
surface: Surface family used for the lift. One of "saddle", "paraboloid", or "ripple".
amplitude: Finite numeric amplitude controlling the non-flat displacement.
freq_u: Positive ripple frequency in the horizontal parameter direction. Used only when surface = "ripple".
freq_v: Positive ripple frequency in the vertical parameter direction. Used only when surface = "ripple".
x_scale: Positive horizontal scaling of the parameter domain.
y_scale: Positive vertical scaling of the parameter domain.
connectivity: Mesh neighborhood rule passed to edges.mesh().
normalize: Normalization applied to the induced edge lengths. One of "median", "mean", or "none".