Type:	Package
Title:	Triangle Meshes and Related Geometry Tools
Version:	0.5.0
Description:	Generate planar and spherical triangle meshes, compute finite element calculations for 1-, 2-, and 3-dimensional flat and curved manifolds with associated basis function spaces, methods for lines and polygons, and transparent handling of coordinate reference systems and coordinate transformation, including 'sf' and 'sp' geometries. The core 'fmesher' library code was originally part of the 'INLA' package, and implements parts of "Triangulations and Applications" by Hjelle and Daehlen (2006) <doi:10.1007/3-540-33261-8>.
Depends:	R (≥ 4.0), methods
Imports:	dplyr, graphics, grDevices, lifecycle, Matrix, Rcpp, rlang, sf, splancs, stats, tibble, utils, withr
Suggests:	geometry, ggplot2, knitr, patchwork, testthat (≥ 3.0.0), terra, tidyterra, rgl, rmarkdown, sp (≥ 1.6-1), gsl
URL:	https://inlabru-org.github.io/fmesher/, https://github.com/inlabru-org/fmesher
BugReports:	https://github.com/inlabru-org/fmesher/issues
License:	MPL-2.0
Copyright:	2010-2025 Finn Lindgren, except src/predicates.cc by Jonathan Richard Shewchuk, 1996
NeedsCompilation:	yes
RoxygenNote:	7.3.2
Encoding:	UTF-8
Config/testthat/edition:	3
Config/testthat/parallel:	true
SystemRequirements:	C++17
LinkingTo:	Rcpp
VignetteBuilder:	knitr
BuildVignettes:	true
Collate:	'RcppExports.R' 'deprecated.R' 'bary.R' 'basis.R' 'bbox.R' 'collect.R' 'components.R' 'print.R' 'crs.R' 'data-fmexample.R' 'diameter.R' 'evaluator.R' 'fem.R' 'fm.R' 'fmesher-package.R' 'fmesher.R' 'ggplot.R' 'integration.R' 'lattice_2d.R' 'lattice_Nd.R' 'list.R' 'local.R' 'manifold.R' 'mapping.R' 'matern.R' 'mesh.R' 'mesh_1d.R' 'mesh_2d.R' 'mesh_3d.R' 'mesh_assessment.R' 'nonconvex_hull.R' 'onload.R' 'plot.R' 'segm.R' 'sf_mesh.R' 'sf_utils.R' 'simplify.R' 'sp_mesh.R' 'split_lines.R' 'tensor.R' 'utils.R'
LazyData:	true
Packaged:	2025-07-07 20:35:17 UTC; flindgre
Author:	Finn Lindgren [aut, cre, cph] (Finn Lindgren wrote the main code), Seaton Andy [ctb] (Andy Seaton constributed features to the sf support), Suen Man Ho [ctb] (Man Ho Suen contributed features and code structure design for the integration methods), Fabian E. Bachl [ctb] (Fabian Bachl co-developed precursors of fm_pixels and fm_split_lines in inlabru)
Maintainer:	Finn Lindgren <finn.lindgren@gmail.com>
Repository:	CRAN
Date/Publication:	2025-07-07 21:20:02 UTC

fmesher: Triangle Meshes and Related Geometry Tools

Description

Generate planar and spherical triangle meshes, compute finite element calculations for 1-, 2-, and 3-dimensional flat and curved manifolds with associated basis function spaces, methods for lines and polygons, and transparent handling of coordinate reference systems and coordinate transformation, including 'sf' and 'sp' geometries. The core 'fmesher' library code was originally part of the 'INLA' package, and implements parts of "Triangulations and Applications" by Hjelle and Daehlen (2006) doi:10.1007/3-540-33261-8.

Author(s)

Maintainer: Finn Lindgren finn.lindgren@gmail.com (ORCID) (Finn Lindgren wrote the main code) [copyright holder]

Other contributors:

• Seaton Andy andy.e.seaton@gmail.com (Andy Seaton constributed features to the sf support) [contributor]

• Suen Man Ho M.H.Suen@sms.ed.ac.uk (Man Ho Suen contributed features and code structure design for the integration methods) [contributor]

• Fabian E. Bachl bachlfab@gmail.com (Fabian Bachl co-developed precursors of fm_pixels and fm_split_lines in inlabru) [contributor]

See Also

Useful links:

• https://inlabru-org.github.io/fmesher/

• https://github.com/inlabru-org/fmesher

• Report bugs at https://github.com/inlabru-org/fmesher/issues

Convert a 3D mesh to a 3D rgl triangulation

Description

Extracts a matrix of coordinates of triangles, suitable for passing to rgl::triangles3d().

Usage

## S3 method for class 'fm_mesh_3d'
as.triangles3d(obj, subset = NULL, ...)

Arguments

Value

A 3-column matrix of coordinates of triangles, suitable for passing to rgl::triangles3d().

Examples

if (requireNamespace("geometry", quietly = TRUE) &&
  requireNamespace("rgl", quietly = TRUE)) {
  (m <- fm_delaunay_3d(matrix(rnorm(30), 10, 3)))
  rgl::open3d()
  rgl::triangles3d(rgl::as.triangles3d(m, "boundary"), col = "blue")
}

Call stack utility functions

Description

Helper functions for displaying call stack information

Usage

fm_caller_name(which = 0L, override = NULL)

fm_call_stack(start = 0L, end = 0L, with_numbers = TRUE, ...)

fm_try_callstack(expr)

Arguments

Value

fm_caller_name returns a string with the the name of a calling function

fm_call_stack returns a character vector

fm_try_callstack If successful, returns (invisibly) the value from the evaluated expression, otherwise an error object with call stack information attached to the error message.

Functions

• fm_call_stack():

• fm_try_callstack(): Inspired by berryFunctions::tryStack

Examples

fun <- function() {
  print(fm_caller_name())
  nm <- fm_caller_name()
  print(nm)
}
fun()

Create a coordinate reference system object

Description

Creates either a CRS object or an inla.CRS object, describing a coordinate reference system

Usage

fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_CRS'
is.na(x)

## S3 method for class 'crs'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_crs'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'Spatial'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_CRS'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'SpatVector'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'SpatRaster'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'sf'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'sfc'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'sfg'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_mesh_2d'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_lattice'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_segm'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_collect'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'matrix'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'CRS'
fm_CRS(x, ..., units = NULL, oblique = NULL)

## Default S3 method:
fm_CRS(
  x,
  oblique = NULL,
  projargs = NULL,
  doCheckCRSArgs = NULL,
  args = NULL,
  SRS_string = NULL,
  ...,
  units = NULL
)

## S3 method for class 'inla.CRS'
is.na(x)

## S3 method for class 'inla.CRS'
fm_CRS(x, ..., units = NULL, oblique = NULL)

Arguments

Details

The first two elements of the oblique vector are the (longitude, latitude) coordinates for the oblique centre point. The third value (orientation) is a counterclockwise rotation angle for an observer looking at the centre point from outside the sphere. The fourth value is the quasi-longitude (orbit angle) for a rotation along the oblique observers equator.

Simple oblique: oblique=c(0, 45)

Polar: oblique=c(0, 90)

Quasi-transversal: oblique=c(0, 0, 90)

Satellite orbit viewpoint: oblique=c(lon0-time*v1, 0, orbitangle, orbit0+time*v2), where lon0 is the longitude at which a satellite orbit crosses the equator at time=0, when the satellite is at an angle orbit0 further along in its orbit. The orbital angle relative to the equatorial plane is orbitangle, and v1 and v2 are the angular velocities of the planet and the satellite, respectively. Note that "forward" from the satellite's point of view is "to the right" in the projection.

When oblique[2] or oblique[3] are non-zero, the resulting projection is only correct for perfect spheres.

Value

Either an sp::CRS object or an inla.CRS object, depending on if the coordinate reference system described by the parameters can be expressed with a pure sp::CRS object or not.

An S3 inla.CRS object is a list, usually (but not necessarily) containing at least one element:

Functions

• is.na(fm_CRS): Check if a fm_CRS has NA crs information and NA obliqueness

• is.na(inla.CRS): Check if a inla.CRS has NA crs information and NA obliqueness

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_crs(), sp::CRS(), fm_crs_wkt, fm_crs_is_identical()

Examples

if (fm_safe_sp()) {
  crs1 <- fm_CRS("longlat_globe")
  crs2 <- fm_CRS("lambert_globe")
  crs3 <- fm_CRS("mollweide_norm")
  crs4 <- fm_CRS("hammer_globe")
  crs5 <- fm_CRS("sphere")
  crs6 <- fm_CRS("globe")
}

Show expanded CRS arguments

Description

Wrappers for sp::CRS and inla.CRS objects to handle the coordinate reference system argument string. These methods should no longer be used with PROJ6/rgdal3; see fm_wkt() and fm_proj4string() for a new approach.

Usage

fm_CRS_as_list(x, ...)

fm_list_as_CRS(x, ...)

fm_CRSargs(x, ...)

fm_list_as_CRSargs(x, ...)

fm_CRSargs_as_list(x, ...)

Arguments

Value

For fm_CRSargs and fm_list_as_CRSargs, a character string with PROJ.4 arguments.

For fm_CRS_as_list and fm_CRSargs_as_list, a list of name/value pairs.

For fm_list_as_CRS, a CRS or inla.CRS object.

For fm_list_as_CRSargs(), a CRS proj4 string for name=value pair list

For fm_CRSargs_as_list(), a list of name=value pairs from CRS proj4string

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_CRS()

Examples

if (fm_safe_sp()) {
  crs0 <- fm_CRS("longlat_norm")
  p4s <- fm_proj4string(crs0)
  lst <- fm_CRSargs_as_list(p4s)
  crs1 <- fm_list_as_CRS(lst)
  lst$a <- 2
  crs2 <- fm_CRS(p4s, args = lst)
  print(fm_proj4string(crs0))
  print(fm_proj4string(crs1))
  print(fm_proj4string(crs2))
}

Calculate the area inside segments

Description

Calculate the (signed) area inside fm_segm boundary objects.

Usage

fm_area(x, ...)

## S3 method for class 'fm_segm'
fm_area(x, ...)

## S3 method for class 'fm_segm_list'
fm_area(x, ...)

Arguments

Convert objects to fm_collect

Description

Convert objects to fm_collect

Usage

fm_as_collect(x, ...)

fm_as_collect_list(x, ...)

## S3 method for class 'fm_collect'
fm_as_collect(x, ...)

Arguments

Value

An fm_collect object

Functions

• fm_as_collect(): Convert an object to fm_collect.

• fm_as_collect_list(): Convert each element of a list

See Also

Other object creation and conversion: fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_as_collect_list(list(fm_collect(list())))

Conversion between sparse matrix types

Description

Conversion between sparse matrix types

Usage

fm_as_dgCMatrix(x)

fm_as_dgTMatrix(x, unique = TRUE, ...)

fm_as_unpackedMatrix(x)

fm_as_fmesher_sparse(x)

## Default S3 method:
fm_as_dgCMatrix(x)

## S3 method for class 'fmesher_sparse'
fm_as_dgCMatrix(x)

## Default S3 method:
fm_as_dgTMatrix(x, unique = TRUE, ...)

## Default S3 method:
fm_as_unpackedMatrix(x)

## S3 method for class 'fmesher_sparse'
fm_as_unpackedMatrix(x)

## S3 method for class 'fmesher_sparse'
fm_as_dgTMatrix(x, unique = TRUE, ...)

Arguments

Value

fm_as_dgCMatrix returns a Matrix::dgCMatrix object.

fm_as_dgTMatrix returns a Matrix::dgTMatrix object.

fm_as_unpackedMatrix returns an object of virtual class Matrix::unpackedMatrix.

fm_as_fmesher_sparse returns an fmesher_sparse object.

Examples

library(Matrix)
str(A <- fm_as_dgCMatrix(matrix(c(1, 2, 0, 0, 0, 3, 4, 0, 5), 3, 3)))
str(fm_as_dgTMatrix(A))
str(fm_as_unpackedMatrix(A))
str(fm_as_fmesher_sparse(A))

Convert objects to fmesher objects

Description

Used for conversion from general objects (usually inla.mesh and other legacy INLA specific classes) to fmesher classes.

Usage

fm_as_fm(x, ...)

## S3 method for class 'NULL'
fm_as_fm(x, ...)

## S3 method for class 'fm_mesh_1d'
fm_as_fm(x, ...)

## S3 method for class 'fm_mesh_2d'
fm_as_fm(x, ...)

## S3 method for class 'fm_mesh_3d'
fm_as_fm(x, ...)

## S3 method for class 'fm_tensor'
fm_as_fm(x, ...)

## S3 method for class 'fm_collect'
fm_as_fm(x, ...)

## S3 method for class 'fm_segm'
fm_as_fm(x, ...)

## S3 method for class 'fm_lattice_Nd'
fm_as_fm(x, ...)

## S3 method for class 'fm_lattice_2d'
fm_as_fm(x, ...)

## S3 method for class 'fm_bbox'
fm_as_fm(x, ...)

## S3 method for class 'crs'
fm_as_fm(x, ...)

## S3 method for class 'CRS'
fm_as_fm(x, ...)

## S3 method for class 'fm_crs'
fm_as_fm(x, ...)

## S3 method for class 'inla.CRS'
fm_as_fm(x, ...)

## S3 method for class 'inla.mesh.1d'
fm_as_fm(x, ...)

## S3 method for class 'inla.mesh'
fm_as_fm(x, ...)

## S3 method for class 'inla.mesh.segment'
fm_as_fm(x, ...)

## S3 method for class 'inla.mesh.lattice'
fm_as_fm(x, ...)

Arguments

Value

An object of some ⁠fm_*⁠ class

See Also

Other object creation and conversion: fm_as_collect(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_as_fm(NULL)

Convert objects to fm_lattice_2d

Description

Convert objects to fm_lattice_2d

Usage

fm_as_lattice_2d(...)

fm_as_lattice_2d_list(x, ...)

## S3 method for class 'fm_lattice_2d'
fm_as_lattice_2d(x, ...)

## S3 method for class 'inla.mesh.lattice'
fm_as_lattice_2d(x, ...)

Arguments

Value

An fm_lattice_2d or fm_lattice_2d_list object

Functions

• fm_as_lattice_2d(): Convert an object to fm_lattice_2d.

• fm_as_lattice_2d_list(): Convert each element of a list

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

str(fm_as_lattice_2d_list(list(fm_lattice_2d(), fm_lattice_2d())))

Convert objects to fm_lattice_Nd

Description

Convert objects to fm_lattice_Nd

Usage

fm_as_lattice_Nd(...)

fm_as_lattice_Nd_list(x, ...)

## S3 method for class 'fm_lattice_Nd'
fm_as_lattice_Nd(x, ...)

Arguments

Value

An fm_lattice_Md or fm_lattice_Nd_list object

Functions

• fm_as_lattice_Nd(): Convert an object to fm_lattice_Nd.

• fm_as_lattice_Nd_list(): Convert each element of a list

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

(fm_as_lattice_Nd_list(list(
  fm_lattice_Nd(list(1:3, 1:2)),
  fm_lattice_Nd(list(1:4))
)))

Convert objects to fm_segm

Description

Convert objects to fm_segm

Usage

fm_as_mesh_1d(x, ...)

fm_as_mesh_1d_list(x, ...)

## S3 method for class 'fm_mesh_1d'
fm_as_mesh_1d(x, ...)

## S3 method for class 'inla.mesh.1d'
fm_as_mesh_1d(x, ...)

Arguments

Value

An fm_mesh_1d or fm_mesh_1d_list object

Functions

• fm_as_mesh_1d(): Convert an object to fm_mesh_1d.

• fm_as_mesh_1d_list(): Convert each element of a list

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_as_mesh_1d_list(list(fm_mesh_1d(1:4)))

Convert objects to fm_mesh_2d

Description

Convert objects to fm_mesh_2d

Usage

fm_as_mesh_2d(x, ...)

fm_as_mesh_2d_list(x, ...)

## S3 method for class 'fm_mesh_2d'
fm_as_mesh_2d(x, ...)

## S3 method for class 'inla.mesh'
fm_as_mesh_2d(x, ...)

## S3 method for class 'fm_mesh_3d'
fm_as_mesh_2d(x, ...)

## S3 method for class 'sfg'
fm_as_mesh_2d(x, ...)

## S3 method for class 'sfc_MULTIPOLYGON'
fm_as_mesh_2d(x, ...)

## S3 method for class 'sfc_POLYGON'
fm_as_mesh_2d(x, ...)

## S3 method for class 'sf'
fm_as_mesh_2d(x, ...)

Arguments

Value

An fm_mesh_2d or fm_mesh_2d_list object

Methods (by class)

• fm_as_mesh_2d(fm_mesh_3d): Construct a 2D mesh of the boundary of a 3D mesh

Functions

• fm_as_mesh_2d(): Convert an object to fm_mesh_2d.

