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Voronoi tessellation

Source: R/stat-voronoi.r
stat_voronoi.Rd

Compute Voronoi regions from point data.

Usage

stat_voronoi(
  mapping = NULL,
  data = NULL,
  geom = "voronoi",
  position = "identity",
  engine = NULL,
  show.legend = NA,
  inherit.aes = TRUE,
  ...
)

Arguments

mapping

Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.

data

The data to be displayed in this layer. There are three options:

If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot().

A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created.

A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).

geom

The geometric object to use to display the data for this layer. When using a stat_*() function to construct a layer, the geom argument can be used to override the default coupling between stats and geoms. The geom argument accepts the following:

  • A Geom ggproto subclass, for example GeomPoint.

  • A string naming the geom. To give the geom as a string, strip the function name of the geom_ prefix. For example, to use geom_point(), give the geom as "point".

  • For more information and other ways to specify the geom, see the layer geom documentation.

position

A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following:

  • The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position.

  • A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter".

  • For more information and other ways to specify the position, see the layer position documentation.

engine

A single character string specifying the package implementation to use; "deldir" or "geometry". Only "geometry" can handle higher-dimensional data.

show.legend

logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.

inherit.aes

If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. annotation_borders().

...

Additional arguments passed to ggplot2::layer().

Value

A ggproto layer.

Details

The Voronoi tessellation (also associated with the names Dirichlet and Thiessen) of a set of points in a metric space comprises the nearest-neighbor classification region around each point. When computed in higher-dimensional real space, StatVoronoi$compute_layer() computes their intersections with the plane.

stat_voronoi() is designed to pair with geom_voronoi() and geom_thiessen(). The computed cell variable is a list-column of data frames, each containing the vertex coordinates and border indicator for a Voronoi cell.

Because linear discriminant analysis (LDA) assumes constant within-group inertia, the Voronoi regions about the group centroids serve as prediction regions in an LDA biplot (Gardner, 2001). When the LDA models more than three groups, proper prediction regions must be constructed in model space, then intersected with the biplot plane.

Voronoi cells are delimited within a rectangular border that extends to the edges of the plot window.

By default, deldir::deldir() is deployed on 2-dimensional data while geometry::delaunayn() is deployed on higher-dimensional data; the user may use the engine argument to override the default in 2 dimensions, but in higher dimensions the geometry package is required.

Multidimensional position aesthetics

This statistical transformation is compatible with the convenience function aes_coord().

Some transformations (e.g. stat_center()) commute with projection to the lower (1 or 2)-dimensional biplot space. If they detect aesthetics of the form ..coord[0-9]+, then ..coord1 and ..coord2 are converted to x and y while any remaining are ignored.

Other transformations (e.g. stat_spantree()) yield different results in a lower-dimensional biplot when they are computed before versus after projection. If the stat layer detects these aesthetics, then the transformation is performed before projection, and the results in the first two dimensions are returned as x and y.

A small number of transformations (stat_rule()) are incompatible with these aesthetics but will accept aes_coord() without warning.

Computed variables

These are calculated during the statistical transformation and can be accessed with delayed evaluation.

cell

a list-column of data frames, each containing the cell vertex coordinates (x, y) and the border indicator border

References

Voronoï MG (1908) "Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier Mémoire. Sur quelques propriétés des formes quadratiques positives parfaites." J. Reine Angew. Math. 133, 97–178. doi:10.1515/crll.1908.133.97

Voronoï MG (1908) "Nouvelles applications des paramètres continus à la théorie des formes quadratiquess. Deuxième Mémoire. Recherches sur les parallélloèdres primitifs." J. Reine Angew. Math. 134, 198–287. doi:10.1515/crll.1908.134.198

Gardner S (2001) Extensions of biplot methodology to discriminant analysis with applications of non-parametric principal components. PhD thesis, Stellenbosch University. http://hdl.handle.net/10019.1/52264

See also

Other stat layers: stat_bagplot(), stat_center(), stat_chull(), stat_cone(), stat_delaunay(), stat_depth(), stat_rule(), stat_scale(), stat_spantree()

Examples

eurodist %>% 
  cmdscale(k = 6) %>% 
  as.data.frame() %>% 
  tibble::rownames_to_column(var = "city") ->
  euro_mds
# planar regions (note superimposed perimeters)
ggplot(euro_mds, aes(V1, V2, label = city)) +
  coord_equal() +
  stat_voronoi(color = "black", fill = "transparent", linetype = "dashed") +
  geom_point() +
  geom_text(alpha = .5, size = 3)

# intersection of plane with full-dimensional regions, tight bounds
ggplot(euro_mds, aes_c(aes_coord(euro_mds, "V"), aes(label = city))) +
  coord_equal() +
  stat_voronoi(color = "black") +
  geom_point(aes(V1, V2)) +
  geom_text(aes(V1, V2), alpha = .5, size = 3)

# facet by a variable
set.seed(0)
euro_mds %>%
  transform(random = LETTERS[sample(3, nrow(euro_mds), replace = TRUE)]) %>%
  ggplot(aes_c(aes_coord(euro_mds, "V"), aes(label = city))) +
  coord_equal() +
  facet_grid(cols = vars(random)) +
  stat_voronoi(color = "black") +
  geom_point(aes(V1, V2)) +
  geom_text(aes(V1, V2), alpha = .5, size = 3)

# overlay Voronoi tiles and Thiessen segments
set.seed(0)
euro_mds %>%
  transform(random = LETTERS[sample(3, nrow(euro_mds), replace = TRUE)]) %>%
  ggplot(aes_c(aes_coord(euro_mds, "V"), aes(label = city))) +
  coord_equal() +
  stat_voronoi(aes(fill = random)) +
  stat_voronoi(geom = "thiessen", linetype = "dotted") +
  geom_point(aes(V1, V2)) +
  geom_text(aes(V1, V2), alpha = .5, size = 3)