# Basic fmesher use

suppressPackageStartupMessages(library(fmesher))
set.seed(1234L)

## Mesh construction

domain <- cbind(rnorm(4, sd = 3), rnorm(4))
(mesh2 <- fm_mesh_2d(
boundary = fm_extensions(domain, c(2.5, 5)),
max.edge = c(0.5, 2)
))
#> fm_mesh_2d object:
#>   Manifold:  R2
#>   V / E / T: 880 / 2598 / 1719
#>   Euler char.:   1
#>   Constraints:   39 boundary edges (1 group: 1), 111 interior edges (1 group: 1)
#>   Bounding box: (-11.963110,  8.246925) x (-5.522181, 5.499657)
#>   Basis d.o.f.:  880
plot(mesh2, axes = TRUE)

(mesh1 <- fm_mesh_1d(
c(0, 2, 4, 7, 10),
boundary = "free", # c("neumann", "dirichlet"),
degree = 2
))
#> fm_mesh_1d object:
#>   Manifold:  R1
#>   #{knots}:  5
#>   Interval:  ( 0, 10)
#>   Boundary:  (free, free)
#>   B-spline degree:   2
#>   Basis d.o.f.:  6

## Point lookup and evaluation

pts <- cbind(rnorm(400, sd = 3), rnorm(400))

# Find what triangle each point is in, and it's triangular Barycentric coordinates
bary <- fm_bary(mesh2, loc = pts)
# How many points are outside the mesh?
sum(is.na(bary$t)) #> [1] 2 head(bary$bary)
#>            [,1]      [,2]      [,3]
#> [1,] 0.04720217 0.5813611 0.3714367
#> [2,] 0.13930150 0.7219260 0.1387725
#> [3,] 0.43189448 0.1384910 0.4296145
#> [4,] 0.20127814 0.3716721 0.4270498
#> [5,] 0.21259133 0.3686084 0.4188003
#> [6,] 0.44390951 0.1739205 0.3821700

# Construct an evaluator object
evaluator <- fm_evaluator(mesh2, loc = pts)
sum(!evaluator$proj$ok)
#> [1] 2

# Values for the basis function weights; for ordinary 2d meshes this coincides
# with the resulting values at the vertices, but this is not true for e.g.
# 2nd order B-splines on 1d meshes.
field <- mesh2$loc[, 1] value <- fm_evaluate(evaluator, field = field) sum(abs(pts[, 1] - value), na.rm = TRUE) #> [1] 5.438358e-14 pts1 <- seq(-2, 12, length.out = 1000) # Find what segment, and its interval Barycentric coordinates bary1 <- fm_bary(mesh1, loc = pts1) # Points outside the interval are treated differently depending on the # boundary conditions: sum(is.na(bary1$t))
#> [1] 0