• fm_as_mesh_2d_list(): Convert each element of a list

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_as_mesh_2d_list(list(fm_mesh_2d(cbind(2, 1))))

Convert objects to fm_mesh_3d

Description

Convert objects to fm_mesh_3d

Usage

fm_as_mesh_3d(x, ...)

fm_as_mesh_3d_list(x, ...)

## S3 method for class 'fm_mesh_3d'
fm_as_mesh_3d(x, ...)

Arguments

Value

An fm_mesh_3d or fm_mesh_3d_list object

Functions

• fm_as_mesh_3d(): Convert an object to fm_mesh_3d.

• fm_as_mesh_3d_list(): Convert each element of a list

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

(m <- fm_mesh_3d(
  matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0), 4, 3, byrow = TRUE),
  matrix(c(1, 2, 3, 4), 1, 4, byrow = TRUE)
))
fm_as_mesh_3d_list(list(m))

Convert objects to fm_segm

Description

Convert objects to fm_segm

Usage

fm_as_segm(x, ...)

fm_as_segm_list(x, ...)

## S3 method for class 'fm_segm'
fm_as_segm(x, ...)

## S3 method for class 'inla.mesh.segment'
fm_as_segm(x, ...)

## S3 method for class 'sfg'
fm_as_segm(x, ...)

## S3 method for class 'sfc_POINT'
fm_as_segm(x, reverse = FALSE, grp = NULL, is.bnd = TRUE, ...)

## S3 method for class 'sfc_LINESTRING'
fm_as_segm(x, join = TRUE, grp = NULL, reverse = FALSE, ...)

## S3 method for class 'sfc_MULTILINESTRING'
fm_as_segm(x, join = TRUE, grp = NULL, reverse = FALSE, ...)

## S3 method for class 'sfc_POLYGON'
fm_as_segm(x, join = TRUE, grp = NULL, ...)

## S3 method for class 'sfc_MULTIPOLYGON'
fm_as_segm(x, join = TRUE, grp = NULL, ...)

## S3 method for class 'sfc_GEOMETRY'
fm_as_segm(x, grp = NULL, join = TRUE, ...)

## S3 method for class 'sf'
fm_as_segm(x, ...)

## S3 method for class 'matrix'
fm_as_segm(
  x,
  reverse = FALSE,
  grp = NULL,
  is.bnd = FALSE,
  crs = NULL,
  closed = FALSE,
  ...
)

## S3 method for class 'SpatialPoints'
fm_as_segm(x, reverse = FALSE, grp = NULL, is.bnd = TRUE, closed = FALSE, ...)

## S3 method for class 'SpatialPointsDataFrame'
fm_as_segm(x, ...)

## S3 method for class 'Line'
fm_as_segm(x, reverse = FALSE, grp = NULL, crs = NULL, ...)

## S3 method for class 'Lines'
fm_as_segm(x, join = TRUE, grp = NULL, crs = NULL, ...)

## S3 method for class 'SpatialLines'
fm_as_segm(x, join = TRUE, grp = NULL, ...)

## S3 method for class 'SpatialLinesDataFrame'
fm_as_segm(x, ...)

## S3 method for class 'SpatialPolygons'
fm_as_segm(x, join = TRUE, grp = NULL, ...)

## S3 method for class 'SpatialPolygonsDataFrame'
fm_as_segm(x, ...)

## S3 method for class 'Polygons'
fm_as_segm(x, join = TRUE, crs = NULL, grp = NULL, ...)

## S3 method for class 'Polygon'
fm_as_segm(x, crs = NULL, ...)

Arguments

Value

An fm_segm or fm_segm_list object

Functions

• fm_as_segm(): Convert an object to fm_segm.

• fm_as_segm_list(): Convert each element, making a fm_segm_list object

See Also

c.fm_segm(), c.fm_segm_list(), [.fm_segm_list()

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_as_segm_list(list(
  fm_segm(fmexample$mesh),
  fm_segm(fmexample$mesh, boundary = FALSE)
))

(segm <- fm_segm(fmexample$mesh, boundary = FALSE))
(segm_sfc <- fm_as_sfc(segm))
(fm_as_segm(segm_sfc))

Conversion methods from mesh related objects to sfc

Description

Conversion methods from mesh related objects to sfc

Usage

fm_as_sfc(x, ...)

## S3 method for class 'fm_mesh_2d'
fm_as_sfc(x, ..., format = NULL, multi = FALSE)

## S3 method for class 'fm_segm'
fm_as_sfc(x, ..., multi = FALSE)

## S3 method for class 'fm_segm_list'
fm_as_sfc(x, ...)

## S3 method for class 'sfc'
fm_as_sfc(x, ...)

## S3 method for class 'sf'
fm_as_sfc(x, ...)

Arguments

Value

• fm_as_sfc: An sfc_MULTIPOLYGON/LINESTRING/POINT/GEOMETRYCOLLECTION or sfc_POLYGON/LINESTRING/POINT object

Methods (by class)

• fm_as_sfc(fm_mesh_2d):

• fm_as_sfc(fm_segm):

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_as_sfc(fmexample$mesh)
fm_as_sfc(fmexample$mesh, multi = TRUE)
fm_as_sfc(fmexample$mesh, format = "loc")

# Boundary edge conversion to polygons is supported from version 0.4.0.9002:
fm_as_sfc(fmexample$mesh, format = "bnd")

Convert objects to fm_tensor

Description

Convert objects to fm_tensor

Usage

fm_as_tensor(x, ...)

fm_as_tensor_list(x, ...)

## S3 method for class 'fm_tensor'
fm_as_tensor(x, ...)

Arguments

Value

An fm_tensor object

Functions

• fm_as_tensor(): Convert an object to fm_tensor.

• fm_as_tensor_list(): Convert each element of a list

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_as_tensor_list(list(fm_tensor(list())))

Interactive mesh building and diagnostics

Description

Assess the finite element approximation errors in a mesh for interactive R sessions.

Usage

fm_assess(mesh, spatial.range, alpha = 2, dims = NULL)

Arguments

Value

An sf object with gridded mesh assessment information

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_mesh_2d(), fm_rcdt_2d

Examples

bnd <- fm_segm(cbind(
  c(0, 10, 10, 0, 0),
  c(0, 0, 10, 10, 0)
), is.bnd = TRUE)
mesh <- fm_rcdt_2d_inla(boundary = bnd, max.edge = 1)
out <- fm_assess(mesh, spatial.range = 3, alpha = 2)

Compute barycentric coordinates

Description

Identify knot intervals or triangles and compute barycentric coordinates

Usage

fm_bary(...)

## S3 method for class 'fm_bary'
fm_bary(bary, ..., extra_class = NULL)

## S3 method for class 'list'
fm_bary(bary, ..., extra_class = NULL)

## S3 method for class 'tbl_df'
fm_bary(bary, ..., extra_class = NULL)

## S3 method for class 'fm_mesh_1d'
fm_bary(mesh, loc, method = c("linear", "nearest"), restricted = FALSE, ...)

## S3 method for class 'fm_mesh_2d'
fm_bary(mesh, loc, crs = NULL, ..., max_batch_size = NULL)

## S3 method for class 'fm_mesh_3d'
fm_bary(mesh, loc, ..., max_batch_size = NULL)

## S3 method for class 'fm_lattice_2d'
fm_bary(mesh, loc, crs = NULL, ...)

## S3 method for class 'fm_lattice_Nd'
fm_bary(mesh, loc, ...)

Arguments

Value

A fm_bary object, a tibble with columns index; either

• vector of triangle indices (triangle meshes),

• vector of knot indices (1D meshes, either for edges or individual knots), or

• vector of lower left box indices (2D lattices),

and where, a matrix of barycentric coordinates.

Methods (by class)

• fm_bary(fm_bary): Returns the bary input unchanged

• fm_bary(list): Converts a list bary to fm_bary. In the list elements are unnamed, the names index and where are assumed.

• fm_bary(tbl_df): Converts a tibble::tibble() bary to fm_bary

• fm_bary(fm_mesh_1d): Return an fm_bary object with elements index (edge index vector pointing to the first knot of each edge) and where (barycentric coordinates, 2-column matrices). Use fm_bary_simplex() to obtain the corresponding endpoint knot indices.

  For method = "nearest", index contains the index of the nearest mesh knot, and where is a single-column all-ones matrix.

• fm_bary(fm_mesh_2d): An fm_bary object with columns index (vector of triangle indices) and where (3-column matrix of barycentric coordinates). Points that were not found give NA entries in index and where.

• fm_bary(fm_mesh_3d): An fm_bary object with columns index (vector of triangle indices) and where (4-column matrix of barycentric coordinates). Points that were not found give NA entries in index and where.

• fm_bary(fm_lattice_2d): An fm_bary object with columns index (vector of lattice cell indices) and where (4-column matrix of barycentric coordinates). Points that are outside the lattice are given NA entries in index and where.

• fm_bary(fm_lattice_Nd): An fm_bary object with columns index (vector of lattice cell indices) and where 2^d-column matrix of barycentric coordinates). Points that are outside the lattice are given NA entries in index and where.

See Also

fm_bary_simplex(), fm_bary_loc()

Examples

bary <- fm_bary(fm_mesh_1d(1:4), seq(0, 5, by = 0.5))
bary
str(fm_bary(fmexample$mesh, fmexample$loc_sf))
m <- fm_mesh_3d(
  rbind(
    c(1, 0, 0),
    c(0, 1, 0),
    c(0, 0, 1),
    c(0, 0, 0)
  ),
  matrix(c(1, 2, 3, 4), 1, 4)
)
b <- fm_bary(m, matrix(c(1, 1, 1) / 4, 1, 3))
str(fm_bary(fmexample$mesh, fmexample$loc_sf))

Extract Euclidean Sgeometry from Barycentric coordinates

Description

Extract the Euclidean coordinates for location identified by an fm_bary object. This acts as the inverse of fm_bary().

Usage

fm_bary_loc(mesh, bary = NULL, ..., format = NULL)

## S3 method for class 'fm_mesh_2d'
fm_bary_loc(mesh, bary = NULL, ..., format = NULL)

## S3 method for class 'fm_mesh_3d'
fm_bary_loc(mesh, bary = NULL, ..., format = NULL)

## S3 method for class 'fm_mesh_1d'
fm_bary_loc(mesh, bary = NULL, ..., format = NULL)

## S3 method for class 'fm_lattice_2d'
fm_bary_loc(mesh, bary = NULL, ..., format = NULL)

## S3 method for class 'fm_lattice_Nd'
fm_bary_loc(mesh, bary = NULL, ..., format = NULL)

Arguments

Value

Output format depends on the mesh class.

Methods (by class)

• fm_bary_loc(fm_mesh_2d): Extract points on a triangle mesh. Implemented formats are "matrix" (default) and "sf".

• fm_bary_loc(fm_mesh_3d): Extract points on a tetrahedron mesh. Implemented format is "matrix" (default).

• fm_bary_loc(fm_mesh_1d): Extract points on a 1D mesh. Implemented formats are "numeric" (default).

• fm_bary_loc(fm_lattice_2d): Extract points on a 2D lattice. Implemented formats are "matrix" (default) and "sf".

• fm_bary_loc(fm_lattice_Nd): Extract points on a ND lattice.

See Also

fm_bary(), fm_bary_simplex()

Examples

head(fm_bary_loc(fmexample$mesh))
bary <- fm_bary(fmexample$mesh, fmexample$loc_sf)
fm_bary_loc(fmexample$mesh, bary, format = "matrix")
fm_bary_loc(fmexample$mesh, bary, format = "sf")
(m <- fm_mesh_3d(
  matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0), 4, 3, byrow = TRUE),
  matrix(c(1, 2, 3, 4), 1, 4, byrow = TRUE)
))
(bary <- fm_bary(m, rbind(
  cbind(0.1, 0.2, 0.3),
  cbind(-0.1, 0.2, 0.3)
)))
fm_bary_loc(m, bary)
mesh1 <- fm_mesh_1d(1:4)
fm_bary_loc(mesh1)
(bary1 <- fm_bary(mesh1, seq(0, 5, by = 0.5)))
fm_bary_loc(mesh1, bary1)
(bary1 <- fm_bary(mesh1, seq(0, 5, by = 0.5), restricted = TRUE))
fm_bary_loc(mesh1, bary1)
fm_basis(mesh1, bary1)
(bary1 <- fm_bary(mesh1, bary1, method = "nearest"))
fm_bary_loc(mesh1, bary1)
fm_basis(mesh1, bary1)
(bary1 <- fm_bary(mesh1, bary1, method = "linear"))
fm_bary_loc(mesh1, bary1)
fm_basis(mesh1, bary1)
m <- fm_lattice_2d(x = 1:3, y = 1:4)
head(fm_bary_loc(m))
(bary <- fm_bary(m, cbind(1.5, 3.2)))
fm_bary_loc(m, bary, format = "matrix")
fm_bary_loc(m, bary, format = "sf")
m <- fm_lattice_Nd(list(x = 1:3, y = 1:4, z = 1:2))
head(fm_bary_loc(m))
(bary <- fm_bary(m, cbind(1.5, 3.2, 1.5)))
fm_bary_loc(m, bary)

Extract Simplex information for Barycentric coordinates

Description

Extract the simplex vertex information for a combination of a mesh and fm_bary coordinates.

Usage

fm_bary_simplex(mesh, bary = NULL, ...)

## S3 method for class 'fm_mesh_2d'
fm_bary_simplex(mesh, bary = NULL, ...)

## S3 method for class 'fm_mesh_3d'
fm_bary_simplex(mesh, bary = NULL, ...)

## S3 method for class 'fm_mesh_1d'
fm_bary_simplex(mesh, bary = NULL, ...)

## S3 method for class 'fm_lattice_2d'
fm_bary_simplex(mesh, bary = NULL, ...)

## S3 method for class 'fm_lattice_Nd'
fm_bary_simplex(mesh, bary = NULL, ...)

Arguments

Value

A matrix of vertex indices, one row per point in bary.

Methods (by class)

• fm_bary_simplex(fm_mesh_2d): Extract the triangle vertex indices for a 2D mesh

• fm_bary_simplex(fm_mesh_3d): Extract the tetrahedron vertex indices for a 3D mesh

• fm_bary_simplex(fm_mesh_1d): Extract the edge vertex indices for a 1D mesh

• fm_bary_simplex(fm_lattice_2d): Extract the cell vertex indices for a 2D lattice

• fm_bary_simplex(fm_lattice_Nd): Extract the cell vertex indices for a ND lattice

See Also

fm_bary(), fm_bary_loc()

Examples

bary <- fm_bary(fmexample$mesh, fmexample$loc_sf)
fm_bary_simplex(fmexample$mesh, bary)
(m <- fm_mesh_3d(
  matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0), 4, 3, byrow = TRUE),
  matrix(c(1, 2, 3, 4), 1, 4, byrow = TRUE)
))
(bary <- fm_bary(m, rbind(
  cbind(0.1, 0.2, 0.3),
  cbind(-0.1, 0.2, 0.3)
)))
fm_bary_simplex(m, bary)
mesh1 <- fm_mesh_1d(1:4)
(bary1 <- fm_bary(mesh1, seq(0, 5, by = 0.5)))
(bary1 <- fm_bary(mesh1, seq(0, 5, by = 0.5), restricted = TRUE))
fm_bary_simplex(mesh1, bary1)
m <- fm_lattice_2d(x = 1:3, y = 1:4)
bary <- fm_bary(m, cbind(1.5, 3.2))
fm_bary_simplex(m, bary)
m <- fm_lattice_Nd(list(x = 1:3, y = 1:4, z = 1:2))
(bary <- fm_bary(m, cbind(1.5, 3.2, 1.5)))
(fm_bary_simplex(m, bary))
fm_bary_loc(m, bary)

Compute mapping matrix between mesh function space and points

Description

Computes the basis mapping matrix between a function space on a mesh, and locations.

