spatstat.geom-package: The spatstat.geom Package

spatstat.geom-packageR Documentation

The spatstat.geom Package


The spatstat.geom package belongs to the spatstat family of packages. It defines classes of geometrical objects such as windows and point patterns, and provides functionality for geometrical operations on them.


spatstat is a family of R packages for the statistical analysis of spatial data. Its main focus is the analysis of spatial patterns of points in two-dimensional space.

The original spatstat package has now been split into several sub-packages.

This sub-package spatstat.geom defines the main classes of geometrical objects (such as windows, point patterns, line segment patterns, pixel images) and supports geometrical operations (such as shifting and rotating, measuring areas and distances, finding nearest neighbours in a point pattern).

Functions for performing statistical analysis and modelling are in the separate sub-packages spatstat.explore and spatstat.model.

Functions for linear networks are in the separate sub-package spatstat.linnet.

For an overview of all the functions available in the spatstat family, see the help file for spatstat in the spatstat package.

Structure of the spatstat family

The original spatstat package grew to be very large, and CRAN requested that the package be divided into several sub-packages. Currently the sub-packages are:

  • spatstat.utils containing basic utilities

  • containing datasets

  • spatstat.sparse containing linear algebra utilities

  • spatstat.geom containing geometrical objects and geometrical operations

  • spatstat.random containing code for generating random spatial patterns

  • spatstat.explore containing the main functionality for exploratory and non-parametric analysis of spatial data

  • spatstat.model containing the main functionality for statistical modelling and inference for spatial data

  • spatstat.linnet containing functions for spatial data on a linear network

  • spatstat, which simply loads the other sub-packages listed above, and provides documentation.

When you install spatstat, these sub-packages are also installed. Then if you load the spatstat package by typing library(spatstat), the other sub-packages listed above will automatically be loaded or imported. For an overview of all the functions available in these sub-packages, see the help file for spatstat in the spatstat package,

Additionally there are several extension packages:

  • spatstat.gui for interactive graphics

  • spatstat.local for local likelihood (including geographically weighted regression)

  • spatstat.Knet for additional, computationally efficient code for linear networks

  • spatstat.sphere (under development) for spatial data on a sphere, including spatial data on the earth's surface

The extension packages must be installed separately and loaded explicitly if needed. They also have separate documentation.


Following is an overview of the capabilities of the spatstat.geom sub-package.

Types of spatial data:

The main types of spatial data supported by spatstat.geom are:

ppp point pattern
owin window (spatial region)
im pixel image
psp line segment pattern
tess tessellation
pp3 three-dimensional point pattern
ppx point pattern in any number of dimensions

Additional data types are supported in spatstat.linnet.

To create a point pattern:

ppp create a point pattern from (x,y) and window information
ppp(x, y, xlim, ylim) for rectangular window
ppp(x, y, poly) for polygonal window
ppp(x, y, mask) for binary image window
as.ppp convert other types of data to a ppp object
clickppp interactively add points to a plot
marks<-, %mark% attach/reassign marks to a point pattern

To simulate a random point pattern:

Most of the methods for generating random data are provided in spatstat.random. The following basic methods are supplied in spatstat.geom:

runifrect generate n independent uniform random points in a rectangle
rsyst systematic random sample of points
rjitter apply random displacements to points in a pattern

Standard point pattern datasets:

Datasets installed in the spatstat family are provided in the sub-package

To manipulate a point pattern:

plot.ppp plot a point pattern (e.g. plot(X))
spatstat.gui::iplot plot a point pattern interactively
edit.ppp interactive text editor
[.ppp extract or replace a subset of a point pattern
pp[subset] or pp[subwindow]
subset.ppp extract subset of point pattern satisfying a condition
superimpose combine several point patterns
by.ppp apply a function to sub-patterns of a point pattern
cut.ppp classify the points in a point pattern
split.ppp divide pattern into sub-patterns
unmark remove marks
npoints count the number of points
coords extract coordinates, change coordinates
marks extract marks, change marks or attach marks
rotate rotate pattern
shift translate pattern
flipxy swap x and y coordinates
reflect reflect in the origin
periodify make several translated copies
affine apply affine transformation
scalardilate apply scalar dilation
nnmark mark value of nearest data point
identify.ppp interactively identify points
unique.ppp remove duplicate points
duplicated.ppp determine which points are duplicates
uniquemap.ppp map duplicated points to unique points
connected.ppp find clumps of points
dirichlet compute Dirichlet-Voronoi tessellation
delaunay compute Delaunay triangulation
delaunayDistance graph distance in Delaunay triangulation
convexhull compute convex hull
discretise discretise coordinates
pixellate.ppp approximate point pattern by pixel image approximate point pattern by pixel image

See spatstat.options to control plotting behaviour.

