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Type:	Package
Title:	Triangle Meshes and Related Geometry Tools
Version:	0.6.1
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 (≥ 4.1.0), 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)
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 byJonathan Richard Shewchuk, 1996
NeedsCompilation:	yes
RoxygenNote:	7.3.3
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:	2025-12-11 23:30:01 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:	2025-12-12 07:10:37 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 Lindgrenfinn.lindgren@gmail.com (ORCID) (Finn Lindgren wrote the main code) [copyright holder]

Other contributors:

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

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

• Fabian E. Bachlbachlfab@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 athttps://github.com/inlabru-org/fmesher/issues

Convert a 3D mesh to a 3D rgl triangulation

Description

Extracts a matrix of coordinates of triangles, suitable forpassing torgl::triangles3d().

Usage

as.triangles3d.fm_mesh_3d(obj, subset = NULL, ...)

Arguments

Value

A 3-column matrix of coordinates of triangles, suitable forpassing torgl::triangles3d().

Examples

# Protect against unavailable rgl device by only running interactivelyif (interactive() &&  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")  rgl::axes3d()}

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 callingfunction

fm_call_stack returns a character vector

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

Functions

• fm_call_stack():

• fm_try_callstack(): Inspired byberryFunctions::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 coordinatereference 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 twoelements of theoblique vector are the (longitude, latitude)coordinates for the oblique centre point. The third value (orientation) is acounterclockwise rotation angle for an observer looking at the centre pointfrom outside the sphere. The fourth value is the quasi-longitude (orbitangle) 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), wherelon0 is the longitude at which a satelliteorbit crosses the equator attime=0, when the satellite is at anangleorbit0 further along in its orbit. The orbital angle relativeto the equatorial plane isorbitangle, andv1 andv2are the angular velocities of the planet and the satellite, respectively.Note that "forward" from the satellite's point of view is "to the right" inthe projection.

Whenoblique[2] oroblique[3] are non-zero, the resultingprojection is only correct for perfect spheres.

Value

Either ansp::CRS object or aninla.CRS object,depending on if the coordinate reference system described by the parameterscan be expressed with a puresp::CRS object or not.

An S3inla.CRS object is a list, usually (but not necessarily)containing at least one element:

Functions

• is.na(fm_CRS): Check if afm_CRS hasNA crs information andNAobliqueness

• is.na(inla.CRS): Check if ainla.CRS hasNA crs information andNAobliqueness

Author(s)

Finn LindgrenFinn.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")}

Calculate the area inside segments

Description

Calculate the (signed) area insidefm_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 tofm_collect

Description

Convert objects tofm_collect

Usage

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

Arguments

Value

Anfm_collect object

Functions

• fm_as_collect(): Convert an object tofm_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 aMatrix::dgCMatrix object.

fm_as_dgTMatrix returns aMatrix::dgTMatrix object.

fm_as_unpackedMatrix returns an object of virtual classMatrix::unpackedMatrix.

fm_as_fmesher_sparse returns anfmesher_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(usuallyinla.mesh and other legacy INLA specific classes)tofmesher 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 some⁠fm_*⁠ 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 tofm_lattice_2d

Description

Convert objects tofm_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

Anfm_lattice_2d orfm_lattice_2d_list object

Functions

• fm_as_lattice_2d(): Convert an object tofm_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 tofm_lattice_Nd

Description

Convert objects tofm_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

Anfm_lattice_Md orfm_lattice_Nd_list object

Functions

• fm_as_lattice_Nd(): Convert an object tofm_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 tofm_segm

Description

Convert objects tofm_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

Anfm_mesh_1d orfm_mesh_1d_list object

Functions

• fm_as_mesh_1d(): Convert an object tofm_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 tofm_mesh_2d

Description

Convert objects tofm_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

Anfm_mesh_2d orfm_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 tofm_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 tofm_mesh_3d

Description

Convert objects tofm_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

Anfm_mesh_3d orfm_mesh_3d_list object

Functions

• fm_as_mesh_3d(): Convert an object tofm_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 tofm_segm

Description

Convert objects tofm_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

Anfm_segm orfm_segm_list object

Functions

• fm_as_segm(): Convert an object tofm_segm.

• fm_as_segm_list(): Convert each element, making afm_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: Ansfc_MULTIPOLYGON/LINESTRING/POINT/GEOMETRYCOLLECTION orsfc_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 tofm_tensor

Description

Convert objects tofm_tensor

Usage

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

Arguments

Value

Anfm_tensor object

Functions

• fm_as_tensor(): Convert an object tofm_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 Rsessions.

Usage

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

Arguments

Value

Ansf object with gridded mesh assessment information

Author(s)

Finn LindgrenFinn.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 barycentriccoordinates

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

Afm_bary object, atibble with columnsindex; either

• vector of triangle indices (triangle meshes),

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

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

andwhere, a matrix of barycentric coordinates.

Methods (by class)

• fm_bary(fm_bary): Returns thebary input unchanged

• fm_bary(list): Converts alistbary tofm_bary.In the list elements are unnamed, the namesindex andwhere are assumed.