Usage

fm_basis(x, ..., full = FALSE)

## Default S3 method:
fm_basis(x, ..., full = FALSE)

## S3 method for class 'fm_mesh_1d'
fm_basis(x, loc, weights = NULL, derivatives = NULL, ..., full = FALSE)

## S3 method for class 'fm_mesh_2d'
fm_basis(x, loc, weights = NULL, derivatives = NULL, ..., full = FALSE)

## S3 method for class 'fm_mesh_3d'
fm_basis(x, loc, weights = NULL, ..., full = FALSE)

## S3 method for class 'fm_lattice_2d'
fm_basis(x, loc, weights = NULL, ..., full = FALSE)

## S3 method for class 'fm_lattice_Nd'
fm_basis(x, loc, weights = NULL, ..., full = FALSE)

## S3 method for class 'fm_tensor'
fm_basis(x, loc, weights = NULL, ..., full = FALSE)

## S3 method for class 'fm_collect'
fm_basis(x, loc, weights = NULL, ..., full = FALSE)

## S3 method for class 'matrix'
fm_basis(x, ok = NULL, weights = NULL, ..., full = FALSE)

## S3 method for class 'Matrix'
fm_basis(x, ok = NULL, weights = NULL, ..., full = FALSE)

## S3 method for class 'list'
fm_basis(x, weights = NULL, ..., full = FALSE)

## S3 method for class 'fm_basis'
fm_basis(x, ..., full = FALSE)

## S3 method for class 'fm_evaluator'
fm_basis(x, ..., full = FALSE)

Arguments

Value

A sparseMatrix object (if full = FALSE), or a fm_basis object (if full = TRUE or isTRUE(derivatives)). The fm_basis object contains at least the projection matrix A and logical vector ok; If x_j denotes the latent basis coefficient for basis function j, the field is defined as ⁠u(loc_i)=sum_j A_ij x_j⁠ for all i where ok[i] is TRUE, and u(loc_i)=0.0 where ok[i] is FALSE.

Methods (by class)

• fm_basis(fm_mesh_1d): If derivatives=TRUE, the fm_basis object contains additional derivative weight matrices, d1A and d2A, ⁠du/dx(loc_i)=sum_j dx_ij w_i⁠.

• fm_basis(fm_mesh_2d): If derivatives=TRUE, additional derivative weight matrices are included in the full=TRUE output: Derivative weight matrices dx, dy, dz; ⁠du/dx(loc_i)=sum_j dx_ij w_i⁠, etc.

• fm_basis(fm_mesh_3d): fm_mesh_3d basis functions.

• fm_basis(fm_lattice_2d): fm_lattice_2d bilinear basis functions.

• fm_basis(fm_lattice_Nd): fm_lattice_Nd multilinear basis functions.

• fm_basis(fm_tensor): Evaluates a basis matrix for a fm_tensor function space.

• fm_basis(fm_collect): Evaluates a basis matrix for a fm_collect function space. The loc argument must be a list or tibble with elements loc (the locations) and index (the indices into the function space collection).

• fm_basis(matrix): Creates a new fm_basis object with elements A and ok, from a pre-evaluated basis matrix, including optional additional elements in the ... arguments. If a ok is NULL, it is inferred as rep(TRUE, NROW(x)), indicating that all rows correspond to successful basis evaluations. If full = FALSE, returns the matrix unchanged.

• fm_basis(Matrix): Creates a new fm_basis object with elements A and ok, from a pre-evaluated basis matrix, including optional additional elements in the ... arguments. If a ok is NULL, it is inferred as rep(TRUE, NROW(x)), indicating that all rows correspond to successful basis evaluations. If full = FALSE, returns the matrix unchanged.

• fm_basis(list): Creates a new fm_basis object from a plain list containing at least an element A. If an ok element is missing, it is inferred as rep(TRUE, NROW(x$A)). If full = FALSE, extracts the A matrix.

• fm_basis(fm_basis): If full is TRUE, returns x unchanged, otherwise returns the A matrix contained in x.

• fm_basis(fm_evaluator): Extract fm_basis information from an fm_evaluator object. If full = FALSE, returns the A matrix contained in the fm_basis object.

See Also

fm_raw_basis()

Examples

# Compute basis mapping matrix
dim(fm_basis(fmexample$mesh, fmexample$loc))
print(fm_basis(fmexample$mesh, fmexample$loc, full = TRUE))

# From precomputed `fm_bary` information:
bary <- fm_bary(fmexample$mesh, fmexample$loc)
print(fm_basis(fmexample$mesh, bary, full = TRUE))

Internal helper functions for mesh field evaluation

Description

Methods called internally by fm_basis() methods.

Usage

fm_basis_mesh_2d(
  mesh,
  loc = NULL,
  weights = NULL,
  derivatives = NULL,
  crs = NULL,
  ...
)

fm_basis_mesh_1d(mesh, loc, weights = NULL, derivatives = NULL, ...)

Arguments

Value

A fm_basis object; a list of evaluator information objects, at least a matrix A and logical vector ok.

Examples

str(fm_basis_mesh_2d(fmexample$mesh, loc = fmexample$loc))

Bounding box class

Description

Simple class for handling bounding box information

Usage

fm_bbox(...)

## S3 method for class 'list'
fm_bbox(x, ...)

## S3 method for class 'NULL'
fm_bbox(...)

## S3 method for class 'numeric'
fm_bbox(x, ...)

## S3 method for class 'matrix'
fm_bbox(x, ...)

## S3 method for class 'Matrix'
fm_bbox(x, ...)

## S3 method for class 'fm_bbox'
fm_bbox(x, ...)

## S3 method for class 'fm_mesh_1d'
fm_bbox(x, ...)

## S3 method for class 'fm_mesh_2d'
fm_bbox(x, ...)

## S3 method for class 'fm_mesh_3d'
fm_bbox(x, ...)

## S3 method for class 'fm_segm'
fm_bbox(x, ...)

## S3 method for class 'fm_lattice_2d'
fm_bbox(x, ...)

## S3 method for class 'fm_lattice_Nd'
fm_bbox(x, ...)

## S3 method for class 'fm_tensor'
fm_bbox(x, ...)

## S3 method for class 'fm_collect'
fm_bbox(x, ...)

## S3 method for class 'sf'
fm_bbox(x, ...)

## S3 method for class 'sfg'
fm_bbox(x, ...)

## S3 method for class 'sfc'
fm_bbox(x, ...)

## S3 method for class 'bbox'
fm_bbox(x, ...)

fm_as_bbox(x, ...)

## S3 method for class 'fm_bbox'
x[i]

## S3 method for class 'fm_bbox'
c(..., .join = FALSE)

fm_as_bbox_list(x, ...)

Arguments

Value

For c.fm_bbox(), a fm_bbox_list object if .join = FALSE (the default) or an fm_bbox object if .join = TRUE.

Methods (by class)

• fm_bbox(list): Construct a bounding box from precomputed interval information, stored as a list of 2-vector ranges, list(xlim, ylim, ...).

Methods (by generic)

• [: Extract sub-list

• c(fm_bbox): The ... arguments should be fm_bbox objects, or coercible with fm_as_bbox(list(...)).

Functions

• fm_as_bbox_list(): Convert a list to a fm_bbox_list object, with each element converted to an fm_bbox object.

Examples

fm_bbox(matrix(1:6, 3, 2))
m <- c(A = fm_bbox(cbind(1, 2)), B = fm_bbox(cbind(3, 4)))
str(m)
str(m[2])
m <- fm_as_bbox_list(list(
  A = fm_bbox(cbind(1, 2)),
  B = fm_bbox(cbind(3, 4))
))
str(fm_as_bbox_list(m))

Blockwise aggregation matrices

Description

Creates an aggregation matrix for blockwise aggregation, with optional weighting.

Usage

fm_block(
  block = NULL,
  weights = NULL,
  log_weights = NULL,
  rescale = FALSE,
  n_block = NULL
)

fm_block_eval(
  block = NULL,
  weights = NULL,
  log_weights = NULL,
  rescale = FALSE,
  n_block = NULL,
  values = NULL
)

fm_block_logsumexp_eval(
  block = NULL,
  weights = NULL,
  log_weights = NULL,
  rescale = FALSE,
  n_block = NULL,
  values = NULL,
  log = TRUE
)

fm_block_weights(
  block = NULL,
  weights = NULL,
  log_weights = NULL,
  rescale = FALSE,
  n_block = NULL
)

fm_block_log_weights(
  block = NULL,
  weights = NULL,
  log_weights = NULL,
  rescale = FALSE,
  n_block = NULL
)

fm_block_log_shift(block = NULL, log_weights = NULL, n_block = NULL)

fm_block_prep(
  block = NULL,
  log_weights = NULL,
  weights = NULL,
  n_block = NULL,
  values = NULL,
  n_values = NULL,
  force_log = FALSE
)

Arguments

Value

A (sparse) matrix

Functions

• fm_block(): A (sparse) matrix of size n_block times length(block).

• fm_block_eval(): Evaluate aggregation. More efficient alternative to to as.vector(fm_block(...) %*% values).

• fm_block_logsumexp_eval(): Evaluate log-sum-exp aggregation. More efficient and numerically stable alternative to to log(as.vector(fm_block(...) %*% exp(values))).

• fm_block_weights(): Computes (optionally) blockwise renormalised weights

• fm_block_log_weights(): Computes (optionally) blockwise renormalised log-weights

• fm_block_log_shift(): Computes shifts for stable blocked log-sum-exp. To compute \log(\sum_{i; \textrm{block}_i=k} \exp(v_i) w_i) for each block k, first compute combined values and weights, and a shift:

  w_values <- values + fm_block_log_weights(block, log_weights = log_weights)
  shift <- fm_block_log_shift(block, log_weights = w_values)
  

  Then aggregate the values within each block:

  agg <- aggregate(exp(w_values - shift[block]),
                   by = list(block = block),
                   \(x) log(sum(x)))
  agg$x <- agg$x + shift[agg$block]
  

  The implementation uses a faster method:

  as.vector(
    Matrix::sparseMatrix(
      i = block,
      j = rep(1L, length(block)),
      x = exp(w_values - shift[block]),
      dims = c(n_block, 1))
  ) + shift
  

• fm_block_prep(): Helper function for preparing block, weights, and log_weights, n_block inputs.

Examples

block <- rep(1:2, 3:2)
fm_block(block)
fm_block(block, rescale = TRUE)
fm_block(block, log_weights = -2:2, rescale = TRUE)
fm_block_eval(
  block,
  weights = 1:5,
  rescale = TRUE,
  values = 11:15
)
fm_block_logsumexp_eval(
  block,
  weights = 1:5,
  rescale = TRUE,
  values = log(11:15),
  log = FALSE
)

Extract triangle centroids from an fm_mesh_2d

Description

Computes the centroids of the triangles of an fm_mesh_2d() object.

Usage

fm_centroids(x, format = NULL)

Arguments

Value

An sf, data.frame, or SpatialPointsDataFrame object, with the vertex coordinates, and a .triangle column with the triangle indices.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_vertices()

Examples

if (require("ggplot2", quietly = TRUE)) {
  vrt <- fm_centroids(fmexample$mesh, format = "sf")
  ggplot() +
    geom_sf(data = fm_as_sfc(fmexample$mesh)) +
    geom_sf(data = vrt, color = "red")
}

Make a collection function space

Description

Collection function spaces. The interface and object storage model is experimental and may change.

Usage

fm_collect(x, ...)

Arguments

Value

A fm_collect or fm_collect_list object. Elements of fm_collect:

fun_spaces

fm_list of function space objects

manifold

character; manifold type summary, obtained from the function spaces.

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

m <- fm_collect(list(
  A = fmexample$mesh,
  B = fmexample$mesh
))
m2 <- fm_as_collect(m)
m3 <- fm_as_collect_list(list(m, m))
c(fm_dof(m$fun_spaces[[1]]) + fm_dof(m$fun_spaces[[2]]), fm_dof(m))
fm_basis(m, loc = tibble::tibble(
  loc = fmexample$loc_sf,
  index = c(1, 1, 2, 2, 1, 2, 2, 1, 1, 2)
), full = TRUE)
fm_basis(m, loc = tibble::tibble(
  loc = rbind(c(0, 0), c(0.1, 0.1)),
  index = c("B", "A")
), full = TRUE)
fm_evaluator(m, loc = tibble::tibble(loc = cbind(0, 0), index = 2))
names(fm_fem(m))
fm_diameter(m)

Compute connected mesh subsets

Description

Compute subsets of vertices and triangles/tetrahedrons in an fm_mesh_2d or fm_mesh_3d object that are connected by edges/triangles, and split fm_segm objects into connected components.

Usage

fm_components(x, ...)

fm_mesh_components(...)

## S3 method for class 'fm_mesh_2d'
fm_components(x, ...)

## S3 method for class 'fm_mesh_3d'
fm_components(x, ...)

## S3 method for class 'fm_segm'
fm_components(x, ...)

## S3 method for class 'fm_segm_list'
fm_components(x, ...)

Arguments

Value

For fm_mesh_2d and fm_mesh_3d, returns a list with elements vertex and triangle/tetra, vectors of integer labels for which connected component they belong, and info, a data.frame with columns

For fm_segm, returns a list of segments, each with component either a single closed loop of segments, or an open segment chain.

Functions

• fm_mesh_components(): Backwards compatibility for version ⁠0.4.0⁠

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_mesh_2d(), fm_rcdt_2d(), fm_mesh_3d(), fm_segm()

Examples

# Construct two simple meshes:
loc <- matrix(c(0, 1, 0, 1), 2, 2)
mesh1 <- fm_mesh_2d(loc = loc, max.edge = 0.1)
bnd <- fm_nonconvex_hull(loc, 0.3)
mesh2 <- fm_mesh_2d(boundary = bnd, max.edge = 0.1)

# Compute connectivity information:
conn1 <- fm_components(mesh1)
conn2 <- fm_components(mesh2)
# One component, simply connected mesh
conn1$info
# Two disconnected components
conn2$info

# Extract the subset mesh for each component:
# (Note: some information is lost, such as fixed segments,
# and boundary edge labels.)
mesh3_1 <- fm_rcdt_2d_inla(
  loc = mesh2$loc,
  tv = mesh2$graph$tv[conn2$triangle == 1, , drop = FALSE],
  delaunay = FALSE
)
mesh3_2 <- fm_rcdt_2d_inla(
  loc = mesh2$loc,
  tv = mesh2$graph$tv[conn2$triangle == 2, , drop = FALSE],
  delaunay = FALSE
)

if (require("ggplot2")) {
  ggplot() +
    geom_fm(data = mesh3_1, fill = "red", alpha = 0.5) +
    geom_fm(data = mesh3_2, fill = "blue", alpha = 0.5)
}

(m <- fm_mesh_3d(
  matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0), 4, 3, byrow = TRUE),
  matrix(c(1, 2, 3, 4), 1, 4, byrow = TRUE)
))
# Compute connectivity information:
(conn <- fm_components(m))

(segm <- c(
  fm_segm(
    matrix(c(0, 0, 1, 0, 1, 1, 0, 1), 4, 2, byrow = TRUE),
    matrix(c(1, 2, 2, 3, 3, 4, 4, 1), 4, 2, byrow = TRUE)
  ),
  fm_segm(
    matrix(c(0, 0, 1, 0, 1, 1, 0, 1), 4, 2, byrow = TRUE),
    matrix(c(3, 4, 1, 2, 2, 3), 3, 2, byrow = TRUE),
    is.bnd = FALSE
  )
))
# Compute connectivity information:
(conn <- lapply(segm, fm_components))
(conn2 <- fm_components(segm))

Check which mesh triangles are inside a polygon

Description

Wrapper for the sf::st_contains() (previously sp::over()) method to find triangle centroids or vertices inside sf or sp polygon objects

Usage

fm_contains(x, y, ...)

## S3 method for class 'Spatial'
fm_contains(x, y, ...)

## S3 method for class 'sf'
fm_contains(x, y, ...)

## S3 method for class 'sfc'
fm_contains(x, y, ..., type = c("centroid", "vertex"))

Arguments

Value

List of vectors of triangle indices (when type is 'centroid') or vertex indices (when type is 'vertex'). The list has one entry per row of the sf object. Use unlist(fm_contains(...)) if the combined union is needed.

Author(s)

Haakon Bakka, bakka@r-inla.org, and Finn Lindgren Finn.Lindgren@gmail.com

Examples

# Create a polygon and a mesh
obj <- sf::st_sfc(
  sf::st_polygon(
    list(rbind(
      c(0, 0),
      c(50, 0),
      c(50, 50),
      c(0, 50),
      c(0, 0)
    ))
  ),
  crs = fm_crs("longlat_globe")
)
mesh <- fm_rcdt_2d_inla(globe = 2, crs = fm_crs("sphere"))

## 2 vertices found in the polygon
fm_contains(obj, mesh, type = "vertex")

## 3 triangles found in the polygon
fm_contains(obj, mesh)

## Multiple transformations can lead to slightly different results
## due to edge cases:
## 4 triangles found in the polygon
fm_contains(
  obj,
  fm_transform(mesh, crs = fm_crs("mollweide_norm"))
)

(Blockwise) cross product of integration points

Description

Calculates the groupwise cross product of integration points in different dimensions and multiplies their weights accordingly. If the object defining points in a particular dimension has no weights attached to it all weights are assumed to be 1.