To create a window:

An object of class "owin" describes a spatial region (a window of observation).

owin Create a window object
owin(xlim, ylim) for rectangular window
owin(poly) for polygonal window
owin(mask) for binary image window
Window Extract window of another object
Frame Extract the containing rectangle ('frame') of another object
as.owin Convert other data to a window object
square make a square window
disc make a circular window
ellipse make an elliptical window
ripras Ripley-Rasson estimator of window, given only the points
convexhull compute convex hull of something
letterR polygonal window in the shape of the R logo
clickpoly interactively draw a polygonal window
clickbox interactively draw a rectangle

To manipulate a window:

plot.owin plot a window.
boundingbox Find a tight bounding box for the window
erosion erode window by a distance r
dilation dilate window by a distance r
closing close window by a distance r
opening open window by a distance r
border difference between window and its erosion/dilation
complement.owin invert (swap inside and outside)
simplify.owin approximate a window by a simple polygon
rotate rotate window
flipxy swap x and y coordinates
shift translate window
periodify make several translated copies
affine apply affine transformation convert window to data frame

Digital approximations:

as.mask Make a discrete pixel approximation of a given window convert window to pixel image
pixellate.owin convert window to pixel image
commonGrid find common pixel grid for windows
nearest.raster.point map continuous coordinates to raster locations
raster.x raster x coordinates
raster.y raster y coordinates
raster.xy raster x and y coordinates
as.polygonal convert pixel mask to polygonal window

See spatstat.options to control the approximation

Geometrical computations with windows:

edges extract boundary edges
intersect.owin intersection of two windows
union.owin union of two windows
setminus.owin set subtraction of two windows
inside.owin determine whether a point is inside a window
area.owin compute area
perimeter compute perimeter length
diameter.owin compute diameter
incircle find largest circle inside a window
inradius radius of incircle
connected.owin find connected components of window
eroded.areas compute areas of eroded windows
dilated.areas compute areas of dilated windows
bdist.points compute distances from data points to window boundary
bdist.pixels compute distances from all pixels to window boundary
bdist.tiles boundary distance for each tile in tessellation
distmap.owin distance transform image
distfun.owin distance transform
centroid.owin compute centroid (centre of mass) of window
is.subset.owin determine whether one window contains another
is.convex determine whether a window is convex
convexhull compute convex hull
triangulate.owin decompose into triangles
as.mask pixel approximation of window
as.polygonal polygonal approximation of window
is.rectangle test whether window is a rectangle
is.polygonal test whether window is polygonal
is.mask test whether window is a mask
setcov spatial covariance function of window
pixelcentres extract centres of pixels in mask
clickdist measure distance between two points clicked by user

Pixel images: An object of class "im" represents a pixel image. Such objects are returned by some of the functions in spatstat including Kmeasure, setcov and density.ppp.

im create a pixel image convert other data to a pixel image
pixellate convert other data to a pixel image convert pixel image to matrix convert pixel image to data frame convert pixel image to function plot a pixel image on screen as a digital image draw contours of a pixel image draw perspective plot of a pixel image
rgbim create colour-valued pixel image
hsvim create colour-valued pixel image
[.im extract a subset of a pixel image
[< replace a subset of a pixel image rotate pixel image apply vector shift to pixel image apply affine transformation to image
X print very basic information about image X
summary(X) summary of image X histogram of image mean pixel value of image integral of pixel values quantiles of image convert numeric image to factor image test whether an object is a pixel image interpolate a pixel image find connected components test whether two images have compatible dimensions make images compatible
commonGrid find a common pixel grid for images evaluate any expression involving images
im.apply evaluate a function of several images
scaletointerval rescale pixel values set very small pixel values to zero
levelset level set of an image
solutionset region where an expression is true
imcov spatial covariance function of image spatial convolution of images
pixelcentres extract centres of pixels
transmat convert matrix of pixel values
to a different indexing convention

Line segment patterns

An object of class "psp" represents a pattern of straight line segments.