• fm_bary(tbl_df): Converts atibble::tibble()bary tofm_bary

• fm_bary(fm_mesh_1d): Return anfm_bary object with elementsindex(edge index vector pointing to the first knot of each edge) andwhere (barycentric coordinates,2-column matrices). Usefm_bary_simplex() to obtain the correspondingendpoint knot indices.

  Formethod = "nearest",index contains the index of the nearest meshknot, andwhere is a single-column all-ones matrix.

• fm_bary(fm_mesh_2d): Anfm_bary object with columnsindex (vector oftriangle indices) andwhere (3-column matrix of barycentric coordinates).Points that were not found giveNA entries inindex andwhere.

• fm_bary(fm_mesh_3d): Anfm_bary object with columnsindex (vector oftriangle indices) andwhere (4-column matrix of barycentric coordinates).Points that were not found giveNA entries inindex andwhere.

• fm_bary(fm_lattice_2d): Anfm_bary object with columnsindex (vector oflattice cell indices) andwhere (4-column matrix of barycentriccoordinates). Points that are outside the lattice are givenNA entries inindex andwhere.

• fm_bary(fm_lattice_Nd): Anfm_bary object with columnsindex (vector oflattice cell indices) andwhere2^d-column matrix of barycentriccoordinates). Points that are outside the lattice are givenNA entries inindex andwhere.

See Also

fm_bary_simplex(),fm_bary_loc()

Examples

bary <- fm_bary(fm_mesh_1d(1:4), seq(0, 5, by = 0.5))barystr(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 anfm_baryobject. This acts as the inverse offm_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 meshclass.

Methods (by class)

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

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

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

• fm_bary_loc(fm_lattice_2d): Extract points on a 2D lattice. Implementedformats 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 meshandfm_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 inbary.

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 3Dmesh

• 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 amesh, 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

AsparseMatrix object (iffull = FALSE), or afm_basis object(iffull = TRUE orisTRUE(derivatives)). Thefm_basis object containsat least the projection matrixA and logical vectorok; Ifx_jdenotes the latent basis coefficient for basis functionj, the field isdefined as⁠u(loc_i)=sum_j A_ij x_j⁠ for alli whereok[i] isTRUE,andu(loc_i)=0.0 whereok[i] isFALSE.

Methods (by class)

• fm_basis(fm_mesh_1d): Ifderivatives=TRUE, thefm_basis object containsadditional derivative weight matrices,d1A andd2A,⁠du/dx(loc_i)=sum_j dx_ij w_i⁠.

• fm_basis(fm_mesh_2d): Ifderivatives=TRUE, additional derivative weightmatrices are included in thefull=TRUE output: Derivative weight matricesdx,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 afm_tensor functionspace.

• fm_basis(fm_collect): Evaluates a basis matrix for afm_collect functionspace. Theloc argument must be alist ortibble with elementsloc (the locations) andindex (the indices into the function spacecollection).

• fm_basis(matrix): Creates a newfm_basis object with elementsA andok, from a pre-evaluated basis matrix, including optional additionalelements in the... arguments. If aok isNULL, it is inferred asrep(TRUE, NROW(x)), indicating that all rows correspond to successfulbasis evaluations. Iffull = FALSE,returns the matrix unchanged.

• fm_basis(Matrix): Creates a newfm_basis object with elementsA andok, from a pre-evaluated basis matrix, including optional additionalelements in the... arguments. If aok isNULL, it is inferred asrep(TRUE, NROW(x)), indicating that all rows correspond to successfulbasis evaluations. Iffull = FALSE,returns the matrix unchanged.

• fm_basis(list): Creates a newfm_basis object from a plain listcontaining at least an elementA. If anok element is missing,it is inferred asrep(TRUE, NROW(x$A)). Iffull = FALSE,extracts theA matrix.

• fm_basis(fm_basis): Iffull isTRUE, returnsx unchanged, otherwisereturns theA matrix contained inx.

• fm_basis(fm_evaluator): Extractfm_basis information from anfm_evaluatorobject. Iffull = FALSE, returns theA matrix contained in thefm_basis object.

See Also

fm_raw_basis()

Examples

# Compute basis mapping matrixdim(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 byfm_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

Afm_basis object; a list of evaluator information objects,at least a matrixA and logical vectorok.

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

Forc.fm_bbox(), afm_bbox_list object if.join = FALSE (thedefault) or anfm_bbox object if.join = TRUE.

Methods (by class)

• fm_bbox(list): Construct a bounding box fromprecomputed 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 befm_bbox objects, orcoercible withfm_as_bbox(list(...)).

Functions

• fm_as_bbox_list(): Convert a list to afm_bbox_list object, witheach element converted to anfm_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 optionalweighting.

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 sizen_block timeslength(block).

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

• fm_block_logsumexp_eval(): Evaluate log-sum-exp aggregation.More efficient and numerically stable alternative to tolog(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) foreach blockk, 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 preparingblock,weights, andlog_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 anfm_mesh_2d

Description

Computes the centroids of the triangles of anfm_mesh_2d()object.

Usage

fm_centroids(x, format = NULL)

Arguments

Value

Ansf,data.frame, orSpatialPointsDataFrame object, with the vertexcoordinates, and a.triangle column with the triangle indices.

Author(s)

Finn LindgrenFinn.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 modelis experimental and may change.

Usage

fm_collect(x, ...)