Usage

fm_cprod(..., na.rm = NULL, .blockwise = FALSE)

Arguments

Value

A data.frame, sf, or SpatialPointsDataFrame of multidimensional integration points and their weights

Examples

if (require("ggplot2")) {
  # Create integration points in dimension 'myDim' and 'myDiscreteDim'
  ips1 <- fm_int(fm_mesh_1d(1:20),
    rbind(c(0, 3), c(3, 8)),
    name = "myDim"
  )
  ips2 <- fm_int(domain = c(1, 2, 4), name = "myDiscreteDim")

  # Calculate the cross product
  ips <- fm_cprod(ips1, ips2)

  # Plot the integration points
  ggplot(ips) +
    geom_point(aes(myDim, myDiscreteDim, size = weight)) +
    scale_size_area()
}

Obtain coordinate reference system object

Description

Obtain an sf::crs or fm_crs object from a spatial object, or convert crs information to construct a new sf::crs object.

Usage

fm_crs(x, ..., units = NULL, oblique = NULL)

fm_crs_oblique(x)

## S3 method for class 'fm_crs'
st_crs(x, ...)

## S3 method for class 'fm_crs'
x$name

## Default S3 method:
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'crs'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_crs'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_CRS'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'character'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'Spatial'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'SpatVector'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'SpatRaster'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'sf'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'sfc'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'sfg'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_mesh_2d'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_mesh_1d'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_mesh_3d'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_tensor'
fm_crs(x, ..., units = NULL, oblique = NULL, .multi = FALSE)

## S3 method for class 'fm_collect'
fm_crs(x, ..., units = NULL, oblique = NULL, .multi = FALSE)

## S3 method for class 'fm_lattice_2d'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_segm'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_list'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'matrix'
fm_crs(x, ..., units = NULL, oblique = NULL)

## S3 method for class 'fm_list'
fm_CRS(x, ..., units = NULL, oblique = NULL)

fm_wkt_predef()

## S3 method for class 'inla.CRS'
fm_crs(x, ..., units = NULL, oblique = NULL)

Arguments

Details

The first two elements of the oblique vector are the (longitude, latitude) coordinates for the oblique centre point. The third value (orientation) is a counter-clockwise rotation angle for an observer looking at the centre point from outside the sphere. The fourth value is the quasi-longitude (orbit angle) for a rotation along the oblique observers equator.

Simple oblique: oblique=c(0, 45)

Polar: oblique=c(0, 90)

Quasi-transversal: oblique=c(0, 0, 90)

Satellite orbit viewpoint: oblique=c(lon0-time*v1, 0, orbitangle, orbit0+time*v2), where lon0 is the longitude at which a satellite orbit crosses the equator at time=0, when the satellite is at an angle orbit0 further along in its orbit. The orbital angle relative to the equatorial plane is orbitangle, and v1 and v2 are the angular velocities of the planet and the satellite, respectively. Note that "forward" from the satellite's point of view is "to the right" in the projection.

When oblique[2] or oblique[3] are non-zero, the resulting projection is only correct for perfect spheres.

Value

Either an sf::crs object or an fm_crs object, depending on if the coordinate reference system described by the parameters can be expressed with a pure crs object or not.

A crs object (sf::st_crs()) or a fm_crs object. An S3 fm_crs object is a list with elements crs and oblique.

fm_wkt_predef returns a WKT2 string defining a projection

Methods (by class)

• fm_crs(fm_tensor): By default returns the crs of the first space in the tensor product space.

• fm_crs(fm_collect): By default returns the crs of the first space in the collection.

• fm_crs(fm_list): returns a list of 'crs' objects, one for each list element

Methods (by generic)

• st_crs(fm_crs): st_crs(x, ...) is equivalent to fm_crs(x, oblique = NA, ...) when x is a fm_crs object.

• $: For a fm_crs object x, x$name calls the accessor method for the crs object inside it. If name is "crs", the internal crs object itself is returned. If name is "oblique", the internal oblique angle parameter vector is returned.

Functions

• fm_crs_oblique(): Return NA for object with no oblique information, and otherwise a length 4 numeric vector.

• fm_CRS(fm_list): returns a list of 'CRS' objects, one for each list element

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

sf::st_crs(), fm_crs_wkt

fm_crs_is_null

fm_crs<-(), fm_crs_oblique<-()

Examples

crs1 <- fm_crs("longlat_globe")
crs2 <- fm_crs("lambert_globe")
crs3 <- fm_crs("mollweide_norm")
crs4 <- fm_crs("hammer_globe")
crs5 <- fm_crs("sphere")
crs6 <- fm_crs("globe")
names(fm_wkt_predef())

Assignment operators for crs information objects

Description

Assigns new crs information.

Usage

fm_crs(x) <- value

fm_crs_oblique(x) <- value

## S3 replacement method for class 'NULL'
fm_crs(x) <- value

## S3 replacement method for class 'NULL'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'fm_segm'
fm_crs(x) <- value

## S3 replacement method for class 'fm_list'
fm_crs(x) <- value

## S3 replacement method for class 'fm_mesh_2d'
fm_crs(x) <- value

## S3 replacement method for class 'fm_collect'
fm_crs(x) <- value

## S3 replacement method for class 'fm_lattice_2d'
fm_crs(x) <- value

## S3 replacement method for class 'sf'
fm_crs(x) <- value

## S3 replacement method for class 'sfg'
fm_crs(x) <- value

## S3 replacement method for class 'sfc'
fm_crs(x) <- value

## S3 replacement method for class 'Spatial'
fm_crs(x) <- value

## S3 replacement method for class 'crs'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'CRS'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'fm_CRS'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'fm_crs'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'fm_segm'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'fm_mesh_2d'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'fm_collect'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'fm_lattice_2d'
fm_crs_oblique(x) <- value

## S3 replacement method for class 'inla.CRS'
fm_crs_oblique(x) <- value

Arguments

Value

The modified object

Functions

• fm_crs(x) <- value: Automatically converts the input value with fm_crs(value), fm_crs(value, oblique = NA), fm_CRS(value), or fm_CRS(value, oblique = NA), depending on the type of x.

• fm_crs_oblique(x) <- value: Assigns new oblique information.

See Also

fm_crs()

Examples

x <- fm_segm()
fm_crs(x) <- fm_crs("+proj=longlat")
fm_crs(x)$proj4string

Check if two CRS objects are identical

Description

Check if two CRS objects are identical

Usage

fm_crs_is_identical(crs0, crs1, crsonly = FALSE)

Arguments

Value

logical, indicating if the two crs objects are identical in the specified sense (see the crsonly argument)

See Also

fm_crs(), fm_CRS(), fm_crs_is_null()

Examples

crs0 <- crs1 <- fm_crs("longlat_globe")
fm_crs_oblique(crs1) <- c(0, 90)
print(c(
  fm_crs_is_identical(crs0, crs0),
  fm_crs_is_identical(crs0, crs1),
  fm_crs_is_identical(crs0, crs1, crsonly = TRUE)
))

Check if a crs is NULL or NA

Description

Methods of checking whether various kinds of CRS objects are NULL or NA. Logically equivalent to either is.na(fm_crs(x)) or is.na(fm_crs(x, oblique = NA)), but with a short-cut pre-check for is.null(x).

Usage

fm_crs_is_null(x, crsonly = FALSE)

## S3 method for class 'fm_crs'
is.na(x)

Arguments

Value

logical

Functions

• fm_crs_is_null(): Check if an object is or has NULL or NA CRS information. If not NULL, is.na(fm_crs(x)) is returned. This allows the input to be e.g. a proj4string or epsg number, since the default fm_crs() method passes its argument on to sf::st_crs().

• is.na(fm_crs): Check if a fm_crs has NA crs information and NA obliqueness

See Also

fm_crs(), fm_CRS(), fm_crs_is_identical()

Examples

fm_crs_is_null(NULL)
fm_crs_is_null(27700)
fm_crs_is_null(fm_crs())
fm_crs_is_null(fm_crs(27700))
fm_crs_is_null(fm_crs(oblique = c(1, 2, 3, 4)))
fm_crs_is_null(fm_crs(oblique = c(1, 2, 3, 4)), crsonly = TRUE)
fm_crs_is_null(fm_crs(27700, oblique = c(1, 2, 3, 4)))
fm_crs_is_null(fm_crs(27700, oblique = c(1, 2, 3, 4)), crsonly = TRUE)

Plot CRS and fm_crs objects

Description

Plot the outline of a crs or fm_crs() projection, with optional graticules (transformed parallels and meridians) and Tissot indicatrices.

Usage

fm_crs_plot(
  x,
  xlim = NULL,
  ylim = NULL,
  outline = TRUE,
  graticule = c(15, 15, 45),
  tissot = c(30, 30, 30),
  asp = 1,
  add = FALSE,
  eps = 0.05,
  ...
)

fm_crs_graticule(
  x,
  by = c(15, 15, 45),
  add = FALSE,
  do.plot = TRUE,
  eps = 0.05,
  ...
)

fm_crs_tissot(
  x,
  by = c(30, 30, 30),
  add = FALSE,
  do.plot = TRUE,
  eps = 0.05,
  diff.eps = 0.01,
  ...
)

Arguments

Value

NULL, invisibly

Functions

• fm_crs_graticule(): Constructs graticule information for a given CRS or fm_crs() and optionally plots the graticules. Returns a list with two elements, meridians and parallels, which are SpatialLines objects.

• fm_crs_tissot(): Constructs Tissot indicatrix information for a given CRS or fm_crs() and optionally plots the indicatrices. Returns a list with one element, tissot, which is a SpatialLines object.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_crs()

Examples

if (require("sf") && require("sp")) {
  for (projtype in c(
    "longlat_norm",
    "lambert_norm",
    "mollweide_norm",
    "hammer_norm"
  )) {
    fm_crs_plot(fm_crs(projtype), main = projtype)
  }
}

if (require("sf") && require("sp")) {
  oblique <- c(0, 45, 45, 0)
  for (projtype in c(
    "longlat_norm",
    "lambert_norm",
    "mollweide_norm",
    "hammer_norm"
  )) {
    fm_crs_plot(
      fm_crs(projtype, oblique = oblique),
      main = paste("oblique", projtype)
    )
  }
}

Handling CRS/WKT

Description

Get and set CRS object or WKT string properties.

Usage

fm_wkt_is_geocent(wkt)

fm_crs_is_geocent(crs)

fm_wkt_get_ellipsoid_radius(wkt)

fm_crs_get_ellipsoid_radius(crs)

fm_ellipsoid_radius(x)

## Default S3 method:
fm_ellipsoid_radius(x)

## S3 method for class 'character'
fm_ellipsoid_radius(x)

fm_wkt_set_ellipsoid_radius(wkt, radius)

fm_ellipsoid_radius(x) <- value

## S3 replacement method for class 'character'
fm_ellipsoid_radius(x) <- value

## S3 replacement method for class 'CRS'
fm_ellipsoid_radius(x) <- value

## S3 replacement method for class 'fm_CRS'
fm_ellipsoid_radius(x) <- value

## S3 replacement method for class 'crs'
fm_ellipsoid_radius(x) <- value

## S3 replacement method for class 'fm_crs'
fm_ellipsoid_radius(x) <- value

fm_crs_set_ellipsoid_radius(crs, radius)

fm_wkt_unit_params()

fm_wkt_get_lengthunit(wkt)

fm_wkt_set_lengthunit(wkt, unit, params = NULL)

fm_crs_get_lengthunit(crs)

fm_crs_set_lengthunit(crs, unit)

fm_length_unit(x)

## Default S3 method:
fm_length_unit(x)

## S3 method for class 'character'
fm_length_unit(x)

fm_length_unit(x) <- value

## S3 replacement method for class 'character'
fm_length_unit(x) <- value

## S3 replacement method for class 'CRS'
fm_length_unit(x) <- value

## S3 replacement method for class 'fm_CRS'
fm_length_unit(x) <- value

## S3 replacement method for class 'crs'
fm_length_unit(x) <- value

## S3 replacement method for class 'fm_crs'
fm_length_unit(x) <- value

fm_wkt(crs)

fm_proj4string(crs)

fm_wkt_tree_projection_type(wt)

fm_wkt_projection_type(wkt)

fm_crs_projection_type(crs)

fm_crs_bounds(crs, warn.unknown = FALSE)

## S3 replacement method for class 'inla.CRS'
fm_ellipsoid_radius(x) <- value

## S3 replacement method for class 'inla.CRS'
fm_length_unit(x) <- value

Arguments

Value

For fm_wkt_unit_params, a list of named unit definitions

For fm_wkt_get_lengthunit, a list of length units used in the wkt string, excluding the ellipsoid radius unit.

For fm_wkt_set_lengthunit, a WKT2 string with altered length units. Note that the length unit for the ellipsoid radius is unchanged.

For fm_crs_get_lengthunit, a list of length units used in the wkt string, excluding the ellipsoid radius unit.

For ⁠fm_length_unit<-⁠, a crs object with altered length units. Note that the length unit for the ellipsoid radius is unchanged.

Functions

• fm_wkt(): Returns a WKT2 string, for any input supported by fm_crs().

• fm_proj4string(): Returns a proj4 string, for any input supported by fm_crs().

• fm_wkt_tree_projection_type(): Returns "longlat", "lambert", "mollweide", "hammer", "tmerc", or NULL

• fm_wkt_projection_type(): See fm_wkt_tree_projection_type

• fm_crs_projection_type(): See fm_wkt_tree_projection_type

• fm_crs_bounds(): Returns bounds information for a projection, as a list with elements type ("rectangle" or "ellipse"), xlim, ylim, and polygon.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_crs()

Examples

c1 <- fm_crs("globe")
fm_length_unit(c1)
fm_length_unit(c1) <- "m"
fm_length_unit(c1)

Detect manifold type

Description

Detect if a 2d object is on "R2", "S2", or "M2"

Usage

fm_detect_manifold(x)

fm_crs_detect_manifold(x)

## S3 method for class 'crs'
fm_detect_manifold(x)

## S3 method for class 'CRS'
fm_detect_manifold(x)

## S3 method for class 'numeric'
fm_detect_manifold(x)

## S3 method for class 'matrix'
fm_detect_manifold(x)

## S3 method for class 'fm_mesh_2d'
fm_detect_manifold(x)

Arguments

Value

A string containing the detected manifold classification

Functions

• fm_crs_detect_manifold(): Detect if a crs is on "R2" or "S2" (if fm_crs_is_geocent(crs) is TRUE). Returns NA_character_ if the crs is NULL or NA.

Examples

fm_detect_manifold(1:4)
fm_detect_manifold(rbind(c(1, 0, 0), c(0, 1, 0), c(1, 1, 0)))
fm_detect_manifold(rbind(c(1, 0, 0), c(0, 1, 0), c(0, 0, 1)))

Diameter bound for a geometric object

Description

Find an upper bound to the convex hull of a point set or function space

Usage

fm_diameter(x, ...)

## S3 method for class 'matrix'
fm_diameter(x, manifold = NULL, ...)

## S3 method for class 'sf'
fm_diameter(x, ...)

## S3 method for class 'sfg'
fm_diameter(x, ...)

## S3 method for class 'sfc'
fm_diameter(x, ...)

## S3 method for class 'fm_lattice_2d'
fm_diameter(x, ...)

## S3 method for class 'fm_mesh_1d'
fm_diameter(x, ...)

## S3 method for class 'fm_mesh_2d'
fm_diameter(x, ...)

## S3 method for class 'fm_segm'
fm_diameter(x, ...)

## S3 method for class 'fm_mesh_3d'
fm_diameter(x, ...)

## S3 method for class 'fm_tensor'
fm_diameter(x, ...)

## S3 method for class 'fm_collect'
fm_diameter(x, ...)

## S3 method for class 'fm_list'
fm_diameter(x, ...)

Arguments

Value

A scalar, upper bound for the diameter of the convex hull of the point set. For multi-domain spaces (e.g. fm_tensor() and fm_collect()), a vector of upper bounds for each domain is returned.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

fm_diameter(matrix(c(0, 1, 1, 0, 0, 0, 1, 1), 4, 2))

Function spece degrees of freedom

Description

Obtain the degrees of freedom of a function space, i.e. the number of basis functions it uses.

Usage

fm_dof(x)

## S3 method for class 'fm_mesh_1d'
fm_dof(x)

## S3 method for class 'fm_mesh_2d'
fm_dof(x)

## S3 method for class 'fm_mesh_3d'
fm_dof(x)

## S3 method for class 'fm_tensor'
fm_dof(x)

## S3 method for class 'fm_collect'
fm_dof(x)

## S3 method for class 'fm_lattice_2d'
fm_dof(x)

## S3 method for class 'fm_lattice_Nd'
fm_dof(x)

Arguments

Value

An integer

Examples

fm_dof(fmexample$mesh)

Methods for projecting to/from mesh objects

Description

Calculate evaluation information and/or evaluate a function defined on a mesh or function space.

Usage

fm_evaluate(...)

## Default S3 method:
fm_evaluate(mesh, field, ...)

## S3 method for class 'fm_evaluator'
fm_evaluate(projector, field, ...)

## S3 method for class 'fm_basis'
fm_evaluate(basis, field, ...)

fm_evaluator(...)

