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Create a Gradient Field Layer in ggplot2

Source: R/geom_gradient_field.R
geom_gradient_field.Rd

These functions provide convenient ggplot2 layers for drawing gradient fields by computing the gradient of a scalar field. A user-defined function (fun) specifies the behavior of the scalar field by taking a numeric vector of length 2 (representing \((x, y)\)) and returning a single numeric value. The underlying StatStreamField computes the gradient via numerical differentiation (using numDeriv::grad()) and GeomStream renders the resulting vectors.

Usage

geom_gradient_field(
  mapping = NULL,
  data = NULL,
  stat = StatStreamField,
  position = "identity",
  ...,
  na.rm = FALSE,
  show.legend = TRUE,
  inherit.aes = TRUE,
  fun,
  xlim = NULL,
  ylim = NULL,
  n = 11,
  max_it = 1000,
  T = NULL,
  L = NULL,
  center = TRUE,
  type = "vector",
  normalize = TRUE,
  tail_point = FALSE,
  eval_point = FALSE,
  grid = NULL,
  lineend = "butt",
  linejoin = "round",
  linemitre = 10,
  arrow = grid::arrow(angle = 30, length = grid::unit(0.02, "npc"), type = "closed")
)

stat_gradient_field(
  mapping = NULL,
  data = NULL,
  geom = GeomStream,
  position = "identity",
  ...,
  na.rm = FALSE,
  show.legend = TRUE,
  inherit.aes = TRUE,
  fun,
  xlim = NULL,
  ylim = NULL,
  n = 11,
  max_it = 1000,
  T = NULL,
  L = NULL,
  center = TRUE,
  type = "vector",
  normalize = TRUE,
  tail_point = FALSE,
  eval_point = FALSE,
  grid = NULL,
  lineend = "butt",
  linejoin = "round",
  linemitre = 10,
  arrow = grid::arrow(angle = 30, length = grid::unit(0.02, "npc"), type = "closed")
)

geom_gradient_field2(
  mapping = NULL,
  data = NULL,
  stat = StatStreamField,
  position = "identity",
  ...,
  na.rm = FALSE,
  show.legend = TRUE,
  inherit.aes = TRUE,
  fun,
  xlim = NULL,
  ylim = NULL,
  n = 11,
  max_it = 1000,
  T = NULL,
  L = NULL,
  center = FALSE,
  type = "stream",
  normalize = TRUE,
  tail_point = TRUE,
  eval_point = FALSE,
  grid = NULL,
  lineend = "butt",
  linejoin = "round",
  linemitre = 10,
  arrow = NULL
)

stat_gradient_field2(
  mapping = NULL,
  data = NULL,
  geom = GeomStream,
  position = "identity",
  ...,
  na.rm = FALSE,
  show.legend = TRUE,
  inherit.aes = TRUE,
  fun,
  xlim = NULL,
  ylim = NULL,
  n = 11,
  max_it = 1000,
  T = NULL,
  L = NULL,
  center = FALSE,
  type = "stream",
  normalize = TRUE,
  tail_point = TRUE,
  eval_point = FALSE,
  grid = NULL,
  lineend = "butt",
  linejoin = "round",
  linemitre = 10,
  arrow = NULL
)

Arguments

mapping

A set of aesthetic mappings created by ggplot2::aes(). Additional aesthetics such as color, size, linetype, and alpha can be defined. In geom_gradient_field the default mapping includes color = after_stat(norm), whereas in geom_gradient_field2 the default mapping includes length = after_stat(norm).

data

A data frame containing the input data.

stat

The statistical transformation to use on the data for this layer. Defaults to StatStreamField.

position

Position adjustment, either as a string or the result of a position adjustment function.

...

Other arguments passed on to grid::layer().

na.rm

Logical. If FALSE (the default), missing values are removed with a warning.

show.legend

Logical. Should this layer be included in the legends?

inherit.aes

Logical. If FALSE, overrides the default aesthetics rather than combining with them.

fun

A function that defines the scalar field. It should take a numeric vector of length 2 (representing \((x, y)\)) and return a single numeric value. (Required)

xlim

Numeric vector of length two. Specifies the limits of the x-axis domain. Defaults to c(-1, 1).

ylim

Numeric vector of length two. Specifies the limits of the y-axis domain. Defaults to c(-1, 1).

n

Integer. Grid resolution specifying the number of seed points along each axis. Higher values produce a denser gradient field. Defaults to 11.

max_it

Integer. Maximum number of integration steps allowed when computing the gradient stream. Defaults to 1000.