Arguments

Value

Afm_collect orfm_collect_list object.Elements offm_collect:

fun_spaces

fm_list of function space objects

manifold

character; manifold type summary, obtained from thefunction 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 anfm_mesh_2d orfm_mesh_3d object that are connected by edges/triangles,and splitfm_segm objects into connected components.

Usage

fm_components(x, ...)## 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

Forfm_mesh_2d andfm_mesh_3d, returns a list with elementsvertex andtriangle/tetra, vectors ofinteger labels for which connected component they belong, andinfo, adata.frame with columns

Forfm_segm, returns a list of segments, each with componenteither a single closed loop of segments, or an open segment chain.

Author(s)

Finn LindgrenFinn.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 meshconn1$info# Two disconnected componentsconn2$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 thesf::st_contains() (previouslysp::over()) method to findtriangle centroids or vertices insidesf orsp 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 (whentype is'centroid') orvertex indices (whentype is'vertex'). The list has one entry per rowof thesf object. Useunlist(fm_contains(...)) if the combined union isneeded.

Author(s)

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

Examples

# Create a polygon and a meshobj <- 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 polygonfm_contains(obj, mesh, type = "vertex")## 3 triangles found in the polygonfm_contains(obj, mesh)## Multiple transformations can lead to slightly different results## due to edge cases:## 4 triangles found in the polygonfm_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 differentdimensions and multiplies their weights accordingly.If the object defining points in a particular dimension has noweights attached to it all weights are assumed to be 1.

Usage

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

Arguments

Value

Adata.frame,sf, orSpatialPointsDataFrame ofmultidimensional 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 ansf::crs orfm_crs object from a spatial object, orconvert crs information to construct a newsf::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 twoelements of theoblique vector are the (longitude, latitude)coordinates for the oblique centre point. The third value (orientation) is acounter-clockwise rotation angle for an observer looking at the centre pointfrom outside the sphere. The fourth value is the quasi-longitude (orbitangle) 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), wherelon0 is the longitude at which a satelliteorbit crosses the equator attime=0, when the satellite is at anangleorbit0 further along in its orbit. The orbital angle relativeto the equatorial plane isorbitangle, andv1 andv2are the angular velocities of the planet and the satellite, respectively.Note that "forward" from the satellite's point of view is "to the right" inthe projection.

Whenoblique[2] oroblique[3] are non-zero, the resultingprojection is only correct for perfect spheres.

Value

Either ansf::crs object or anfm_crs object,depending on if the coordinate reference system described by the parameterscan be expressed with a purecrs object or not.

Acrs object (sf::st_crs()) or afm_crs object.An S3fm_crs object is a list with elementscrs andoblique.

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 thetensor product space.

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

• 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 tofm_crs(x, oblique = NA, ...)whenx is afm_crs object.

• $: For afm_crs objectx,x$name calls the accessormethod for thecrs object inside it. Ifname is "crs", the internal crsobject itself is returned. Ifname is "oblique", the internal obliqueangle parameter vector is returned.

Functions

• fm_crs_oblique(): ReturnNA 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 LindgrenFinn.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) <- valuefm_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 withfm_crs(value),fm_crs(value, oblique = NA),fm_CRS(value), orfm_CRS(value, oblique = NA),depending on the type ofx.

• fm_crs_oblique(x) <- value: Assigns newoblique 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 thespecified sense (see thecrsonly 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 areNULL orNA.Logically equivalent to eitheris.na(fm_crs(x)) oris.na(fm_crs(x, oblique = NA)), but with a short-cut pre-check foris.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 hasNULL orNA CRSinformation. If notNULL,is.na(fm_crs(x)) is returned. This allows theinput to be e.g. a proj4string or epsg number, since the defaultfm_crs()method passes its argument on tosf::st_crs().

• is.na(fm_crs): Check if afm_crs hasNA crs information andNA 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 acrsorfm_crs() projection, with optional graticules (transformed parallelsand 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 graticuleinformation for a givenCRS orfm_crs() and optionally plots thegraticules.Returns a list with two elements,meridians andparallels, which areSpatialLines objects.

• fm_crs_tissot(): Constructs Tissot indicatrix informationfor a givenCRS orfm_crs() and optionally plots the indicatrices.Returns a list with one element,tissot, which is aSpatialLines object.

Author(s)

Finn LindgrenFinn.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) <- valuefm_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) <- valuefm_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

Forfm_wkt_unit_params, alist of named unit definitions

Forfm_wkt_get_lengthunit, alist of length units used in the wkt string, excluding the ellipsoid radiusunit.

Forfm_wkt_set_lengthunit, aWKT2 string with altered length units.Note that the length unit for the ellipsoid radius is unchanged.

Forfm_crs_get_lengthunit, alist of length units used in the wkt string, excluding the ellipsoid radiusunit.

For⁠fm_length_unit<-⁠, a crs object withaltered length units.Note that the length unit for the ellipsoid radius is unchanged.

Functions

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

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

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

• fm_wkt_projection_type(): Seefm_wkt_tree_projection_type

• fm_crs_projection_type(): Seefm_wkt_tree_projection_type

• fm_crs_bounds(): Returns bounds information for a projection, asa list with elementstype ("rectangle" or "ellipse"),xlim,ylim, andpolygon.

