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Create a Triangular Mesh for SPDE Spatial Models

Source: R/mesh.R, R/sphere.R
tulpa_mesh.Rd

Generates a constrained Delaunay triangulation from point coordinates, optionally with boundary constraints. The resulting mesh can be used directly with tulpa's SPDE spatial fields.

Usage

tulpa_mesh(
  coords,
  data = NULL,
  boundary = NULL,
  max_edge = NULL,
  cutoff = 0,
  extend = 0.1,
  min_angle = NULL,
  max_area = NULL,
  max_steiner = 10000L
)

# S3 method for class 'tulpa_mesh'
print(x, ...)

Arguments

coords

A matrix or data.frame with columns x and y, or a formula like ~ x + y evaluated in data.

data

Optional data.frame for formula evaluation.

boundary

Optional boundary specification: a matrix of boundary vertex coordinates (N x 2), an sf polygon, or NULL for convex hull.

max_edge

Maximum edge length. A single value or a vector of two values c(inner, outer) where inner controls the study area and outer controls the extension region.

cutoff

Minimum distance between mesh vertices. Points closer than this are merged. Default 0 (no merging).

extend

Numeric extension factor beyond the boundary. Default 0.1 (10% of domain diameter). Set to 0 for no extension.

min_angle

Minimum angle (degrees) for Ruppert refinement. If specified, Steiner points are inserted at circumcenters of triangles with angles below this threshold. Theoretical maximum is ~20.7 degrees; values up to 30 usually work. Default NULL (no refinement).

max_area

Maximum triangle area for refinement. Triangles larger than this are refined regardless of angle quality. Default NULL (no area constraint).

max_steiner

Maximum number of Steiner points to insert during Ruppert refinement. Default 10000.

x

A tulpa_mesh object.

...

Additional arguments (ignored).

Value

A tulpa_mesh object with components:

  • vertices: N x 2 matrix of vertex coordinates

  • triangles: M x 3 integer matrix of vertex indices (1-based)

  • edges: K x 2 integer matrix of edge vertex indices (1-based)

  • n_vertices: number of mesh vertices

  • n_triangles: number of triangles

  • n_edges: number of edges

  • n_input_points: number of original input points

The tulpa_mesh object x, returned invisibly.

Examples

# Simple mesh from random points
set.seed(42)
coords <- cbind(runif(50), runif(50))
mesh <- tulpa_mesh(coords)
print(mesh)

# Mesh with Ruppert refinement (min angle 25 degrees)
mesh_refined <- tulpa_mesh(coords, min_angle = 25)