## Default S3 method:
fm_evaluator(...)

## S3 method for class 'fm_mesh_3d'
fm_evaluator(mesh, loc = NULL, lattice = NULL, dims = NULL, ...)

## S3 method for class 'fm_mesh_2d'
fm_evaluator(mesh, loc = NULL, lattice = NULL, crs = NULL, ...)

## S3 method for class 'fm_mesh_1d'
fm_evaluator(mesh, loc = NULL, xlim = mesh$interval, dims = 100, ...)

fm_evaluator_lattice(mesh, ...)

## Default S3 method:
fm_evaluator_lattice(mesh, dims = 100, ...)

## S3 method for class 'fm_bbox'
fm_evaluator_lattice(mesh, dims = 100, ...)

## S3 method for class 'fm_mesh_2d'
fm_evaluator_lattice(
  mesh,
  xlim = NULL,
  ylim = NULL,
  dims = c(100, 100),
  projection = NULL,
  crs = NULL,
  ...
)

Arguments

Value

A vector or matrix of the evaluated function

An fm_evaluator object

Methods (by class)

• fm_evaluate(default): The default method calls proj = fm_evaluator(mesh, ...), followed by fm_evaluate(proj, field).

Functions

• fm_evaluate(): Returns the field function evaluated at the locations determined by an fm_evaluator object. fm_evaluate(mesh, field = field, ...) is a shortcut to fm_evaluate(fm_evaluator(mesh, ...), field = field).

• fm_evaluator(): Returns an fm_evaluator list object with evaluation information. The proj element is a fm_basis object, containing (at least) a mapping matrix A and a logical vector ok, that indicates which locations were mappable to the input mesh. For fm_mesh_2d input, proj also contains a bary fm_bary object, with the barycentric coordinates within the triangle each input location falls in.

• fm_evaluator(default): The default method calls fm_basis and creates a basic fm_evaluator object

• fm_evaluator(fm_mesh_3d): The ... arguments are passed on to fm_evaluator_lattice() if no loc or lattice is provided.

• fm_evaluator(fm_mesh_2d): The ... arguments are passed on to fm_evaluator_lattice() if no loc or lattice is provided.

• fm_evaluator_lattice(): Create a lattice object by default covering the input mesh.

• fm_evaluator_lattice(default): Creates an fm_lattice_2d() object, by default covering the input mesh.

• fm_evaluator_lattice(fm_bbox): Creates an fm_lattice_Nd() object, by default covering the input mesh.

• fm_evaluator_lattice(fm_mesh_2d): Creates an fm_lattice_2d() object, by default covering the input mesh.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_mesh_2d(), fm_mesh_1d(), fm_lattice_2d()

Examples

if (TRUE) {
  n <- 20
  loc <- matrix(runif(n * 2), n, 2)
  mesh <- fm_rcdt_2d_inla(loc, refine = list(max.edge = 0.05))
  proj <- fm_evaluator(mesh)
  field <- cos(mesh$loc[, 1] * 2 * pi * 3) * sin(mesh$loc[, 2] * 2 * pi * 7)
  image(proj$x, proj$y, fm_evaluate(proj, field))
}

# if (require("ggplot2") &&
#  require("ggpolypath")) {
#  ggplot() +
#    gg(data = fm_as_sfc(mesh), col = field)
# }

Compute finite element matrices

Description

Compute finite element mass and structure matrices

Usage

fm_fem(mesh, order = 2, ...)

## S3 method for class 'fm_mesh_1d'
fm_fem(mesh, order = 2, ...)

## S3 method for class 'fm_mesh_2d'
fm_fem(mesh, order = 2, aniso = NULL, ...)

## S3 method for class 'fm_tensor'
fm_fem(mesh, order = 2, ...)

## S3 method for class 'fm_collect'
fm_fem(mesh, order = 2, ...)

## S3 method for class 'fm_mesh_3d'
fm_fem(mesh, order = 2, ...)

Arguments

Value

fm_fem.fm_mesh_1d: A list with elements c0, c1, g1, g2, etc. When mesh$degree == 2, also g01, g02, and g12.

fm_fem.fm_mesh_2d: A list with elements c0, c1, g1, va, ta, and more if order > 1. When aniso is non-NULL, also g1aniso matrices, etc.

fm_fem.fm_tensor: A list with elements cc, g1, g2.

fm_fem.fm_collect: A list with elements c0, c1, g1, g2, etc, and cc (c0 for every model except fm_mesh_1d with degree=2, for which it is c1). If the base type for the collection provides va and ta values, those are also returned.

fm_fem.fm_mesh_3d: A list with elements c0, c1, g1, g2, va, ta, and more if order > 2.

Examples

names(fm_fem(fm_mesh_1d(1:4), order = 3))
names(fm_fem(fmexample$mesh, order = 3))

Generate text RGB color specifications.

Description

Generates a text RGB color specification matrix based on a color palette.

Usage

fm_generate_colors(
  color,
  color.axis = NULL,
  color.n = 512,
  color.palette = cm.colors,
  color.truncate = FALSE,
  alpha = NULL
)

Arguments

Value

A list with character vector colors and numeric vector alpha

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

fm_generate_colors(1:4, color.axis = c(1, 4))

SPDE, GMRF, and Matérn process methods

Description

Methods for SPDEs and GMRFs.

Usage

fm_matern_precision(x, alpha, rho, sigma)

fm_matern_sample(x, alpha = 2, rho, sigma, n = 1, loc = NULL)

fm_covariance(Q, A1 = NULL, A2 = NULL, partial = FALSE)

fm_sample(n, Q, mu = 0, constr = NULL)

Arguments

Value

fm_matern_sample() returns a matrix, where each column is a sampled field. If loc is NULL, the fm_dof(mesh) basis weights are given. Otherwise, the evaluated field at the nrow(loc) locations loc are given (from version ⁠0.1.4.9001⁠)

Functions

• fm_matern_precision(): Construct the (sparse) precision matrix for the basis weights for Whittle-Matérn SPDE models. The boundary behaviour is determined by the provided mesh function space.

• fm_matern_sample(): Simulate a Matérn field given a mesh and covariance function parameters, and optionally evaluate at given locations.

• fm_covariance(): Compute the covariance between "A1 x" and "A2 x", when x is a basis vector with precision matrix Q.

• fm_sample(): Generate n samples based on a sparse precision matrix Q

Examples

library(Matrix)
mesh <- fm_mesh_1d(-20:120, degree = 2)
Q <- fm_matern_precision(mesh, alpha = 2, rho = 15, sigma = 1)
x <- seq(0, 100, length.out = 601)
A <- fm_basis(mesh, x)
plot(x,
  as.vector(Matrix::diag(fm_covariance(Q, A))),
  type = "l",
  ylab = "marginal variances"
)

plot(x,
  fm_evaluate(mesh, loc = x, field = fm_sample(1, Q)[, 1]),
  type = "l",
  ylab = "process sample"
)

Create hexagon lattice points

Description

from ⁠0.3.0.9001⁠. Create hexagon lattice points within a boundary. By default, the hexagonal lattice is anchored at the coordinate system origin, so that grids with different but overlapping boundaries will have matching points.

Usage

fm_hexagon_lattice(
  bnd,
  edge_len = NULL,
  buffer_n = 0.49,
  align = "origin",
  meta = FALSE
)

Arguments

Value

An sfc object with points, if meta is FALSE (default), or if meta=TRUE, a list:

lattice

sfc with lattice points

edge_len

numeric with edge length

bnd_inner

sf object with the inner boundary used to filter points outside of a edge_len * buffer_n distance from the boundary

grid_n

integer with the number of points in each direction prior to filtering

align

numeric with the alignment coordinates of the hexagon lattice

Author(s)

Man Ho Suen M.H.Suen@sms.ed.ac.uk, Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_mesh_2d()

Examples

(m <- fm_mesh_2d(
  fm_hexagon_lattice(
    fmexample$boundary_sf[[1]],
    edge_len = 0.1 * 5
  ),
  max.edge = c(0.2, 1) * 5,
  boundary = fmexample$boundary_sf
))

(m2 <- fm_mesh_2d(
  fm_hexagon_lattice(
    fmexample$boundary_sf[[1]],
    edge_len = 0.1 * 5,
    align = "centroid"
  ),
  max.edge = c(0.2, 1) * 5,
  boundary = fmexample$boundary_sf
))

if (require("ggplot2", quietly = TRUE) &&
  require("patchwork", quietly = TRUE)) {
  ((ggplot() +
    geom_fm(data = m) +
    geom_point(aes(0, 0), col = "red")) |
    (ggplot() +
      geom_fm(data = m2) +
      geom_point(aes(0, 0), col = "red") +
      geom_sf(data = sf::st_centroid(fmexample$boundary_sf[[1]]))
    )
  )
}

Create hexagon lattice points

Description

Create hexagon lattice points within a boundary

Usage

fm_hexagon_lattice_orig(bnd, x_bin = 250, edge_len_n = 1)

Arguments

Value

A list with lattice points, edge length, and inner boundary

Author(s)

Man Ho Suen M.H.Suen@sms.ed.ac.uk

Multi-domain integration

Description

Construct integration points on tensor product spaces

Usage

fm_int(domain, samplers = NULL, ...)

## S3 method for class 'list'
fm_int(domain, samplers = NULL, ...)

## S3 method for class 'numeric'
fm_int(domain, samplers = NULL, name = "x", ...)

## S3 method for class 'character'
fm_int(domain, samplers = NULL, name = "x", ...)

## S3 method for class 'factor'
fm_int(domain, samplers = NULL, name = "x", ...)

## S3 method for class 'SpatRaster'
fm_int(domain, samplers = NULL, name = "x", ...)

## S3 method for class 'fm_lattice_2d'
fm_int(domain, samplers = NULL, name = "x", ...)

## S3 method for class 'fm_mesh_1d'
fm_int(
  domain,
  samplers = NULL,
  name = "x",
  int.args = NULL,
  format = NULL,
  ...
)

## S3 method for class 'fm_mesh_2d'
fm_int(
  domain,
  samplers = NULL,
  name = NULL,
  int.args = NULL,
  format = NULL,
  ...
)

Arguments

Value

A tibble, sf, or SpatialPointsDataFrame of 1D and 2D integration points, including a weight column, a.block column, and a matrix column .block_origin. The .block column is used to identify the integration blocks defined by the samplers. The .block_origin collects the original subdomain block information for tensor product blocks.

Methods (by class)

• fm_int(list): Multi-domain integration

• fm_int(numeric): Discrete double or integer space integration

• fm_int(character): Discrete character space integration

• fm_int(factor): Discrete factor space integration

• fm_int(SpatRaster): SpatRaster integration. Not yet implemented.

• fm_int(fm_lattice_2d): fm_lattice_2d integration. Not yet implemented.

• fm_int(fm_mesh_1d): fm_mesh_1d integration. Supported samplers:

  • NULL for integration over the entire domain;

  • A length 2 vector defining an interval;

  • A 2-column matrix with a single interval in each row;

  • A tibble with a named column containing a matrix, and optionally a weight column.

• fm_int(fm_mesh_2d): fm_mesh_2d integration. Any sampler class with an associated fm_int_mesh_2d() method is supported.

Examples

# Integration on the interval (2, 3.5) with Simpson's rule
ips <- fm_int(fm_mesh_1d(0:4), samplers = cbind(2, 3.5))
plot(ips$x, ips$weight)

# Create integration points for the two intervals [0,3] and [5,10]
ips <- fm_int(
  fm_mesh_1d(0:10),
  rbind(c(0, 3), c(5, 10))
)
plot(ips$x, ips$weight)

# Convert a 1D mesh into integration points
mesh <- fm_mesh_1d(seq(0, 10, by = 1))
ips <- fm_int(mesh, name = "time")
plot(ips$time, ips$weight)

if (require("ggplot2", quietly = TRUE)) {
  #' Integrate on a 2D mesh with polygon boundary subset
  ips <- fm_int(fmexample$mesh, fmexample$boundary_sf[[1]])
  ggplot() +
    geom_sf(data = fm_as_sfc(fmexample$mesh, multi = TRUE), alpha = 0.5) +
    geom_sf(data = fmexample$boundary_sf[[1]], fill = "red", alpha = 0.5) +
    geom_sf(data = ips, aes(size = weight)) +
    scale_size_area()
}

# Individual sampling points:
(ips <- fm_int(0:10, c(0, 3, 5, 6, 10)))
# Sampling blocks:
(ips <- fm_int(0:10, list(c(0, 3), c(5, 6, 10))))

# Continuous integration on intervals
ips <- fm_int(
  fm_mesh_1d(0:10, boundary = "cyclic"),
  rbind(c(0, 3), c(5, 10))
)
plot(ips$x, ips$weight)

Subset integration on a mesh

Description

Integration methods for spatial samplers on fm_mesh_2d meshes.

Usage

fm_int_mesh_2d(samplers, domain, name = NULL, int.args = NULL, ...)

fm_int_mesh_2d_NULL(samplers, domain, name = NULL, int.args = NULL, ...)

## S3 method for class 'sf'
fm_int_mesh_2d(samplers, domain, name = NULL, int.args = NULL, ...)

## S3 method for class 'sfc_POINT'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  .weight = rep(1, NROW(samplers)),
  ...
)

## S3 method for class 'sfc_MULTIPOINT'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  .weight = rep(1, NROW(samplers)),
  ...
)

## S3 method for class 'sfc_LINESTRING'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  .weight = rep(1, NROW(samplers)),
  ...
)

## S3 method for class 'sfc_MULTILINESTRING'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  .weight = rep(1, NROW(samplers)),
  ...
)

## S3 method for class 'sfc_POLYGON'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  .weight = rep(1, NROW(samplers)),
  ...
)

## S3 method for class 'sfc_MULTIPOLYGON'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  .weight = rep(1, NROW(samplers)),
  ...
)

## S3 method for class 'sfc_GEOMETRY'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  .weight = rep(1, NROW(samplers)),
  ...
)

## S3 method for class 'Spatial'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  format = NULL,
  ...
)

## S3 method for class 'fm_segm'
fm_int_mesh_2d(
  samplers,
  domain,
  name = NULL,
  int.args = NULL,
  format = NULL,
  ...
)

Arguments

Value

A list, sf, or Spatial object with point coordinate information and additional columns weight and .block

Methods (by class)

• fm_int_mesh_2d(sf): sf integration

• fm_int_mesh_2d(sfc_POINT): sfc_POINT integration

• fm_int_mesh_2d(sfc_MULTIPOINT): sfc_MULTIPOINT integration

• fm_int_mesh_2d(sfc_LINESTRING): sfc_LINESTRING integration

• fm_int_mesh_2d(sfc_MULTILINESTRING): sfc_MULTILINESTRING integration

• fm_int_mesh_2d(sfc_POLYGON): sfc_POLYGON integration

• fm_int_mesh_2d(sfc_MULTIPOLYGON): sfc_MULTIPOLYGON integration

• fm_int_mesh_2d(sfc_GEOMETRY): sfc_GEOMERY integration

• fm_int_mesh_2d(Spatial): Spatial integration

• fm_int_mesh_2d(fm_segm): fm_segm integration

Functions

• fm_int_mesh_2d_NULL(): Full domain integration

Examples

str(fm_int_mesh_2d(samplers = NULL, domain = fmexample$mesh))

Integration scheme for mesh triangle interiors

Description

Integration scheme for mesh triangle interiors

Usage

fm_int_mesh_2d_core(mesh, tri_subset = NULL, nsub = NULL)

Arguments

Value

tibble with columns loc and weight with integration points for the mesh

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

str(fm_int_mesh_2d_core(fmexample$mesh))

Multi-domain sampler integration

Description

Combine integration over different domains

Usage

fm_int_multi_sampler(domain, samplers, ...)

Arguments

Value

An object with integration points and weights

Examples

fm_int_multi_sampler(
  domain = list(x = fm_mesh_1d(1:4), y = 11:12),
  samplers = tibble::tibble(
    x = rbind(c(1, 3), c(2, 4)),
    y = c(12, 11)
  )
)

Query if points are inside a mesh

Description

Queries whether each input point is within a mesh or not.

Usage

fm_is_within(x, y, ...)

Arguments

Value

A logical vector

Examples

all(fm_is_within(fmexample$loc, fmexample$mesh))

Make a lattice object

Description

Construct a lattice grid for fm_mesh_2d()

Usage

fm_lattice_2d(...)