Author(s)

Finn LindgrenFinn.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"(iffm_crs_is_geocent(crs) isTRUE). ReturnsNA_character_ if the crsis 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 thepoint set. For multi-domain spaces (e.g.fm_tensor() andfm_collect()), a vector of upper bounds for each domain is returned.

Author(s)

Finn LindgrenFinn.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 functiondefined 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

Anfm_evaluator object

Methods (by class)

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

Functions

• fm_evaluate(): Returns the field function evaluated at the locations determined by anfm_evaluator object.fm_evaluate(mesh, field = field, ...) is ashortcut tofm_evaluate(fm_evaluator(mesh, ...), field = field).

• fm_evaluator(): Returns anfm_evaluator list object with evaluation information.Theproj element is afm_basis object, containing (at least)a mapping matrixA and a logical vectorok, that indicates whichlocations were mappable to the input mesh.Forfm_mesh_2dinput,proj also contains abaryfm_bary object, with thebarycentric coordinates within the triangle each input location falls in.

• fm_evaluator(default): The default method callsfm_basis and createsa basicfm_evaluator object

• fm_evaluator(fm_mesh_3d): The... arguments are passed on tofm_evaluator_lattice() if noloc orlattice is provided.

• fm_evaluator(fm_mesh_2d): The... arguments are passed on tofm_evaluator_lattice() if noloc orlattice is provided.

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

• fm_evaluator_lattice(default): Creates anfm_lattice_2d() object, by default covering the input mesh.

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

• fm_evaluator_lattice(fm_mesh_2d): Creates anfm_lattice_2d() object, by default covering the input mesh.

Author(s)

Finn LindgrenFinn.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 elementsc0,c1,g1,g2,etc.Whenmesh$degree == 2, alsog01,g02, andg12.

fm_fem.fm_mesh_2d: A list with elementsc0,c1,g1,va,ta, and more iforder > 1. Whenaniso is non-NULL, alsog1anisomatrices, etc.

fm_fem.fm_tensor: A list with elementscc,g1,g2.

fm_fem.fm_collect: A list with elementsc0,c1,g1,g2, etc, andcc (c0 for every model exceptfm_mesh_1d withdegree=2, for which it isc1). If the base type for the collectionprovidesva andta values, those are also returned.

fm_fem.fm_mesh_3d: A list with elementsc0,c1,g1,g2,va,ta, and more iforder > 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 vectorcolors and numeric vectoralpha

Author(s)

Finn LindgrenFinn.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 asampled field. Ifloc isNULL, thefm_dof(mesh) basis weights aregiven. Otherwise, the evaluated field at thenrow(loc) locationslocare given (from version⁠0.1.4.9001⁠)

Functions

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

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

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

• fm_sample(): Generaten samples based on a sparse precision matrixQ

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

from⁠0.3.0.9001⁠. Createhexagon lattice points within a boundary. By default, the hexagonal latticeis anchored at the coordinate system origin, so that grids with differentbut overlapping boundaries will have matching points.

Usage

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

Arguments

Value

Ansfc object with points, ifmeta isFALSE (default), or ifmeta=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 pointsoutside of aedge_len * buffer_n distance from the boundary

grid_n

integer with the number of points in each direction prior tofiltering

align

numeric with the alignment coordinates of the hexagon lattice

Author(s)

Man Ho SuenM.H.Suen@sms.ed.ac.uk,Finn LindgrenFinn.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 SuenM.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, ..., extra = 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

Atibble,sf, orSpatialPointsDataFrame of 1Dand 2D integration points, including aweight column, a.block column,and a matrix column.block_origin.The.block column is used to identify the integrationblocks defined by the samplers. The.block_origin collects the originalsubdomain 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 vector defining points for summation (up to⁠0.5.0⁠, length 2 vectorswere interpreted as intervals. From 0.6.0 intervals must be specified asrows of a 2-column matrix);

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

  • A list of such vectors or matrices

  • A tibble with a named column containing a vector/matrix/list as above,and optionally aweight column.

• fm_int(fm_mesh_2d):fm_mesh_2d integration. Any sampler class with anassociatedfm_int_mesh_2d() method is supported.

Examples

# Integration on the interval (2, 3.5) with Simpson's ruleips <- 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 pointsmesh <- 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 intervalsips <- 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 onfm_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

Alist,sf, orSpatial object withpoint coordinate information and additional columnsweight 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 columnsloc andweight withintegration points for the mesh

Author(s)

Finn LindgrenFinn.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, ..., extra = NULL)

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 forfm_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

Anfm_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 byfm_transform()

segm

fm_segm object

crs

fm_crs object forloc, orNULL

crs0

fm_crs object for⁠(x,y)⁠, orNULL

Author(s)

Finn LindgrenFinn.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

Anfm_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 theNULLx and creates a latticebased onvalues (if non-NULL) anddims unit hypercubelattice grid withdims dimensions.

Author(s)

Finn LindgrenFinn.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 manipulatingfm_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

Anfm_list object, potentially with⁠fm_{class_stub}_list⁠added.

