Constructs a potentially nonconvex extension of a spatial object by
performing dilation by `convex + concave`

followed by
erosion by `concave`

. This is equivalent to dilation by `convex`

followed
by closing (dilation + erosion) by `concave`

.

## Usage

```
fm_nonconvex_hull(x, ...)
# S3 method for sfc
fm_nonconvex_hull(
x,
convex = -0.15,
concave = convex,
preserveTopology = TRUE,
dTolerance = NULL,
crs = fm_crs(x),
...
)
fm_extensions(x, convex = -0.15, concave = convex, dTolerance = NULL, ...)
# S3 method for matrix
fm_nonconvex_hull(x, ...)
# S3 method for sf
fm_nonconvex_hull(x, ...)
# S3 method for Spatial
fm_nonconvex_hull(x, ...)
# S3 method for sfg
fm_nonconvex_hull(x, ...)
```

## Arguments

- x
A spatial object

- ...
Arguments passed on to the

`fm_nonconvex_hull()`

sub-methods- convex
numeric vector; How much to extend

- concave
numeric vector; The minimum allowed reentrant curvature. Default equal to

`convex`

- preserveTopology
logical; argument to

`sf::st_simplify()`

- dTolerance
If not zero, controls the

`dTolerance`

argument to`sf::st_simplify()`

. The default is`pmin(convex, concave) / 40`

, chosen to give approximately 4 or more subsegments per circular quadrant.- crs
Options crs object for the resulting polygon

## Value

`fm_nonconvex_hull()`

returns an extended object as an `sfc`

polygon object (regardless of the `x`

class).

`fm_extensions()`

returns a list of `sfc`

objects.

## Details

Morphological dilation by `convex`

, followed by closing by
`concave`

, with minimum concave curvature radius `concave`

. If
the dilated set has no gaps of width between $$2 \textrm{convex} (\sqrt{1+2
\textrm{concave}/\textrm{convex}} - 1)$$
and \(2\textrm{concave}\), then the minimum convex curvature radius is
`convex`

.

The implementation is based on the identity $$\textrm{dilation}(a) \& \textrm{closing}(b) = \textrm{dilation}(a+b) \& \textrm{erosion}(b)$$ where all operations are with respect to disks with the specified radii.

When `convex`

, `concave`

, or `dTolerance`

are negative,
`fm_diameter * abs(...)`

is used instead.

Differs from `sf::st_buffer(x, convex)`

followed by
`sf::st_concave_hull()`

(available from GEOS 3.11)
in how the amount of allowed concavity is controlled.

## Functions

`fm_nonconvex_hull()`

: Basic nonconvex hull method.`fm_extensions()`

: Constructs a potentially nonconvex extension of a spatial object by performing dilation by`convex + concave`

followed by erosion by`concave`

. This is equivalent to dilation by`convex`

followed by closing (dilation + erosion) by`concave`

.

## INLA compatibility

For mesh and curve creation, the `fm_rcdt_2d_inla()`

, `fm_mesh_2d_inla()`

,
and `fm_nonconvex_hull_inla()`

methods will keep the interface syntax used by
`INLA::inla.mesh.create()`

, `INLA::inla.mesh.2d()`

, and
`INLA::inla.nonconvex.hull()`

functions, respectively, whereas the
`fm_rcdt_2d()`

, `fm_mesh_2d()`

, and `fm_nonconvex_hull()`

interfaces may be
different, and potentially change in the future.