## Default S3 method:
fm_lattice_2d(
  x = seq(0, 1, length.out = 2),
  y = seq(0, 1, length.out = 2),
  z = NULL,
  dims = if (is.matrix(x)) {
     dim(x)
 } else {
     c(length(x), length(y))
 },
  units = NULL,
  crs = NULL,
  ...
)

Arguments

Value

An fm_lattice_2d object with elements

dims

integer vector

x

x-values for original vector input

y

y-values for original vector input

loc

matrix of ⁠(x, y)⁠ values or ⁠(x, y, z)⁠ values. May be altered by fm_transform()

segm

fm_segm object

crs

fm_crs object for loc, or NULL

crs0

fm_crs object for ⁠(x,y)⁠, or NULL

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_mesh_2d()

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

lattice <- fm_lattice_2d(
  seq(0, 1, length.out = 17),
  seq(0, 1, length.out = 10)
)

## Use the lattice "as-is", without refinement:
mesh <- fm_rcdt_2d_inla(lattice = lattice, boundary = lattice$segm)
mesh <- fm_rcdt_2d_inla(lattice = lattice, extend = FALSE)

## Refine the triangulation, with limits on triangle angles and edges:
mesh <- fm_rcdt_2d(
  lattice = lattice,
  refine = list(max.edge = 0.08),
  extend = FALSE
)

## Add an extension around the lattice, but maintain the lattice edges:
mesh <- fm_rcdt_2d(
  lattice = lattice,
  refine = list(max.edge = 0.08),
  interior = lattice$segm
)

## Only add extension:
mesh <- fm_rcdt_2d(lattice = lattice, refine = list(max.edge = 0.08))

Lattice grids for N dimensions

Description

Construct an N-dimensional lattice grid

Usage

fm_lattice_Nd(x = NULL, ...)

## S3 method for class 'matrix'
fm_lattice_Nd(x = NULL, dims = NULL, values = NULL, ...)

## S3 method for class 'data.frame'
fm_lattice_Nd(x = NULL, ...)

## S3 method for class 'list'
fm_lattice_Nd(x = NULL, dims = NULL, ...)

## S3 method for class 'fm_bbox'
fm_lattice_Nd(x = NULL, dims = NULL, ...)

## S3 method for class ''NULL''
fm_lattice_Nd(x = NULL, ..., dims = NULL)

Arguments

Value

An fm_lattice_Nd object with elements

dims

integer vector

values

the grid coordinate axis values

loc

matrix of constructed grid coordinates

Methods (by class)

• fm_lattice_Nd(`NULL`): Ignores the NULL x and creates a lattice based on values (if non-NULL) and dims unit hypercube lattice grid with dims dimensions.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_mesh_3d()

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

(lattice <- fm_lattice_Nd(
  list(
    seq(0, 1, length.out = 3),
    seq(0, 1, length.out = 4),
    seq(0, 1, length.out = 2)
  )
))

if (requireNamespace("geometry", quietly = TRUE)) {
  (mesh <- fm_delaunay_3d(lattice$loc))
}

Handle lists of fmesher objects

Description

Methods for constructing and manipulating fm_list objects.

Usage

fm_list(x, ..., .class_stub = NULL)

fm_as_list(x, ..., .class_stub = NULL)

## S3 method for class 'fm_list'
c(...)

## S3 method for class 'fm_list'
x[i]

Arguments

Value

An fm_list object, potentially with ⁠fm_{class_stub}_list⁠ added.

Methods (by generic)

• c(fm_list): The ... arguments should be coercible to fm_list objects.

• [: Extract sub-list

Functions

• fm_list(): Convert each element of a list, or convert a single non-list object and return in a list

• fm_as_list(): Convert each element of a list, or convert a single non-list object and return in a list

Examples

fm_as_list(list(fmexample$mesh, fm_segm_join(fmexample$boundary_fm)))

Query the mesh manifold type

Description

Extract a manifold definition string, or a logical for matching manifold type

Usage

fm_manifold(x, type = NULL)

fm_manifold_get(x)

## Default S3 method:
fm_manifold_get(x)

## S3 method for class 'character'
fm_manifold_get(x)

## S3 method for class 'fm_lattice_2d'
fm_manifold_get(x)

## S3 method for class 'fm_lattice_Nd'
fm_manifold_get(x)

fm_manifold_type(x)

fm_manifold_dim(x)

Arguments

Value

fm_manifold(): Either logical (matching manifold type yes/no), or character (the stored manifold, when is.null(type) is TRUE)

fm_manifold_get(): character or NULL

fm_manifold_type(): character or NULL; "M" (curved manifold), "R" (flat space), "S" (generalised spherical space), "T" (general tensor product space), or "G" (metric graph)

fm_manifold_dim(): integer or NULL

Functions

• fm_manifold_get(): Method for obtaining a text representation of the manifold characteristics, e.g. "R1", "R2", "M2", or "T3". The default method assumes that the manifold is stored as a character string in a "manifold" element of the object, so it can be extracted with x[["manifold"]]. Object classes that do not store the information in this way need to implement their own method.

Examples

fm_manifold_get(fmexample$mesh)
fm_manifold(fmexample$mesh)
fm_manifold(fmexample$mesh, "R2")
fm_manifold_type(fmexample$mesh)
fm_manifold_dim(fmexample$mesh)

Make a 1D mesh object

Description

Create a fm_mesh_1d object.

Usage

fm_mesh_1d(
  loc,
  interval = range(loc),
  boundary = NULL,
  degree = 1,
  free.clamped = FALSE,
  ...
)

Arguments

Value

An fm_mesh_1d object

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_2d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

if (require("ggplot2")) {
  m1 <- fm_mesh_1d(c(1, 2, 3, 5, 8, 10),
    boundary = c("neumann", "free")
  )
  weights <- c(2, 3, 6, 3, 4, 7)
  ggplot() +
    geom_fm(data = m1, xlim = c(0.5, 11), weights = weights)

  m2 <- fm_mesh_1d(c(1, 2, 3, 5, 8, 10),
    boundary = c("neumann", "free"),
    degree = 2
  )
  ggplot() +
    geom_fm(data = m2, xlim = c(0.5, 11), weights = weights)

  # The knot interpretation is different for degree=2 and degree=1 meshes:
  ggplot() +
    geom_fm(data = m1, xlim = c(0.5, 11), weights = weights) +
    geom_fm(data = m2, xlim = c(0.5, 11), weights = weights)

  # The `mid` values are the representative basis function midpoints,
  # and can be used to connect degree=2 and degree=1 mesh interpretations:
  m1b <- fm_mesh_1d(m2$mid,
    boundary = c("neumann", "free"),
    degree = 1
  )
  ggplot() +
    geom_fm(data = m2, xlim = c(0.5, 11), weights = weights) +
    geom_fm(data = m1b, xlim = c(0.5, 11), weights = weights)
}

Make a 2D mesh object

Description

Make a 2D mesh object

Usage

fm_mesh_2d(...)

fm_mesh_2d_inla(
  loc = NULL,
  loc.domain = NULL,
  offset = NULL,
  n = NULL,
  boundary = NULL,
  interior = NULL,
  max.edge = NULL,
  min.angle = NULL,
  cutoff = 1e-12,
  max.n.strict = NULL,
  max.n = NULL,
  plot.delay = NULL,
  crs = NULL,
  ...
)

Arguments

Value

An fm_mesh_2d object.

Functions

• fm_mesh_2d_inla(): Legacy method for INLA::inla.mesh.2d() Create a triangle mesh based on initial point locations, specified or automatic boundaries, and mesh quality parameters.

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.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_rcdt_2d(), fm_mesh_2d(), fm_delaunay_2d(), fm_nonconvex_hull(), fm_extensions(), fm_refine()

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_segm(), fm_simplify(), fm_tensor()

Examples

fm_mesh_2d_inla(boundary = fm_extensions(cbind(2, 1), convex = 1, 2))

Special coordinate mappings for fm_mesh_2d projections.

Description

Calculates coordinate mappings for spherical fm_mesh_2d projections. This is an internal function not intended for general use.

Usage

fm_mesh_2d_map(loc, projection = NULL, inverse = TRUE)

fm_mesh_2d_map_lim(loc = NULL, projection = NULL)

Arguments

Value

For fm_mesh_2d_map_lim, a list:

No attempt is made to find minimal limits for partial spherical domains.

Functions

• fm_mesh_2d_map_lim(): Projection extent limit calculations

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_evaluator()

Examples

(loc <- fm_mesh_2d_map(cbind(20, 10), "longlat"))
fm_mesh_2d_map(loc, "longlat", inverse = FALSE)

Construct a 3D tetrahedralisation

Description

Constructs a 3D tetrahedralisation object.

Usage

fm_mesh_3d(loc = NULL, tv = NULL, ...)

fm_delaunay_3d(loc, ...)

Arguments

Value

An fm_mesh_3d object

Functions

• fm_delaunay_3d(): Construct a plain Delaunay triangulation in 3D. Requires the geometry package.

Examples

(m <- fm_mesh_3d(
  matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0), 4, 3, byrow = TRUE),
  matrix(c(1, 2, 3, 4), 1, 4, byrow = TRUE)
))

(m <- fm_delaunay_3d(matrix(rnorm(30), 10, 3)))

Construct the intersection mesh of a mesh and a polygon

Description

Construct the intersection mesh of a mesh and a polygon

Usage

fm_mesh_intersection(mesh, poly)

Arguments

Value

An fm_mesh_2d object

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

segm <- fm_segm(rbind(c(-4, -4), c(4, -4), c(0, 4)),
  is.bnd = TRUE
)
str(m <- fm_mesh_intersection(fmexample$mesh, segm))
plot(fmexample$mesh)
lines(segm, col = 4)
plot(m, edge.color = 2, add = TRUE)

Compute an extension of a spatial object

Description

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, ..., format = "sf", method = "fm")

fm_extensions(
  x,
  convex = -0.15,
  concave = convex,
  ...,
  format = "sf",
  method = "fm"
)

fm_nonconvex_hull_fm(
  x,
  convex = -0.15,
  concave = convex,
  resolution = 40,
  eps = NULL,
  eps_rel = NULL,
  crs = fm_crs(x),
  ...
)

fm_nonconvex_hull_sf(
  x,
  convex = -0.15,
  concave = convex,
  preserveTopology = TRUE,
  dTolerance = NULL,
  crs = fm_crs(x),
  ...
)

## S3 method for class 'sfc'
fm_nonconvex_hull(x, ..., format = "sf", method = "fm")

## S3 method for class 'matrix'
fm_nonconvex_hull(x, ..., format = "sf", method = "fm")

## S3 method for class 'sf'
fm_nonconvex_hull(x, ..., format = "sf", method = "fm")

## S3 method for class 'Spatial'
fm_nonconvex_hull(x, ..., format = "sf", method = "fm")

## S3 method for class 'sfg'
fm_nonconvex_hull(x, ..., format = "sf", method = "fm")

## S3 method for class 'fm_segm'
fm_nonconvex_hull(x, ..., format = "sf", method = "fm")

## S3 method for class 'fm_segm_list'
fm_nonconvex_hull(x, ..., format = "sf", method = "fm")

Arguments

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.

Value

fm_nonconvex_hull() returns an extended object as an sfc polygon object (if format = "sf") or an fm_segm object (if 'format = "fm")

fm_extensions() returns a list of sfc objects.

Functions

• 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.

  The ... arguments are passed on to fm_nonconvex_hull_fm() or fm_nonconvex_hull_sf(), depending on the method argument.

• fm_nonconvex_hull_fm(): fmesher method for fm_nonconvex_hull(), which uses the splancs::nndistF() function to compute nearest-neighbour distances.

• fm_nonconvex_hull_sf(): 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.

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.

References

Gonzalez and Woods (1992), Digital Image Processing

See Also

fm_nonconvex_hull_inla()

Examples

inp <- matrix(rnorm(20), 10, 2)
out <- fm_nonconvex_hull(inp, convex = 1, method = "sf")
plot(out)
points(inp, pch = 20)

out <- fm_nonconvex_hull(inp, convex = 1, method = "fm", format = "fm")
lines(out, col = 2, add = TRUE)
if (TRUE) {
  inp <- sf::st_as_sf(as.data.frame(matrix(1:6, 3, 2)), coords = 1:2)
  bnd <- fm_extensions(inp, convex = c(0.75, 2))
  plot(fm_mesh_2d(boundary = bnd, max.edge = c(0.25, 1)), asp = 1)
}

Non-convex hull computation

Description

Legacy method for INLA::inla.nonconvex.hull(). Use fm_nonconvex_hull() with method = "fm" instead, with either format = "fm" (for compatibility with code expecting fm_segm output) or format = "sf".

Usage

fm_nonconvex_hull_inla(
  x,
  convex = -0.15,
  concave = convex,
  resolution = 40,
  eps = NULL,
  eps_rel = NULL,
  crs = NULL,
  ...
)

fm_nonconvex_hull_inla_basic(
  x,
  convex = -0.15,
  resolution = 40,
  eps = NULL,
  crs = fm_crs(x)
)

Arguments

Value

fm_nonconvex_hull_inla() returns an fm_segm object, for compatibility with inla.nonconvex.hull().

Functions

• fm_nonconvex_hull_inla_basic(): Special method fm_nonconvex_hull_fm() method for concave = 0. Requires splancs::nndistF().

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.

See Also

fm_nonconvex_hull()

Other nonconvex inla legacy support: fm_segm_contour_helper(), fm_simplify_helper()

Examples

fm_nonconvex_hull_inla(cbind(0, 0), convex = 1)

Generate lattice points covering a mesh

Description

Generate terra, sf, or sp lattice locations

Usage

fm_pixels(
  mesh,
  dims = c(150, 150),
  xlim = NULL,
  ylim = NULL,
  mask = TRUE,
  format = "sf",
  minimal = TRUE
)

Arguments

Value

sf, SpatRaster, or SpatialPixelsDataFrame covering the mesh or mask.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

if (require("ggplot2", quietly = TRUE)) {
  dims <- c(50, 50)
  pxl <- fm_pixels(
    fmexample$mesh,
    dims = dims,
    mask = fmexample$boundary_sf[[1]],
    minimal = TRUE
  )
  pxl$val <- rnorm(NROW(pxl)) +
    fm_evaluate(fmexample$mesh, pxl, field = 2 * fmexample$mesh$loc[, 1])
  ggplot() +
    geom_tile(
      data = pxl,
      aes(geometry = geometry, fill = val),
      stat = "sf_coordinates"
    ) +
    geom_sf(data = fm_as_sfc(fmexample$mesh), alpha = 0.2)
}


if (require("ggplot2", quietly = TRUE) &&
  require("terra", quietly = TRUE) &&
  require("tidyterra", quietly = TRUE)) {
  pxl <- fm_pixels(fmexample$mesh,
    dims = c(50, 50), mask = fmexample$boundary_sf[[1]],
    format = "terra"
  )
  pxl$val <- rnorm(NROW(pxl) * NCOL(pxl))
  pxl <-
    terra::mask(
      pxl,
      mask = pxl$.mask,
      maskvalues = c(FALSE, NA),
      updatevalue = NA
    )
  ggplot() +
    geom_spatraster(data = pxl, aes(fill = val)) +
    geom_sf(data = fm_as_sfc(fmexample$mesh), alpha = 0.2)
}

Sparse partial inverse

Description

Compute sparse partial matrix inverse. As of ⁠0.2.0.9010⁠, an R implementation of the Takahashi recursion method, unless a special build of the fmesher package is used.

Usage

fm_qinv(A)

Arguments

Value

A sparse symmetric matrix, with the elements of the inverse of A for the non-zero pattern of A plus potential Cholesky in-fill locations.

Examples

A <- Matrix::Matrix(
  c(2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2),
  4,
  4
)
# Partial inverse:
(S <- fm_qinv(A))
# Full inverse (not guaranteed to be symmetric):
(S2 <- solve(A))
# Matrix symmetry:
c(sum((S - Matrix::t(S))^2), sum((S2 - Matrix::t(S2))^2))
# Accuracy (not that S2 is non-symmetric, and S may be more accurate):
sum((S - S2)[S != 0]^2)

Basis functions for mesh manifolds

Description

Calculate basis functions on fm_mesh_1d() or fm_mesh_2d(), without necessarily matching the default function space of the given mesh object.

Usage

fm_raw_basis(
  mesh,
  type = "b.spline",
  n = 3,
  degree = 2,
  knot.placement = "uniform.area",
  rot.inv = TRUE,
  boundary = "free",
  free.clamped = TRUE,
  ...
)

Arguments

Value

A matrix with evaluated basis function

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_mesh_1d(), fm_mesh_2d(), fm_basis()

Examples

loc <- rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1))
mesh <- fm_mesh_2d(loc, max.edge = 0.15)
basis <- fm_raw_basis(mesh, n = c(4, 5))

proj <- fm_evaluator(mesh, dims = c(10, 10))
image(proj$x, proj$y, fm_evaluate(proj, basis[, 7]), asp = 1)

if (interactive() && require("rgl")) {
  plot_rgl(mesh, col = basis[, 7], draw.edges = FALSE, draw.vertices = FALSE)
}

Refined Constrained Delaunay Triangulation

Description

Computes a refined constrained Delaunay triangulation on R2 or S2.