Methods (by generic)

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

• [: Extract sub-list

Functions

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

• fm_as_list(): Convert each element of a list, or convert a singlenon-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 matchingmanifold 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, whenis.null(type) isTRUE)

fm_manifold_get():character orNULL

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 themanifold characteristics, e.g. "R1", "R2", "M2", or "T3". The defaultmethod assumes that the manifold is stored as acharacter string in a"manifold" element of the object, so it can be extracted withx[["manifold"]].Object classes that do not store the information in this way need toimplement 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 afm_mesh_1d object.

Usage

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

Arguments

Value

Anfm_mesh_1d object

Author(s)

Finn LindgrenFinn.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

Anfm_mesh_2d object.

Functions

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

INLA compatibility

For mesh and curve creation, thefm_rcdt_2d_inla(),fm_mesh_2d_inla(),andfm_nonconvex_hull_inla() methods will keep the interface syntax used byINLA::inla.mesh.create(),INLA::inla.mesh.2d(), andINLA::inla.nonconvex.hull() functions, respectively, whereas thefm_rcdt_2d(),fm_mesh_2d(), andfm_nonconvex_hull() interfaces may bedifferent, and potentially change in the future.

Author(s)

Finn LindgrenFinn.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 forfm_mesh_2d projections.

Description

Calculates coordinate mappings for sphericalfm_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

Forfm_mesh_2d_map_lim, a list:

No attempt ismade to find minimal limits for partial spherical domains.

Functions

• fm_mesh_2d_map_lim(): Projection extent limit calculations

Author(s)

Finn LindgrenFinn.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

Anfm_mesh_3d object

Functions

• fm_delaunay_3d(): Construct a plain Delaunay triangulation in 3D.Requires thegeometry 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

(from version⁠0.5.0.9006⁠)

Usage

fm_mesh_intersection(mesh, poly)

Arguments

Value

Anfm_mesh_2d object

Author(s)

Finn LindgrenFinn.Lindgren@gmail.com

Examples

segm <- fm_segm(  rbind(c(-4, -4), c(4, -3), c(0, 4)),  is.bnd = TRUE)(m <- fm_mesh_intersection(fmexample$mesh, segm))plot(fmexample$mesh)lines(segm, col = 4)plot(m, edge.color = 2, add = TRUE)# Non-overlapping additionsegm2 <- fm_segm(c(  segm,  fm_segm(    rbind(c(-4, 0), c(-3, 0), c(-2, 2)),    is.bnd = TRUE  )))(m2 <- fm_mesh_intersection(fm_subdivide(fmexample$mesh, 2), segm2))m2_int <- fm_int(m2)plot(m2, edge.color = 2)lines(segm2, col = 4)plot(fmexample$mesh, edge.color = 1, add = TRUE)plot(m2_int$geometry, pch = 20, cex = sqrt(m2_int$weight) * 4, add = TRUE)# Add a hole and restrict to inner part of the original mesh# To avoid issues with intersecting boundary segments, compute# two separate intersection calculations in sequence.# To allow this to be done as a single step, would need to first# cross-intersect the boundary segments.inner_bnd <- fm_segm(fmexample$mesh, boundary = FALSE)fm_is_bnd(inner_bnd) <- TRUEsegm3 <- fm_segm(c(  segm2,  fm_segm(    rbind(c(-1.5, 0), c(1, -0.5), c(0, -1.5)),    is.bnd = TRUE  )))(m3 <- fm_mesh_intersection(  fm_mesh_intersection(    fm_subdivide(fmexample$mesh, 2),    inner_bnd  ),  segm3))m3_int <- fm_int(m3)plot(fmexample$mesh)plot(m3, edge.color = 2, add = TRUE)lines(segm3, col = 4)plot(m3_int$geometry, pch = 20, cex = sqrt(m3_int$weight) * 4, add = TRUE)# Spherical mesh(m_s2 <- fm_rcdt_2d(globe = 4))segm4 <- fm_segm(  rbind(    c(1, 0, 0.1) / sqrt(1.01),    c(0, 1, 0),    c(-1, -1, 1) / sqrt(3)  ),  is.bnd = TRUE)(m4 <- fm_mesh_intersection(fm_subdivide(m_s2, 1), segm4))m4_int <- fm_int(m4)plot(m_s2)plot(m4, edge.color = 2, add = TRUE)plot(m4_int$geometry, pch = 20, cex = sqrt(m4_int$weight) * 8, add = TRUE)

Compute an extension of a spatial object

Description

Constructs a potentially nonconvex extension of a spatial object byperforming dilation byconvex + concave followed byerosion byconcave. This is equivalent to dilation byconvex followedby closing (dilation + erosion) byconcave.

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 byconvex, followed by closing byconcave, with minimum concave curvature radiusconcave. Ifthe dilated set has no gaps of width between

2 \textrm{convex}(\sqrt{1+2\textrm{concave}/\textrm{convex}} - 1)

and2\textrm{concave}, then the minimum convex curvatureradius isconvex.

The implementation is based on the identity

\textrm{dilation}(a) \&\textrm{closing}(b) = \textrm{dilation}(a+b) \& \textrm{erosion}(b)

where all operationsare with respect to disks with the specified radii.

Whenconvex,concave, ordTolerance are negative,fm_diameter * abs(...) is used instead.