psp create a line segment pattern
as.psp convert other data into a line segment pattern
edges extract edges of a window
is.psp determine whether a dataset has class "psp"
plot.psp plot a line segment pattern
print.psp print basic information
summary.psp print summary information
[.psp extract a subset of a line segment pattern
subset.psp extract subset of line segment pattern convert line segment pattern to data frame
marks.psp extract marks of line segments
marks<-.psp assign new marks to line segments
unmark.psp delete marks from line segments
midpoints.psp compute the midpoints of line segments
endpoints.psp extract the endpoints of line segments
lengths_psp compute the lengths of line segments
angles.psp compute the orientation angles of line segments
superimpose combine several line segment patterns
flipxy swap x and y coordinates
rotate.psp rotate a line segment pattern
shift.psp shift a line segment pattern
periodify make several shifted copies
affine.psp apply an affine transformation
pixellate.psp approximate line segment pattern by pixel image
as.mask.psp approximate line segment pattern by binary mask
distmap.psp compute the distance map of a line segment pattern
distfun.psp compute the distance map of a line segment pattern
selfcrossing.psp find crossing points between line segments
selfcut.psp cut segments where they cross
crossing.psp find crossing points between two line segment patterns
extrapolate.psp extrapolate line segments to infinite lines
nncross find distance to nearest line segment from a given point
nearestsegment find line segment closest to a given point
project2segment find location along a line segment closest to a given point
pointsOnLines generate points evenly spaced along line segment
rlinegrid generate a random array of parallel lines through a window


An object of class "tess" represents a tessellation.

tess create a tessellation
quadrats create a tessellation of rectangles
hextess create a tessellation of hexagons
polartess tessellation using polar coordinates
quantess quantile tessellation
venn.tess Venn diagram tessellation
dirichlet compute Dirichlet-Voronoi tessellation of points
delaunay compute Delaunay triangulation of points
as.tess convert other data to a tessellation
plot.tess plot a tessellation
tiles extract all the tiles of a tessellation
[.tess extract some tiles of a tessellation
[<-.tess change some tiles of a tessellation
intersect.tess intersect two tessellations
or restrict a tessellation to a window
chop.tess subdivide a tessellation by a line
tile.areas area of each tile in tessellation
bdist.tiles boundary distance for each tile in tessellation
connected.tess find connected components of tiles
shift.tess shift a tessellation
rotate.tess rotate a tessellation
reflect.tess reflect about the origin
flipxy.tess reflect about the diagonal
affine.tess apply affine transformation

Three-dimensional point patterns

An object of class "pp3" represents a three-dimensional point pattern in a rectangular box. The box is represented by an object of class "box3".

pp3 create a 3-D point pattern
plot.pp3 plot a 3-D point pattern
coords extract coordinates
as.hyperframe extract coordinates
subset.pp3 extract subset of 3-D point pattern
unitname.pp3 name of unit of length
npoints count the number of points
box3 create a 3-D rectangular box
as.box3 convert data to 3-D rectangular box
unitname.box3 name of unit of length
diameter.box3 diameter of box
volume.box3 volume of box
shortside.box3 shortest side of box
eroded.volumes volumes of erosions of box

Multi-dimensional space-time point patterns

An object of class "ppx" represents a point pattern in multi-dimensional space and/or time.

ppx create a multidimensional space-time point pattern
coords extract coordinates
as.hyperframe extract coordinates
subset.ppx extract subset
unitname.ppx name of unit of length
npoints count the number of points
boxx define multidimensional box
diameter.boxx diameter of box
volume.boxx volume of box
shortside.boxx shortest side of box
eroded.volumes.boxx volumes of erosions of box

Linear networks

An object of class "linnet" represents a linear network (for example, a road network). This is supported in the sub-package spatstat.linnet.

An object of class "lpp" represents a point pattern on a linear network (for example, road accidents on a road network).


A hyperframe is like a data frame, except that the entries may be objects of any kind.

hyperframe create a hyperframe
as.hyperframe convert data to hyperframe
plot.hyperframe plot hyperframe
with.hyperframe evaluate expression using each row of hyperframe
cbind.hyperframe combine hyperframes by columns
rbind.hyperframe combine hyperframes by rows convert hyperframe to data frame
subset.hyperframe method for subset
head.hyperframe first few rows of hyperframe
tail.hyperframe last few rows of hyperframe

Layered objects

A layered object represents data that should be plotted in successive layers, for example, a background and a foreground.

layered create layered object
plot.layered plot layered object
[.layered extract subset of layered object

Colour maps

A colour map is a mechanism for associating colours with data. It can be regarded as a function, mapping data to colours. Using a colourmap object in a plot command ensures that the mapping from numbers to colours is the same in different plots.

colourmap create a colour map
plot.colourmap plot the colour map only
tweak.colourmap alter individual colour values
interp.colourmap make a smooth transition between colours
beachcolourmap one special colour map