T

Numeric. Time increment used for numerical integration when normalize is FALSE. If not provided, it is computed automatically based on grid spacing and the vector field’s magnitude.

L

Numeric. Target length for the gradient vectors or streamlines. When normalize is TRUE, computed vectors are scaled to have length L. If not provided, L is computed automatically from the grid spacing.

center

Logical. If TRUE, centers the seed points so that the original (x, y) becomes the midpoint.

type

Character. Specifies the type of field to compute: use "stream" to generate integrated streamlines or "vector" for individual vector segments. Defaults to "stream".

normalize

Logical. If TRUE, gradient vectors are normalized based on grid spacing. Defaults to TRUE.

tail_point

Logical. If TRUE, a point is drawn at the tail of each gradient vector.

eval_point

Logical. If TRUE, a point is drawn at the evaluation point where the gradient was computed. Defaults to FALSE.

grid

A data frame containing precomputed grid points for seed placement. If NULL (default), a regular Cartesian grid is generated based on xlim, ylim, and n.

lineend

Line end style (round, butt, square).

linejoin

Line join style (round, mitre, bevel).

linemitre

Line mitre limit (number greater than 1).

arrow

A grid::arrow() specification to add arrowheads to the gradient vectors. In geom_gradient_field, the default is a closed arrow with a 30° angle and length 0.02 npc; in geom_gradient_field2(), the default is NULL.

geom

The geometric object used to render the streamline (only used in stat_stream(); defaults to GeomStream).

Value

A ggplot2 layer that computes and plots a gradient field by numerically differentiating a scalar field.

Details

Two variants are provided:

  • geom_gradient_field() uses a default mapping that sets color = after_stat(norm).

  • geom_gradient_field2() uses a default mapping that sets length = after_stat(norm) (with color unmapped by default).

Aesthetics

geom_gradient_field() and geom_gradient_field2() understand the following aesthetics (required aesthetics are in bold):

  • x: The x-coordinate of the seed point.

  • y: The y-coordinate of the seed point.

  • color: In geom_gradient_field, the color of the gradient vector. In geom_gradient_field2, color is not mapped by default.

  • length: In geom_gradient_field2, the computed vector norm.

  • size, linetype, alpha: Additional aesthetics to control appearance.

Computed Variables

The following variables are computed internally by StatStreamField when generating the gradient field from a scalar function:

norm

The Euclidean norm of the gradient vector, calculated as \(\sqrt{fx^2 + fy^2}\). This value is used, by default, for mapping color or scaling arrow lengths in the visualization.

avg_spd

This variable may represent an average speed computed from the gradient magnitude. In the default mapping for geom_gradient_field, the color aesthetic is mapped to after_stat(avg_spd).

Examples

Si <- matrix(c(1, 0.75, 0.75, 1), nrow = 2)
f <- function(u) exp(-as.numeric(u %*% solve(Si) %*% u) / 2) / (2 * pi * det(Si))

ggplot() +
  geom_gradient_field(fun = f, xlim = c(-3, 3), ylim = c(-3, 3))


if (FALSE) { # \dontrun{
df <- expand.grid(x = seq(-3, 3, 0.1), y = seq(-3, 3, 0.1)) |>
  transform(fxy = apply(cbind(x, y), 1, f))

ggplot() +
  geom_raster(aes(x, y, fill = fxy), data = df) +
  geom_gradient_field(fun = f, xlim = c(-3, 3), ylim = c(-3, 3)) +
  coord_equal()

fxy <- function(x, y) apply(cbind(x,y), 1, f)

ggplot() +
  ggdensity::geom_hdr_fun(fun = fxy, xlim = c(-3,3), ylim = c(-3,3)) +
  geom_gradient_field(fun = f, xlim = c(-3,3), ylim = c(-3,3)) +
  coord_equal()

  library("ggdensity")
  fxy <- function(x, y) apply(cbind(x, y), 1, f)
  fxy(1, 2)
  f(1:2)

  ggplot() +
    geom_hdr_fun(fun = fxy, xlim = c(-3, 3), ylim = c(-3, 3)) +
    geom_gradient_field(fun = f, xlim = c(-3, 3), ylim = c(-3, 3)) +
    coord_equal()
} # }