Value

fm_nonconvex_hull() returns an extended object as ansfc polygonobject (ifformat = "sf") or anfm_segm object (if 'format = "fm")

fm_extensions() returns a list ofsfc objects.

Functions

• fm_extensions(): Constructs a potentially nonconvex extension of a spatial object byperforming dilation byconvex + concave followed byerosion byconcave. This is equivalent to dilation byconvex followedby closing (dilation + erosion) byconcave.

  The... arguments are passed on tofm_nonconvex_hull_fm()orfm_nonconvex_hull_sf(), depending on themethod argument.

• fm_nonconvex_hull_fm():fmesher method forfm_nonconvex_hull(),which uses thesplancs::nndistF() function to compute nearest-neighbourdistances.

• fm_nonconvex_hull_sf(): Differs fromsf::st_buffer(x, convex) followed bysf::st_concave_hull() (available from GEOS 3.11)in how the amount of allowed concavity is controlled.

INLA compatibility

For mesh and curve creation, thefm_rcdt_2d_inla(),fm_mesh_2d_inla(),andfm_nonconvex_hull_inla() methods will keep the interface syntax used byINLA::inla.mesh.create(),INLA::inla.mesh.2d(), andINLA::inla.nonconvex.hull() functions, respectively, whereas thefm_rcdt_2d(),fm_mesh_2d(), andfm_nonconvex_hull() interfaces may bedifferent, 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 forINLA::inla.nonconvex.hull().Usefm_nonconvex_hull() withmethod = "fm" instead, witheitherformat = "fm" (for compatibility with codeexpectingfm_segm output) orformat = "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 anfm_segmobject, for compatibility withinla.nonconvex.hull().

Functions

• fm_nonconvex_hull_inla_basic(): Special methodfm_nonconvex_hull_fm()method forconcave = 0. Requiressplancs::nndistF().

INLA compatibility

For mesh and curve creation, thefm_rcdt_2d_inla(),fm_mesh_2d_inla(),andfm_nonconvex_hull_inla() methods will keep the interface syntax used byINLA::inla.mesh.create(),INLA::inla.mesh.2d(), andINLA::inla.nonconvex.hull() functions, respectively, whereas thefm_rcdt_2d(),fm_mesh_2d(), andfm_nonconvex_hull() interfaces may bedifferent, and potentially change in the future.

See Also

fm_nonconvex_hull()

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

Examples

# New preferred method for "fm_segm" output:fm_nonconvex_hull(cbind(0, 0), convex = 1, format = "fm")# Deprecated:suppressWarnings(  fm_nonconvex_hull_inla(cbind(0, 0), convex = 1))

Generate lattice points covering a mesh

Description

Generateterra,sf, orsp lattice locations

Usage

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

Arguments

Value

sf,SpatRaster, orSpatialPixelsDataFrame covering the mesh ormask.

Author(s)

Finn LindgrenFinn.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 of⁠0.2.0.9010⁠, an Rimplementation of the Takahashi recursion method, unless a special build ofthefmesher package is used.

Usage

fm_qinv(A)

Arguments

Value

A sparse symmetric matrix, with the elements of the inverse ofAfor the non-zero pattern ofA 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 onfm_mesh_1d() orfm_mesh_2d(),without necessarily matching the default function space of the given meshobject.

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 LindgrenFinn.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

Anfm_mesh_2d object

Functions

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

• fm_delaunay_2d(): Construct a plain Delaunay triangulation.

INLA compatibility

For mesh and curve creation, thefm_rcdt_2d_inla(),fm_mesh_2d_inla(),andfm_nonconvex_hull_inla() methods will keep the interface syntax used byINLA::inla.mesh.create(),INLA::inla.mesh.2d(), andINLA::inla.nonconvex.hull() functions, respectively, whereas thefm_rcdt_2d(),fm_mesh_2d(), andfm_nonconvex_hull() interfaces may bedifferent, 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 refinedfm_mesh_2d object

Author(s)

Finn LindgrenFinn.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. Optionallyapplies row-wise weights and/or applies an additional 0/1 row-wise Kroneckermatrix product.

Usage

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

Arguments

Value

AMatrix::sparseMatrix object.

Author(s)

Finn LindgrenFinn.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 potentialsp version compatibility issues

Description

Loads the sp package withrequireNamespace("sp", quietly = TRUE), andchecks and optionally sets thesp evolution status flag ifrgdal isunavailable.This function is only needed for backwards compatibility withsp versionsbefore2.0-0.

Usage

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

Arguments

Value

Returns (invisibly)FALSE if a potential issue is detected, andgive a message ifquietly isFALSE. Otherwise returnsTRUE

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

Anfm_segm orfm_segm_list object

Methods (by class)

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

• fm_segm(fm_segm_list): Joinfm_segm objects from afm_segm_list intoa singlefm_segm object. Equivalent tofm_segm_join(x)

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

Functions

• fm_segm(): Create a newfm_segm object.

• fm_segm_join(): Join multiplefm_segm objects into a singlefm_segmobject. Ifis.bnd is non-NULL, it overrides the segment information.Otherwise it checks for consistency.

• fm_segm_split(): Split anfm_segm object bygrp into anfm_segm_listobject, 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 legacyINLA::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

Anfm_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 intofm_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

Afm_segm_list object

Methods (by generic)

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

• [: Extract sub-list

Functions

• c(fm_segm): The... arguments should befm_segmobjects, or coercible withfm_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 nearlyco-linear segments.

