Refine a mesh

Ruppert-style Delaunay refinement with CGAL's Delaunay_mesher_2, by minimum angle, maximum area, and a sizing field. The mesher is kept on the handle so lari_step() can continue it one point at a time; any edit to the mesh discards it.

Usage

lari_refine(
  m,
  min_angle = NULL,
  max_area = NULL,
  size = NULL,
  max_steiner = Inf,
  min_edge_length = NULL,
  seeds = NULL,
  erase = c("outer", "holes", "hull")
)

Arguments

m

a mesh from lari_new()

min_angle

minimum triangle angle in degrees, NULL for none. Above about 20.7 degrees termination is not guaranteed by theory; the floor keeps it finite.

max_area

maximum triangle area, NULL for none

size

a sizing field giving the local maximum triangle area: a function(x, y) (called with scalars at each triangle centroid), or a grid as list(x, y, z) in graphics::image() convention (x and y are cell centres, z is length(x) by length(y); nearest cell, NA is unbounded). Combined with max_area by taking the smaller bound.

max_steiner

budget of new vertices for this call (Inf for none)

min_edge_length

the edge-length floor; NULL chooses default_min_edge_length() from the current segments and the area bound, taking the smaller of max_area and the finest area the sizing field asks for so a sizing field is honoured rather than capped; 0 never gives up

seeds

optional points (two-column matrix or list with x, y) marking regions NOT to mesh, CGAL style; when given they replace erase

erase

which region is meshed: "outer" (everything inside the outermost constraints, depth > 0), "holes" (odd depth only), or "hull"

Value

the unrefined report as a one-row data frame, invisibly

Details

The refiner never splits a triangle whose shortest edge is below min_edge_length: that floor is what stops refinement cascading into sharp input corners. Whatever could not be refined is reported by lari_counts() (unrefined) and returned here as a data frame.

Examples

x <- c(0, 1, 1, 0); y <- c(0, 0, 1, 1)
m <- lari_new(x, y, 1:4, c(2, 3, 4, 1))
lari_refine(m, max_area = 0.01)
## a sizing field: small triangles near the origin
m2 <- lari_new(x, y, 1:4, c(2, 3, 4, 1))
lari_refine(m2, size = function(x, y) 0.0005 + 0.02 * (x^2 + y^2))
nrow(lari_triangles(m2))
#> [1] 244