Usage

fm_rcdt_2d(...)

fm_rcdt_2d_inla(
  loc = NULL,
  tv = NULL,
  boundary = NULL,
  interior = NULL,
  extend = (missing(tv) || is.null(tv)),
  refine = FALSE,
  lattice = NULL,
  globe = NULL,
  cutoff = 1e-12,
  quality.spec = NULL,
  crs = NULL,
  delaunay = TRUE,
  ...
)

fm_delaunay_2d(loc, crs = NULL, ...)

Arguments

Value

An fm_mesh_2d object

Functions

• fm_rcdt_2d_inla(): Legacy method for the INLA::inla.mesh.create() interface

• fm_delaunay_2d(): Construct a plain Delaunay triangulation.

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.

Examples

(m <- fm_rcdt_2d_inla(
  boundary = fm_nonconvex_hull(cbind(0, 0), convex = 5)
))

fm_delaunay_2d(matrix(rnorm(30), 15, 2))

Refine a 2d mesh

Description

Refine an existing mesh

Usage

fm_refine(mesh, refine = list(max.edge = 1))

Arguments

Value

A refined fm_mesh_2d object

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

fm_dof(fmexample$mesh)
fm_dof(fm_refine(fmexample$mesh, refine = list(max.edge = 1)))

Row-wise Kronecker products

Description

Takes two Matrices and computes the row-wise Kronecker product. Optionally applies row-wise weights and/or applies an additional 0/1 row-wise Kronecker matrix product.

Usage

fm_row_kron(M1, M2, repl = NULL, n.repl = NULL, weights = NULL)

Arguments

Value

A Matrix::sparseMatrix object.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

fm_row_kron(rbind(c(1, 1, 0), c(0, 1, 1)), rbind(c(1, 2), c(3, 4)))

Check for potential sp version compatibility issues

Description

Loads the sp package with requireNamespace("sp", quietly = TRUE), and checks and optionally sets the sp evolution status flag if rgdal is unavailable. This function is only needed for backwards compatibility with sp versions before 2.0-0.

Usage

fm_safe_sp(quietly = FALSE, force = FALSE, minimum_version = "1.4-5")

Arguments

Value

Returns (invisibly) FALSE if a potential issue is detected, and give a message if quietly is FALSE. Otherwise returns TRUE

Examples

if (fm_safe_sp()) {
  # Run sp dependent calculations
}

Make a spatial segment object

Description

Make a spatial segment object

Usage

fm_segm(...)

## Default S3 method:
fm_segm(loc = NULL, idx = NULL, grp = NULL, is.bnd = TRUE, crs = NULL, ...)

## S3 method for class 'fm_segm'
fm_segm(..., grp = NULL, grp.default = 0L, is.bnd = NULL)

## S3 method for class 'fm_segm_list'
fm_segm(x, grp = NULL, grp.default = 0L, ...)

fm_segm_join(x, grp = NULL, grp.default = 0L, is.bnd = NULL)

fm_segm_split(x, grp = NULL, grp.default = 0L)

## S3 method for class 'inla.mesh.segment'
fm_segm(..., grp.default = 0)

## S3 method for class 'fm_mesh_2d'
fm_segm(x, boundary = TRUE, grp = NULL, ...)

fm_is_bnd(x)

fm_is_bnd(x) <- value

Arguments

Value

An fm_segm or fm_segm_list object

Methods (by class)

• fm_segm(fm_segm): Join multiple fm_segm objects into a single fm_segm object. If is.bnd is non-NULL, it overrides the input segment information. Otherwise, it checks if the inputs are consistent.

• fm_segm(fm_segm_list): Join fm_segm objects from a fm_segm_list into a single fm_segm object. Equivalent to fm_segm_join(x)

• fm_segm(fm_mesh_2d): Extract the boundary or interior segments of a 2d mesh. If grp is non-NULL, extracts only segments matching the matching the set of groups given by grp.

Functions

• fm_segm(): Create a new fm_segm object.

• fm_segm_join(): Join multiple fm_segm objects into a single fm_segm object. If is.bnd is non-NULL, it overrides the segment information. Otherwise it checks for consistency.

• fm_segm_split(): Split an fm_segm object by grp into an fm_segm_list object, optionally keeping only some groups.

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_simplify(), fm_tensor()

Examples

fm_segm(rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1)), is.bnd = FALSE)
fm_segm(rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1)), is.bnd = TRUE)

fm_segm_join(fmexample$boundary_fm)

fm_segm(fmexample$mesh, boundary = TRUE)
fm_segm(fmexample$mesh, boundary = FALSE)

Contour segment

Description

Helper from legacy INLA::inla.contour.segment()

Usage

fm_segm_contour_helper(
  x = seq(0, 1, length.out = nrow(z)),
  y = seq(0, 1, length.out = ncol(z)),
  z,
  nlevels = 10,
  levels = NULL,
  groups = NULL,
  positive = TRUE,
  eps = NULL,
  eps_rel = NULL,
  crs = NULL
)

Arguments

Value

An fm_segm object

See Also

Other nonconvex inla legacy support: fm_nonconvex_hull_inla(), fm_simplify_helper()

Examples

fm_segm_contour_helper(z = matrix(1:16, 4, 4))

Methods for fm_segm lists

Description

fm_segm lists can be combined into fm_segm_list list objects.

Usage

## S3 method for class 'fm_segm'
c(...)

## S3 method for class 'fm_segm_list'
c(...)

## S3 method for class 'fm_segm_list'
x[i]

Arguments

Value

A fm_segm_list object

Methods (by generic)

• c(fm_segm_list): The ... arguments should be coercible to fm_segm_list objects.

• [: Extract sub-list

Functions

• c(fm_segm): The ... arguments should be fm_segm objects, or coercible with fm_as_segm_list(list(...)).

See Also

fm_as_segm_list()

Examples

m <- c(A = fm_segm(1:2), B = fm_segm(3:4))
str(m)
str(m[2])

Recursive curve simplification.

Description

Simplifies polygonal curve segments by joining nearly co-linear segments.

Uses a variation of the binary splitting Ramer-Douglas-Peucker algorithm, with an ellipse of half-width eps ellipse instead of a rectangle, motivated by prediction ellipse for Brownian bridge.

Usage

fm_simplify(x, eps = NULL, eps_rel = NULL, ...)

Arguments

Details

Variation of Ramer-Douglas-Peucker. Uses width epsilon ellipse instead of rectangle, motivated by prediction ellipse for Brownian bridge.

Value

The simplified fm_segm() object.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

References

Ramer, Urs (1972). "An iterative procedure for the polygonal approximation of plane curves". Computer Graphics and Image Processing. 1 (3): 244–256. doi:10.1016/S0146-664X(72)80017-0

Douglas, David; Peucker, Thomas (1973). "Algorithms for the reduction of the number of points required to represent a digitized line or its caricature". The Canadian Cartographer. 10 (2): 112–122. doi:10.3138/FM57-6770-U75U-7727

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_tensor()

Examples

theta <- seq(0, 2 * pi, length.out = 1000)
(segm <- fm_segm(cbind(cos(theta), sin(theta)),
  idx = seq_along(theta)
))
(segm1 <- fm_simplify(segm, eps_rel = 0.1))
(segm2 <- fm_simplify(segm, eps_rel = 0.2))
plot(segm)
lines(segm1, col = 2)
lines(segm2, col = 3)

(segm <- fm_segm(cbind(theta, sin(theta * 4)),
  idx = seq_along(theta)
))
(segm1 <- fm_simplify(segm, eps_rel = 0.1))
(segm2 <- fm_simplify(segm, eps_rel = 0.2))
plot(segm)
lines(segm1, col = 2)
lines(segm2, col = 3)

Recursive curve simplification.

Description

Helper from legacy INLA::inla.simplify.curve()

Attempts to simplify a polygonal curve by joining nearly colinear segments.

Uses a variation of the binary splitting Ramer-Douglas-Peucker algorithm, with an ellipse of half-width eps ellipse instead of a rectangle, motivated by prediction ellipse for Brownian bridge.

Usage

fm_simplify_helper(loc, idx, eps = NULL, eps_rel = NULL)

Arguments

Details

Variation of Ramer-Douglas-Peucker. Uses width epsilon ellipse instead of rectangle, motivated by prediction ellipse for Brownian bridge.

Value

An index vector into loc specifying the simplified polygonal curve.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

Other nonconvex inla legacy support: fm_nonconvex_hull_inla(), fm_segm_contour_helper()

Examples

theta <- seq(0, 2 * pi, length.out = 1000)
loc <- cbind(cos(theta), sin(theta))
idx <- fm_simplify_helper(loc = loc, idx = 1:nrow(loc), eps = 0.01)
print(c(nrow(loc), length(idx)))
plot(loc, type = "l")
lines(loc[idx, ], col = "red")

fm_sizes

Description

Compute effective sizes of faces/cells and vertices in a mesh

Usage

fm_sizes(...)

## S3 method for class 'fm_mesh_2d'
fm_sizes(mesh, ...)

## S3 method for class 'fm_mesh_3d'
fm_sizes(mesh, ...)

Arguments

Value

A list with elements face and vertex for 2D meshes, or cell and vertex for 3D meshes. The elements are vectors of effective sizes of the faces/cells and vertices, respectively.

Examples

str(fm_sizes(fmexample$mesh))

Split lines at triangle edges

Description

Compute intersections between line segments and triangle edges, and filter out segment of length zero.

Usage

fm_split_lines(mesh, ...)

## S3 method for class 'fm_mesh_2d'
fm_split_lines(mesh, segm, ...)

Arguments

Value

An fm_segm() object with the same crs as the mesh, with an added field origin, that for each new segment gives the originator index into to original segm object for each new line segment.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

mesh <- fm_mesh_2d(
  boundary = fm_segm(
    rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1)),
    is.bnd = TRUE
  )
)
splitter <- fm_segm(rbind(c(0.8, 0.2), c(0.2, 0.8)))
segm_split <- fm_split_lines(mesh, splitter)

plot(mesh)
lines(splitter)
points(segm_split$loc)

Store points in different formats

Description

Convert a matrix of points into different formats.

Usage

fm_store_points(loc, crs = NULL, info = NULL, format = NULL)

Arguments

Value

An sf, data.frame, or SpatialPointsDataFrame object, with optional added information.

Examples

fm_store_points(fmexample$loc, format = "sf")

Split triangles of a mesh into subtriangles

Description

Splits each mesh triangle into (n + 1)^2 subtriangles. The current version drops any edge constraint information from the mesh.

Usage

fm_subdivide(mesh, n = 1, delaunay = FALSE)

Arguments

Value

A refined fm_mesh_2d object

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

Examples

mesh <- fm_rcdt_2d_inla(
  loc = rbind(c(0, 0), c(1, 0), c(0, 1)),
  tv = rbind(c(1, 2, 3))
)
mesh_sub <- fm_subdivide(mesh, 3)
mesh
mesh_sub

plot(mesh_sub, edge.color = 2)

plot(fm_subdivide(fmexample$mesh, 3), edge.color = 2)
plot(fmexample$mesh, add = TRUE, edge.color = 1)

Make a tensor product function space

Description

Tensor product function spaces. The interface and object storage model is experimental and may change.

Usage

fm_tensor(x, ...)

Arguments

Value

A fm_tensor or fm_tensor_list object. Elements of fm_tensor:

fun_spaces

fm_list of function space objects

manifold

character; manifold type summary. Regular subset of Rd "Rd", if all function spaces have type "R", torus connected "Td" if all function spaces have type "S", and otherwise "Md" In all cases, d is the sum of the manifold dimensions of the function spaces.

See Also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify()

Examples

m <- fm_tensor(list(
  space = fmexample$mesh,
  time = fm_mesh_1d(1:5)
))
m2 <- fm_as_tensor(m)
m3 <- fm_as_tensor_list(list(m, m))
c(fm_dof(m$fun_spaces$space) * fm_dof(m$fun_spaces$time), fm_dof(m))
str(fm_evaluator(m, loc = list(space = cbind(0, 0), time = 2.5)))
str(fm_basis(m, loc = list(space = cbind(0, 0), time = 2.5)))
str(fm_fem(m))

Object coordinate transformation

Description

Handle transformation of various inla objects according to coordinate reference systems of crs (from sf::st_crs()), fm_crs, sp::CRS, fm_CRS, or INLA::inla.CRS class.

Usage

fm_transform(x, crs, ...)

## Default S3 method:
fm_transform(x, crs, ..., crs0 = NULL)

## S3 method for class 'NULL'
fm_transform(x, crs, ...)

## S3 method for class 'matrix'
fm_transform(x, crs, ..., passthrough = FALSE, crs0 = NULL)

## S3 method for class 'sf'
fm_transform(x, crs, ..., passthrough = FALSE)

## S3 method for class 'sfc'
fm_transform(x, crs, ..., passthrough = FALSE)

## S3 method for class 'sfg'
fm_transform(x, crs, ..., passthrough = FALSE)

## S3 method for class 'Spatial'
fm_transform(x, crs, ..., passthrough = FALSE)

## S3 method for class 'fm_mesh_2d'
fm_transform(x, crs = fm_crs(x), ..., passthrough = FALSE, crs0 = fm_crs(x))

## S3 method for class 'fm_collect'
fm_transform(x, crs = fm_crs(x), ..., passthrough = FALSE, crs0 = NULL)

## S3 method for class 'fm_lattice_2d'
fm_transform(x, crs = fm_crs(x), ..., passthrough = FALSE, crs0 = fm_crs(x))

## S3 method for class 'fm_segm'
fm_transform(x, crs = fm_crs(x), ..., passthrough = FALSE, crs0 = fm_crs(x))

## S3 method for class 'fm_list'
fm_transform(x, crs, ...)

Arguments

Value

A transformed object, normally of the same class as the input object.

See Also

fm_CRS()

Examples

fm_transform(
  rbind(c(0, 0), c(0, 90), c(0, 91)),
  crs = fm_crs("sphere"),
  crs0 = fm_crs("longlat_norm")
)

Unify coordinates to 3-column matrix

Description

Convert coordinate information to a 3-column matrix. This is mainly an internal function, and the interface may change.

Usage

fm_unify_coords(x, crs = NULL)

## S3 method for class 'NULL'
fm_unify_coords(x, crs = NULL)

## Default S3 method:
fm_unify_coords(x, crs = NULL)

## S3 method for class 'Spatial'
fm_unify_coords(x, crs = NULL)

## S3 method for class 'sf'
fm_unify_coords(x, crs = NULL)

## S3 method for class 'sfc'
fm_unify_coords(x, crs = NULL)

Arguments

Value

A coordinate matrix

Examples

fm_unify_coords(fmexample$loc_sf)

Project integration points to mesh vertices

Description

Compute information for assigning points to the vertices of the covering triangle

Usage

fm_vertex_projection(points, mesh)

Arguments

Value

SpatialPointsDataFrame, sf, tibble, or list of mesh vertices with projected data attached

Examples

head(fm_vertex_projection(list(loc = fmexample$loc), fmexample$mesh))
head(fm_vertex_projection(fmexample$loc_sf, fmexample$mesh))

Extract vertex locations from an fm_mesh_2d

Description

Extracts the vertices of an fm_mesh_2d object.

Usage

fm_vertices(x, format = NULL)

Arguments

Value

An sf, data.frame, or SpatialPointsDataFrame object, with the vertex coordinates, and a .vertex column with the vertex indices.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_centroids()

Examples

if (require("ggplot2", quietly = TRUE)) {
  vrt <- fm_vertices(fmexample$mesh, format = "sf")
  ggplot() +
    geom_sf(data = fm_as_sfc(fmexample$mesh)) +
    geom_sf(data = vrt, color = "red")
}

Internal WKT handling

Description

Conversion between WKT and a tree representation

Usage

fm_wkt_as_wkt_tree(x, ...)

fm_wkt_tree_as_wkt(x, pretty = FALSE, ...)

fm_wkt_tree_get_item(x, item, duplicate = 1)

fm_wkt_tree_set_item(x, item_tree, duplicate = 1)

Arguments

Value

A hierarchical list, describing WKT information as a tree

fm_wkt_tree_as_wkt character; the WKT corresponding to the tree.

fm_wkt_tree_get_item returns the value of an item found in the tree

fm_wkt_tree_set_item returns the modified tree

Examples

str(fm_wkt_as_wkt_tree(fm_crs("longlat_norm")$wkt))

Deprecated functions in fmesher

Description

These functions still attempt to do their job, but will be removed in a future version.

Usage

fm_spTransform(x, ...)