Uses a variation of the binary splitting Ramer-Douglas-Peucker algorithm,with an ellipse of half-widtheps ellipse instead of a rectangle, motivatedby 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 simplifiedfm_segm() object.

Author(s)

Finn LindgrenFinn.Lindgren@gmail.com

References

Ramer, Urs (1972). "An iterative procedure for the polygonal approximation ofplane 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 ofthe number of points required to represent a digitized line or itscaricature".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 legacyINLA::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-widtheps ellipse instead of a rectangle, motivatedby 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 intoloc specifying the simplified polygonalcurve.

Author(s)

Finn LindgrenFinn.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

Alist with elementsface andvertex for 2D meshes, orcellandvertex for 3D meshes. The elements are vectors of effective sizes ofthe 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

Anfm_segm() object with the same crs as the mesh,with an added fieldorigin, that for each new segment gives theoriginator index into to originalsegm object for each new line segment.

Author(s)

Finn LindgrenFinn.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

Ansf,data.frame, orSpatialPointsDataFrame object, withoptional 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 refinedfm_mesh_2d object, with addedbary information(anfm_bary() object), that can be used for interpolating functions fromthe original mesh to the new mesh (from version⁠0.5.0.9002⁠).

Author(s)

Finn LindgrenFinn.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)meshmesh_sub# Difference should be zero for flat triangle meshes:sum((mesh_sub$loc - fm_basis(mesh, mesh_sub$bary) %*% mesh$loc)^2)plot(mesh_sub, edge.color = 2)plot(fm_subdivide(fmexample$mesh, 3), edge.color = 2)plot(fmexample$mesh, add = TRUE, edge.color = 1)

Extract a subset of a mesh

Description

(from version⁠0.5.0.9003⁠)Constructs a new mesh based on a subset of the triangles of an existing mesh.The current version drops any edge constraint information from the mesh.

Usage

fm_subset(mesh, t_sub)

Arguments

Value

A subset mesh.

Author(s)

Finn LindgrenFinn.Lindgren@gmail.com

Examples

mesh_sub <- fm_subset(fmexample$mesh, 1:100)mesh_subplot(mesh_sub)if (requireNamespace("geometry", quietly = TRUE)) {  print(m <- fm_delaunay_3d(matrix(rnorm(30), 10, 3)))  print(fm_subset(m, seq_len(min(5, nrow(m$graph$tv)))))}

Make a tensor product function space

Description

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

Usage

fm_tensor(x, ...)

Arguments

Value

Afm_tensor orfm_tensor_list object. Elements offm_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 functionspaces.

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 coordinatereference systems ofcrs (fromsf::st_crs()),fm_crs,sp::CRS,fm_CRS, orINLA::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 asthe 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 coveringtriangle

Usage

fm_vertex_projection(points, mesh)

Arguments

Value

SpatialPointsDataFrame,sf,tibble, orlist of meshvertices 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 anfm_mesh_2d

Description

Extracts the vertices of anfm_mesh_2d object.

Usage

fm_vertices(x, format = NULL)

Arguments

Value

Ansf,data.frame, orSpatialPointsDataFrame object, with the vertexcoordinates, and a.vertex column with the vertex indices.

Author(s)

Finn LindgrenFinn.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 thetree

fm_wkt_tree_set_item returns the modified tree

Examples

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

Add or remove Z/M information

Description

Add and/or remove Z and/or M information from simple feature geometries.

Usage

fm_zm(x, ...)## S3 method for class 'sf'fm_zm(x, ...)## S3 method for class 'sfc'fm_zm(x, ..., add = NULL, remove = NULL, target = NULL)## S3 method for class 'list'fm_zm(x, ..., add = NULL, remove = NULL, target = NULL)## S3 method for class 'sfg'fm_zm(x, ..., add = NULL, remove = NULL, target = NULL)## S3 method for class 'numeric'fm_zm(x, ..., add = NULL, remove = NULL, target = NULL, input = NULL)## S3 method for class 'matrix'fm_zm(x, ..., add = NULL, remove = NULL, target = NULL, input = NULL)fm_zm_input(x, ...)## S3 method for class 'sf'fm_zm_input(x, ...)## S3 method for class 'sfc'fm_zm_input(x, ...)## S3 method for class 'list'fm_zm_input(x, ...)## S3 method for class 'sfg'fm_zm_input(x, ...)## S3 method for class 'numeric'fm_zm_input(x, ..., input = NULL)## S3 method for class 'matrix'fm_zm_input(x, ..., input = NULL)fm_zm_target(input, add = NULL, remove = NULL, target = NULL)

Arguments

Value

An object of the same class asx, with modified Z/M dimensions.

Functions

• fm_zm_input(): Find the set of distinct XY/XYZ/XYM/XYZM types

• fm_zm_target(): Determines the target XY/XYZ/XYM/XYZM format

Author(s)

Finn LindgrenFinn.Lindgren@gmail.com

See Also

sf::st_zm() that supports a subset of these operations.

