Package 'tissot'

Subset an indicatrix_list

Description

Subset an indicatrix_list

Usage

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

Arguments

x	an indicatrix_list
i	indices

Value

An indicatrix_list with the selected elements

---

Compute Tissot indicatrix ellipse geometry

Description

Generates indicatrix objects for plotting at each point. Returns an indicatrix_list containing individual indicatrix objects.

Usage

indicatrix(x, target = NULL, ..., source = "EPSG:4326")

Arguments

x	a tissot_tbl, or any xy-ish input (see tissot())
target	target projection CRS (extracted from tissot_tbl attributes if x is one; required otherwise)
...	passed to tissot()
source	source CRS (default "EPSG:4326")

Details

indicatrix() accepts either:

• A tissot_tbl object (from tissot()) — projection is extracted from attributes, target is optional

• Any xy-ish input with an explicit target

Value

An indicatrix_list object (a list of indicatrix objects with source and target stored as attributes)

See Also

tissot(), plot.indicatrix(), plot.indicatrix_list(), ti_ellipse()

Examples

## From a tissot_tbl
r <- tissot(cbind(seq(-150, 150, by = 30), 0), "+proj=robin")
ii <- indicatrix(r)
plot(ii, scale = 5e5)

## From raw coordinates
ii2 <- indicatrix(c(0, 45), "+proj=stere +lat_0=90")
plot(ii2)

---

Plot an indicatrix

Description

Draws a single Tissot indicatrix ellipse on the current plot. The ellipse shows the distortion of a unit circle under the map projection. Optional overlays include a reference unit circle, and lambda/phi direction axes.

Usage

## S3 method for class 'indicatrix'
plot(
  x,
  scale = 1e+05,
  n = 72,
  col = "#FF990055",
  border = "black",
  add = TRUE,
  show.axes = TRUE,
  show.circle = TRUE,
  ...
)

Arguments

x	an indicatrix object (from indicatrix())
scale	scaling factor for the ellipse size in projected units
n	number of points on the ellipse
col	fill colour for the ellipse
border	border colour
add	logical; add to existing plot?
show.axes	TRUE, FALSE, or a named list of graphical parameters for the direction lines. Defaults: list(col.lambda = "red", col.phi = "blue", lwd = 1.5).
show.circle	TRUE, FALSE, or a named list of graphical parameters for the reference circle. Defaults: list(col = adjustcolor("white", alpha.f = 0.6), border = "grey70", lwd = 2.5, lty = 2).
...	passed to graphics::polygon()

Details

show.circle and show.axes accept TRUE (use defaults), FALSE (hide), or a named list of graphical parameters to override defaults. For example, show.circle = list(border = "blue", lty = 3).

Value

The input x, invisibly.

See Also

indicatrix(), plot.indicatrix_list(), ti_ellipse()

---

Plot a list of indicatrixes

Description

Draws all indicatrixes in an indicatrix_list, optionally creating a new plot or adding to an existing one. Can colour-code the fill by a distortion metric.

Usage

## S3 method for class 'indicatrix_list'
plot(
  x,
  scale = 1e+05,
  n = 72,
  col = "#FF990055",
  border = "black",
  add = FALSE,
  show.axes = TRUE,
  show.circle = TRUE,
  fill.by = NULL,
  palette = NULL,
  ncolors = 64L,
  ...
)

Arguments

x	an indicatrix_list (from indicatrix())
scale	scaling factor for ellipse size in projected units
n	number of points per ellipse
col	fill colour. If a single colour, used for all ellipses. If NULL and fill.by is set, colours are generated automatically.
border	border colour
add	logical; add to existing plot? If FALSE, creates a new plot sized to contain all ellipses.
show.axes	TRUE, FALSE, or a named list of graphical parameters. See plot.indicatrix() for defaults.
show.circle	TRUE, FALSE, or a named list of graphical parameters. Default TRUE for the list method (the circle-vs-ellipse comparison makes distortion visible at map scale). See plot.indicatrix() for defaults.
fill.by	character; name of a distortion metric to colour-code the fill. One of "scale_area", "angle_deformation", "scale_h", "scale_k", "scale_a", "scale_b". Default NULL (uniform fill).
palette	colour palette function (default grDevices::hcl.colors())
ncolors	number of colours in the palette (default 64)
...	passed to plot.indicatrix()

Value

The input x, invisibly.

See Also

indicatrix(), plot.indicatrix(), tissot_map()

Examples

xy <- expand.grid(seq(-150, 150, by = 30), seq(-60, 60, by = 30))
r <- tissot(xy, "+proj=robin")
ii <- indicatrix(r)

## Uniform fill
plot(ii, scale = 6e5, add = FALSE)
tissot_map()

## Colour by areal distortion
plot(ii, scale = 6e5, add = FALSE, fill.by = "scale_area")
tissot_map()

---

Generate ellipse coordinates for an indicatrix

Description

Generate ellipse coordinates for an indicatrix

Usage

ti_ellipse(x, scale = 1e+05, n = 72, ...)