## Default S3 method:
fm_spTransform(x, crs0 = NULL, crs1 = NULL, passthrough = FALSE, ...)

## S3 method for class 'SpatialPoints'
fm_spTransform(x, CRSobj, passthrough = FALSE, ...)

## S3 method for class 'SpatialPointsDataFrame'
fm_spTransform(x, CRSobj, passthrough = FALSE, ...)

fm_sp2segment(...)

Arguments

Functions

• fm_spTransform(): (See fm_transform() instead) Handle transformation of various inla objects according to coordinate reference systems of sp::CRS or INLA::inla.CRS class.

• fm_spTransform(default): The default method handles low level transformation of raw coordinates.

• fm_sp2segment(): in favour of fm_as_segm()

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_transform()

Print objects

Description

Print objects

Usage

## S3 method for class 'fm_segm'
print(x, ..., digits = NULL, verbose = TRUE, newline = TRUE)

## S3 method for class 'fm_segm_list'
print(x, ..., digits = NULL, verbose = FALSE, newline = TRUE)

## S3 method for class 'fm_list'
print(x, ..., digits = NULL, verbose = FALSE, newline = TRUE)

## S3 method for class 'fm_mesh_2d'
print(x, ..., digits = NULL, verbose = FALSE)

## S3 method for class 'fm_mesh_3d'
print(x, ..., digits = NULL, verbose = FALSE)

## S3 method for class 'fm_mesh_1d'
print(x, ..., digits = NULL, verbose = FALSE)

## S3 method for class 'fm_bbox'
print(x, ..., digits = NULL, verbose = TRUE, newline = TRUE)

## S3 method for class 'fm_tensor'
print(x, ..., digits = NULL, verbose = FALSE)

## S3 method for class 'fm_collect'
print(x, ..., digits = NULL, verbose = FALSE)

## S3 method for class 'fm_lattice_2d'
print(x, ..., digits = NULL, verbose = FALSE)

## S3 method for class 'fm_lattice_Nd'
print(x, ..., digits = NULL, verbose = FALSE)

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

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

Arguments

Value

The input object x

Examples

fm_bbox(matrix(1:6, 3, 2))
print(fm_bbox(matrix(1:6, 3, 2)), verbose = FALSE)

print(fmexample$mesh)
print(fmexample$boundary_fm)

print(fm_mesh_1d(c(1, 2, 3, 5, 7), degree = 2))

Barycentric coordinate computation

Description

Locate points and compute triangular barycentric coordinates

Usage

fmesher_bary(mesh_loc, mesh_tv, loc, options)

Arguments

Value

A list with vector index (triangle index) and matrix where (3-column barycentric matrix)

Examples

m <- fmesher_rcdt(list(cet_margin = 1), matrix(0, 1, 2))
b <- fmesher_bary(m$s,
                  m$tv,
                  matrix(c(0.5, 0.5), 1, 2),
                  list())

Barycentric coordinate computation

Description

Locate points and compute triangular barycentric coordinates

Usage

fmesher_bary3d(mesh_loc, mesh_tv, loc, options)

Arguments

Value

A list with vector index (tetra index) and matrix where (4-column barycentric matrix)

Examples

m <- fmesher_mesh3d(list(cet_margin = 1),
                    matrix(rnorm(15), 5, 3),
                    matrix(c(0,1,2,3), 1, 4))
b <- fmesher_bary3d(m$loc,
                    m$tv,
                    matrix(c(0.5, 0.5, 0.5), 1, 3),
                    list())

Finite element matrix computation

Description

Construct finite element structure matrices

Usage

fmesher_fem(mesh_loc, mesh_tv, fem_order_max, aniso, options)

Arguments

Value

A list of matrices

Examples

m <- fmesher_rcdt(list(cet_margin = 1), matrix(0, 1, 2))
b <- fmesher_fem(m$s, m$tv, fem_order_max = 2, aniso = NULL, options = list())

Globe points

Description

Create points on a globe

Usage

fmesher_globe_points(globe)

Arguments

Value

A matrix of points on a unit radius globe

Examples

fmesher_globe_points(1)

3D tetrahedralisation storage

Description

(...)

Usage

fmesher_mesh3d(options, loc, tv)

Arguments

Value

A list of information objects for a generated tetrahedralisation

Examples

m <- fmesher_mesh3d(list(),
                    matrix(c(1,0,0,0,1,0,0,0,1,0,0,0), 4, 3, byrow=TRUE),
                    matrix(c(0,1,2,3), 1, 4, byrow=TRUE))

Compute sparse matrix inverse

Description

Requires RcppEigen which is not compiled in by default. Enable with PKG_CPPFLAGS=-DFMESHER_WITH_EIGEN in src/Makevars and add RcppEigen to the DESCRIPTION LinkingTo field.

Usage

fmesher_qinv(AA)

Arguments

Refined Constrained Delaunay Triangulation

Description

(...)

Usage

fmesher_rcdt(
  options,
  loc,
  tv = NULL,
  boundary = NULL,
  interior = NULL,
  boundary_grp = NULL,
  interior_grp = NULL
)

Arguments

Value

A list of information objects for a generated triangulation

Examples

m <- fmesher_rcdt(list(cet_margin = 1), matrix(0, 1, 2))

Rotationally invariant spherical B-splines

Description

Compute rotationally invariant spherical B-splines on the unit sphere

Usage

fmesher_spherical_bsplines1(loc, n, degree, uniform)

fmesher_spherical_bsplines(loc, n, degree, uniform)

Arguments

Value

A matrix of evaluated b-spline basis functions

Examples

m <- fm_rcdt_2d(globe = 1)
fmesher_spherical_bsplines(m$loc, n = 3, degree = 2, uniform = FALSE)
fmesher_spherical_bsplines1(m$loc[, 3], n = 3, degree = 2, uniform = FALSE)

Split lines at triangle edges

Description

Split a sequence of line segments at triangle edges

Usage

fmesher_split_lines(mesh_loc, mesh_tv, loc, idx, options)

Arguments

Value

A list of line splitting information objects

See Also

fm_split_lines()

Examples

mesh <- fm_mesh_2d(
  boundary = fm_segm(rbind(c(0,0), c(1,0), c(1,1), c(0, 1)), is.bnd = TRUE)
)
splitter <- fm_segm(rbind(c(0.8, 0.2), c(0.2, 0.8)))
segm_split <- fm_split_lines(mesh, splitter)

Subdivide triangles

Description

Subdivide a mesh with congruent and anti-congruent subtriangles

Usage

fmesher_subdivide(
  mesh_loc,
  mesh_tv,
  mesh_boundary,
  mesh_interior,
  subdivisions,
  options
)

Arguments

Value

A list of new loc and tv information

See Also

fm_subdivide()

Examples

mesh <- fm_mesh_2d(
  boundary = fm_segm(rbind(c(0,0), c(1,0), c(1,1), c(0, 1)), is.bnd = TRUE)
)
new_mesh <- fm_subdivide(mesh, n = 3)
plot(new_mesh, edge.color = 2)
plot(mesh, add = TRUE, edge.color = 1)

Example mesh data

Description

This is an example data set used for fmesher package examples.

Usage

fmexample

Format

The data is a list containing these elements:

loc:

A matrix of points.

loc_sf:

An sfc version of loc.

boundary_fm:

A fm_segm_list of two fm_segm objects used in the mesh construction.

boundary_sf:

An sfc list version of boundary.

mesh:

An fm_mesh_2d() object.

Source

Generated by data-raw/fmexample.R.

See Also

fmexample_sp()

Examples

if (require(ggplot2, quietly = TRUE)) {
  ggplot() +
    geom_sf(data = fm_as_sfc(fmexample$mesh)) +
    geom_sf(data = fmexample$boundary_sf[[1]], fill = "red", alpha = 0.5)
}

Add sp data to fmexample

Description

Adds loc_sp and boundary_sp to fmexample for use in sp related code examples and tests.

Usage

fmexample_sp()

Value

Returns a copy of fmexample with loc_sp (SpatialPoints) and boundary_sp (SpatialPolygons) added.

Examples

if (fm_safe_sp()) {
  fmexample_sp()
}

ggplot2 geomes for fmesher related objects

Description

geom_fm is a generic function for generating geomes from various kinds of fmesher objects, e.g. fm_segm and fm_mesh_2d. The function invokes particular methods which depend on the class of the data argument. Requires the ggplot2 package.

Note: geom_fm is not yet a "proper" ggplot2 geom method; the interface may therefore change in the future.

Usage

geom_fm(mapping = NULL, data = NULL, ...)

## S3 method for class 'fm_mesh_2d'
geom_fm(
  mapping = NULL,
  data = NULL,
  ...,
  mappings = NULL,
  defs = NULL,
  crs = NULL,
  mapping_int = deprecated(),
  mapping_bnd = deprecated(),
  defs_int = deprecated(),
  defs_bnd = deprecated()
)

## S3 method for class 'fm_segm'
geom_fm(mapping = NULL, data = NULL, ..., crs = NULL)

## S3 method for class 'fm_mesh_1d'
geom_fm(
  mapping = NULL,
  data = NULL,
  ...,
  mappings = NULL,
  defs = NULL,
  xlim = NULL,
  basis = TRUE,
  knots = TRUE,
  derivatives = FALSE,
  weights = NULL
)

Arguments

Value

A combination of ggplot2 geoms.

Methods (by class)

• geom_fm(fm_mesh_2d): Converts an fm_mesh_2d() object to sf with fm_as_sfc() and uses geom_sf to visualize the triangles and edges.

  The mesh vertices are only plotted if mappings$loc or defs$loc is non-NULL, e.g. defs = list(loc = list()). Default argument settings:

  ... = linewidth = 0.25, color = "grey" # default for triangle mapping
  defs = list(
    int = list(linewidth = 0.5, color = "blue"),
    bnd = list(linewidth = 1, color = "black", alpha = 0),
    loc = list(size = 1, color = "red")
  )
  

• geom_fm(fm_segm): Converts an fm_segm() object to sf with fm_as_sfc() and uses geom_sf to visualize it.

• geom_fm(fm_mesh_1d): Evaluates and plots the basis functions defined by an fm_mesh_1d() object.

Examples

ggplot() +
  geom_fm(data = fmexample$mesh)


m <- fm_mesh_2d(
  cbind(10, 20),
  boundary = fm_extensions(cbind(10, 20), c(25, 65)),
  max.edge = c(4, 10),
  crs = fm_crs("+proj=longlat")
)
ggplot() +
  geom_fm(data = m)
ggplot() +
  geom_fm(data = m, defs = list(loc = list()))
ggplot() +
  geom_fm(data = m, crs = fm_crs("epsg:27700"))

# Compute a mesh vertex based function on a different grid
px <- fm_pixels(
  fm_transform(m, fm_crs("mollweide_globe")),
  dims = c(50, 50) # Speed up the example by lowering the resolution
)
px$fun <- fm_evaluate(m,
  loc = px,
  field = sin(m$loc[, 1] / 5) * sin(m$loc[, 2] / 5)
)
ggplot() +
  geom_tile(aes(geometry = geometry, fill = fun),
    data = px,
    stat = "sf_coordinates"
  ) +
  geom_fm(
    data = m, alpha = 0.2, linewidth = 0.05,
    crs = fm_crs("mollweide_globe")
  )



m1 <- fm_segm(rbind(c(1, 2), c(4, 3), c(2, 4)), is.bnd = TRUE)
m2 <- fm_segm(rbind(c(2, 2), c(3, 4), c(2, 3)), is.bnd = FALSE)
ggplot() +
  geom_fm(data = m1) +
  geom_fm(data = m2)


m <- fm_mesh_1d(
  c(1, 2, 3, 5, 7),
  boundary = c("dirichlet", "neumann"),
  degree = 2
)
ggplot() +
  geom_fm(data = m)

Unit test helpers

Description

Local helper functions for package unit tests

Usage

local_fm_testthat_assign(x, values, envir = parent.frame())

local_fm_testthat_tolerances(
  tolerances = c(1e-04, 0.01, 0.1),
  envir = parent.frame()
)

local_fm_testthat_setup(envir = parent.frame())

Arguments

Value

None

Functions

• local_fm_testthat_assign(): Assign local variable. Useful for easy cleanup of global workspace with withr::deferred_run() when running tests interactively.

• local_fm_testthat_tolerances(): Assign test tolerances Assign local tolerance variables. Useful for easy cleanup of global workspace with withr::deferred_run() when running tests interactively.

• local_fm_testthat_setup(): Initialise environment for tests. To be called either at the top of a testfile, or inside tests.

Examples

outer_fun <- function() {
  fun <- function(envir = parent.frame()) {
    local_fm_testthat_assign("local_var_name", 1:4, envir = envir)
  }
  fun()
  local_var_name
}
exists("local_var_name")
outer_fun()
exists("local_var_name")

Draw a triangulation mesh object

Description

Plots an fm_mesh_2d() object using standard graphics.

Usage

## S3 method for class 'fm_mesh_2d'
lines(x, ..., add = TRUE)

## S3 method for class 'fm_mesh_2d'
plot(
  x,
  col = "white",
  t.sub = seq_len(nrow(x$graph$tv)),
  add = FALSE,
  lwd = 1,
  xlim = range(x$loc[, 1]),
  ylim = range(x$loc[, 2]),
  main = NULL,
  size = 1,
  draw.vertices = FALSE,
  vertex.color = "black",
  draw.edges = TRUE,
  edge.color = rgb(0.3, 0.3, 0.3),
  draw.segments = draw.edges,
  rgl = deprecated(),
  visibility = "front",
  asp = 1,
  axes = FALSE,
  xlab = "",
  ylab = "",
  ...
)

Arguments

Value

None

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

plot.fm_segm(), plot_rgl.fm_mesh_2d()

Examples

mesh <- fm_rcdt_2d(globe = 10)
plot(mesh)

mesh <- fm_mesh_2d(cbind(0, 1), offset = c(1, 1.5), max.edge = 0.5)
plot(mesh)

Draw fm_segm objects.

Description

Draws a fm_segm() object with generic or rgl graphics.

Usage

## S3 method for class 'fm_segm'
plot(x, ..., add = FALSE)

## S3 method for class 'fm_segm'
lines(
  x,
  loc = NULL,
  col = NULL,
  colors = c("black", "blue", "red", "green"),
  add = TRUE,
  xlim = NULL,
  ylim = NULL,
  rgl = FALSE,
  asp = 1,
  axes = FALSE,
  xlab = "",
  ylab = "",
  visibility = "front",
  ...
)

## S3 method for class 'fm_segm_list'
plot(x, ...)

## S3 method for class 'fm_segm_list'
lines(x, ...)

Arguments

Value

None

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

fm_segm(), plot.fm_mesh_2d

Examples

plot(fm_segm(fmexample$mesh, boundary = TRUE))
lines(fm_segm(fmexample$mesh, boundary = FALSE), col = 2)

Low level triangulation mesh plotting

Description

Plots a triangulation mesh using rgl.

Usage

plot_rgl(x, ...)

lines_rgl(x, ..., add = TRUE)

## S3 method for class 'fm_segm'
lines_rgl(
  x,
  loc = NULL,
  col = NULL,
  colors = c("black", "blue", "red", "green"),
  ...,
  add = TRUE
)

## S3 method for class 'fm_mesh_2d'
plot_rgl(
  x,
  col = "white",
  color.axis = NULL,
  color.n = 512,
  color.palette = cm.colors,
  color.truncate = FALSE,
  alpha = NULL,
  lwd = 1,
  specular = "black",
  draw.vertices = TRUE,
  draw.edges = TRUE,
  draw.faces = TRUE,
  draw.segments = draw.edges,
  size = 2,
  edge.color = rgb(0.3, 0.3, 0.3),
  t.sub = seq_len(nrow(x$graph$tv)),
  visibility = "",
  S = deprecated(),
  add = FALSE,
  ...
)

## S3 method for class 'fm_segm'
plot_rgl(x, ..., add = FALSE)

## S3 method for class 'fm_segm_list'
plot_rgl(x, ...)

## S3 method for class 'fm_segm_list'
lines_rgl(x, ...)

Arguments

Value

An rgl device identifier, invisibly.

Author(s)

Finn Lindgren Finn.Lindgren@gmail.com

See Also

plot.fm_mesh_2d()

Examples

if (interactive() && require("rgl")) {
  mesh <- fm_rcdt_2d(globe = 10)
  plot_rgl(mesh, col = mesh$loc[, 1])
}

Print method for fm_basis

Description

Prints information for an fm_basis object.

Usage

## S3 method for class 'fm_basis'
print(x, ..., prefix = "")

Arguments

Value

invisible(x)

See Also

fm_basis()

Examples

print(fm_basis(fmexample$mesh, fmexample$loc, full = TRUE))

Print method for fm_evaluator()

Description

Prints information for an fm_evaluator object.

Usage

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

Arguments

Value

invisible(x)

See Also

fm_evaluator()

Examples

print(fm_evaluator(fmexample$mesh, fmexample$loc))