Examples

fm_zm(fmexample$loc_sf, add = "Z")fm_zm_input(fmexample$loc_sf)fm_zm_target(c("XY", "XYZ"))fm_zm_target("XY", add = "Z")fm_zm_target(c("XY", "XYZM"), remove = "M")

Deprecated functions in fmesher

Description

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

Usage

fm_mesh_components(...)fm_int_object(...)fm_sp2segment(...)

Arguments

Functions

• fm_mesh_components(): Backwards compatibility forfm_components(), deprecated sinceversion⁠0.4.0.9001⁠, disabled since⁠0.6.0⁠

• fm_int_object(): Deprecated function since⁠0.5.0.9013⁠;usenew_fm_int() instead.

• fm_sp2segment(): in favouroffm_as_segm()

Author(s)

Finn LindgrenFinn.Lindgren@gmail.com

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 objectx

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 vectorindex (triangle index) and matrixwhere(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 vectorindex (tetra index) and matrixwhere(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 withPKG_CPPFLAGS=-DFMESHER_WITH_EIGEN insrc/Makevars and addRcppEigento theDESCRIPTIONLinkingTo 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)

Spherical harmonics

Description

Compute spherical harmonics on the unit sphere

Usage

fmesher_spherical_harmonics(loc, max_order, rot_inv)

Arguments

Value

A matrix of evaluated spherical harmonic basis functions

Examples

m <- fm_rcdt_2d(globe = 1)fmesher_spherical_harmonics(m$loc, max_order = 2, TRUE)fmesher_spherical_harmonics(m$loc, max_order = 2, 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 newloc andtv information, andbary_index andbary_where containing the fm_bary information for the new points.Can be e.g. used to construct an interpolation mapping matrix from the oldto new mesh.

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 forfmesher package examples.

Usage

fmexample

Format

The data is a list containing these elements:

loc:

Amatrix of points.

loc_sf:

Ansfc version ofloc.

boundary_fm:

Afm_segm_list of twofm_segm objects used inthe mesh construction.

boundary_sf:

Ansfc list version ofboundary.

mesh:

Anfm_mesh_2d() object.

Source

Generated bydata-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

Addsloc_sp andboundary_sp tofmexample for useinsp related code examples and tests.

Usage

fmexample_sp()

Value

Returns a copy offmexample withloc_sp (SpatialPoints) andboundary_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 offmesher objects, e.g.fm_segm andfm_mesh_2d.The function invokes particular methods which dependon theclass of thedata argument.Requires theggplot2 package.

Note:geom_fm is not yet a "proper"ggplot2 geom method; the interfacemay 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)## 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 ofggplot2 geoms.

Methods (by class)

• geom_fm(fm_mesh_2d): Converts anfm_mesh_2d() object tosf withfm_as_sfc() and usesgeom_sf to visualize the triangles and edges.

  The mesh vertices are only plotted ifmappings$loc ordefs$locis non-NULL, e.g.defs = list(loc = list()). Default argument settings:

  ... = linewidth = 0.25, color = "grey" # default for triangle mappingdefs = 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 anfm_segm() object tosf withfm_as_sfc() and usesgeom_sf to visualize it.

• geom_fm(fm_mesh_1d): Evaluates and plots the basis functions defined by anfm_mesh_1d() object.

Examples

ggplot() +  geom_fm(data = fmexample$mesh)m <- fm_mesh_2d(  cbind(10, 20),  boundary = fm_extensions(cbind(10, 20), c(25, 65)),  max.edge = c(4, 10),  crs = fm_crs("+proj=longlat"))ggplot() +  geom_fm(data = m)ggplot() +  geom_fm(data = m, defs = list(loc = list()))ggplot() +  geom_fm(data = m, crs = fm_crs("epsg:27700"))# Compute a mesh vertex based function on a different gridpx <- fm_pixels(  fm_transform(m, fm_crs("mollweide_globe")),  dims = c(50, 50) # Speed up the example by lowering the resolution)px$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 cleanupof global workspace withwithr::deferred_run() when running testsinteractively.

• local_fm_testthat_tolerances(): Assign test tolerancesAssign local tolerance variables. Useful for easy cleanupof global workspace withwithr::deferred_run() when running testsinteractively.

• 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")

Construct integration scheme objects

Description

Constructor method for integration scheme objects, allowingdefault construction of.block information. Primarily meant for internaluse, but can be used to manually create data of the same structure asfm_int() output.

Usage

new_fm_int(  object,  blocks = FALSE,  weight = NULL,  name = NULL,  override = FALSE)

Arguments

Value

A tibble or sf/tibble object. May acquire additional classattributes in the future.

See Also

fm_int()

Examples

new_fm_int(1:4, blocks = TRUE, weight = c(1, 2, 1, 3), name = "z")

Draw a triangulation mesh object

Description

Plots anfm_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 LindgrenFinn.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)

Drawfm_segm objects.

Description

Draws afm_segm() object with generic orrglgraphics.

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,  asp = 1,  axes = FALSE,  xlab = "",  ylab = "",  visibility = "front",  rgl = deprecated(),  ...)## S3 method for class 'fm_segm_list'plot(x, ...)## S3 method for class 'fm_segm_list'lines(x, ...)

Arguments

Value

None

Author(s)

Finn LindgrenFinn.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 usingrgl.

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