Arguments

x	an indicatrix object
scale	scaling factor for the ellipse size in projected units
n	number of points on the ellipse
...	ignored

Value

A two-column matrix of projected coordinates tracing the ellipse

See Also

indicatrix(), plot.indicatrix()

---

Compute Tissot indicatrix properties

Description

Compute the Tissot indicatrix at given longitude/latitude locations for a map projection. Returns scale factors, angular deformation, convergence, and related distortion properties.

Usage

tissot(
  x,
  target,
  ...,
  source = "EPSG:4326",
  A = 6378137,
  f.inv = 298.257223563,
  dx = 1e-04
)

Arguments

x	input coordinates — any xy-ish object: a two-column matrix, data.frame, tibble, list with x/y or lon/lat components, or a length-2 numeric vector for a single point
target	target projection CRS string (required)
...	ignored
source	source CRS (default "EPSG:4326")
A	semi-major axis of the ellipsoid (default WGS84)
f.inv	inverse flattening (default WGS84)
dx	finite difference step in degrees (default 1e-4)

Details

The Jacobian of the projection is computed via finite differences, projecting all base and offset points in a single batched call to gdalraster::transform_xy(). All subsequent calculations (SVD, distortion metrics) are fully vectorized.

Input 'x' is assumed to be longitude,latitude values, with default 'EPSG:4326'. Set 'source' for a different 'geographic' coordinate reference system.

Value

A tissot_tbl tibble with columns: x (lon), y (lat), dx_dlam, dy_dlam, dx_dphi, dy_dphi, scale_h, scale_k, scale_omega, scale_a, scale_b, scale_area, angle_deformation, convergence. The source and target CRS strings are stored as attributes.

See Also

indicatrix(), tissot_map(), tissot_unproject(), gdalraster::transform_xy()

Examples

tissot(c(0, 45), "+proj=robin")
tissot(cbind(seq(-180, 180, by = 30), 0), "+proj=robin")

---

Get or set the current plot projection

Description

Deprecated. Prefer passing target explicitly.

These functions access a global option. Prefer passing target explicitly to tissot_map() and tissot_abline(), or let plot.indicatrix_list() set the projection automatically.

Usage

tissot_get_proj()

tissot_set_proj(target)

Arguments

target

projection CRS string

Value

tissot_get_proj() returns the current projection string or NULL

---

Plot world coastline on a projected map

Description

tissot_map() draws the bundled world coastline, projected if a projection is current. The projection is determined in this order:

1. An explicit target argument

2. The projection stored by the last plot.indicatrix_list() call

Usage

tissot_map(..., target = NULL, add = TRUE)

tissot_abline(x, y = NULL, ..., source = "EPSG:4326", target = NULL)

Arguments

...	graphical parameters passed to graphics::lines() (if adding) or graphics::plot() (if creating new)
target	target CRS. If NULL, uses the last plot projection (from plot.indicatrix_list()) or draws in lon/lat.
add	logical; add to existing plot (default TRUE) or create new
x	longitude values (or any xy-ish input; see tissot())
y	latitude values (ignored if x is a matrix)
source	source CRS for the coordinates (default "EPSG:4326")

Details

tissot_abline() draws vertical and horizontal reference lines at a given longitude/latitude in projected coordinates.

Value

tissot_map() invisibly returns the (projected) world coastline matrix

tissot_abline() is called for its side effect

See Also

plot.indicatrix_list(), tissot()

Examples

r <- tissot(cbind(seq(-150, 150, by = 30), 0), "+proj=robin")
ii <- indicatrix(r)
plot(ii, scale = 6e5, add = FALSE)
tissot_map()

---

Unproject coordinates to geographic (lon/lat) CRS

Description

A convenience wrapper around gdalraster::transform_xy() for converting projected coordinates to geographic. Useful for generating regular grids in a projected CRS to feed to tissot(), which requires lon/lat input.

Usage

tissot_unproject(x, target = "EPSG:4326", ..., source = NULL)

Arguments

x	input coordinates — any xy-ish object: a two-column matrix, data.frame, tibble, list with x/y or lon/lat components, or a length-2 numeric vector for a single point
target	target CRS string (default "EPSG:4326"). Must be geographic.
...	ignored
source	source CRS string (required). Must be a projected CRS.

Value

A two-column matrix of longitude and latitude values.

See Also

tissot(), gdalraster::transform_xy()

Examples

## regular grid in UTM zone 55S, unprojected to lon/lat for tissot()
xy <- expand.grid(x = seq(4e5, 6e5, length.out = 5),
                  y = seq(5200000, 5400000, length.out = 4))
ll <- tissot_unproject(xy, source = "EPSG:32755")
tissot(ll, "+proj=utm +zone=55 +south")

---

World coastline

Description

A matrix of longitude/latitude coordinates representing a simplified world coastline, derived from the maps package. Continent boundaries are separated by NA rows. Longitudes are constrained to abs(lon) <= 180.

Usage

world

Format

A two-column numeric matrix (longitude, latitude)

---