Inspection of data:

summary(X) print useful summary of point pattern X
X print basic description of point pattern X
any(duplicated(X)) check for duplicated points in pattern X
intensity Mean intensity
quadratcount Quadrat counts

Distances in a point pattern:

nndist nearest neighbour distances
nnwhich find nearest neighbours
pairdist distances between all pairs of points
crossdist distances between points in two patterns
nncross nearest neighbours between two point patterns
exactdt distance from any location to nearest data point
distmap distance map image
distfun distance map function
nnmap nearest point image
nnfun nearest point function

Programming tools:

applynbd apply function to every neighbourhood in a point pattern
markstat apply function to the marks of neighbours in a point pattern
pppdist find the optimal match between two point patterns

Distances in a three-dimensional point pattern:

pairdist.pp3 distances between all pairs of points
crossdist.pp3 distances between points in two patterns
nndist.pp3 nearest neighbour distances
nnwhich.pp3 find nearest neighbours
nncross.pp3 find nearest neighbours in another pattern

Distances in multi-dimensional point pattern:

These are for multi-dimensional space-time point pattern objects (class ppx).

pairdist.ppx distances between all pairs of points
crossdist.ppx distances between points in two patterns
nndist.ppx nearest neighbour distances
nnwhich.ppx find nearest neighbours


This library and its documentation are usable under the terms of the "GNU General Public License", a copy of which is distributed with the package.


Kasper Klitgaard Berthelsen, Ottmar Cronie, Tilman Davies, Yongtao Guan, Ute Hahn, Abdollah Jalilian, Marie-Colette van Lieshout, Greg McSwiggan, Tuomas Rajala, Suman Rakshit, Dominic Schuhmacher, Rasmus Waagepetersen and Hangsheng Wang made substantial contributions of code.

Additional contributions and suggestions from Monsuru Adepeju, Corey Anderson, Ang Qi Wei, Ryan Arellano, Jens Astrom, Robert Aue, Marcel Austenfeld, Sandro Azaele, Malissa Baddeley, Guy Bayegnak, Colin Beale, Melanie Bell, Thomas Bendtsen, Ricardo Bernhardt, Andrew Bevan, Brad Biggerstaff, Anders Bilgrau, Leanne Bischof, Christophe Biscio, Roger Bivand, Jose M. Blanco Moreno, Florent Bonneu, Jordan Brown, Ian Buller, Julian Burgos, Simon Byers, Ya-Mei Chang, Jianbao Chen, Igor Chernayavsky, Y.C. Chin, Bjarke Christensen, Lucia Cobo Sanchez, Jean-Francois Coeurjolly, Kim Colyvas, Hadrien Commenges, Rochelle Constantine, Robin Corria Ainslie, Richard Cotton, Marcelino de la Cruz, Peter Dalgaard, Mario D'Antuono, Sourav Das, Peter Diggle, Patrick Donnelly, Ian Dryden, Stephen Eglen, Ahmed El-Gabbas, Belarmain Fandohan, Olivier Flores, David Ford, Peter Forbes, Shane Frank, Janet Franklin, Funwi-Gabga Neba, Oscar Garcia, Agnes Gault, Jonas Geldmann, Marc Genton, Shaaban Ghalandarayeshi, Julian Gilbey, Jason Goldstick, Pavel Grabarnik, C. Graf, Ute Hahn, Andrew Hardegen, Martin \Bogsted Hansen, Martin Hazelton, Juha Heikkinen, Mandy Hering, Markus Herrmann, Maximilian Hesselbarth, Paul Hewson, Hamidreza Heydarian, Kassel Hingee, Kurt Hornik, Philipp Hunziker, Jack Hywood, Ross Ihaka, Cenk Icos, Aruna Jammalamadaka, Robert John-Chandran, Devin Johnson, Mahdieh Khanmohammadi, Bob Klaver, Lily Kozmian-Ledward, Peter Kovesi, Mike Kuhn, Jeff Laake, Robert Lamb, Frederic Lavancier, Tom Lawrence, Tomas Lazauskas, Jonathan Lee, George Leser, Angela Li, Li Haitao, George Limitsios, Andrew Lister, Nestor Luambua, Ben Madin, Martin Maechler, Kiran Marchikanti, Jeff Marcus, Robert Mark, Peter McCullagh, Monia Mahling, Jorge Mateu Mahiques, Ulf Mehlig, Frederico Mestre, Sebastian Wastl Meyer, Mi Xiangcheng, Lore De Middeleer, Robin Milne, Enrique Miranda, Jesper \Moller, Annie Mollie, Ines Moncada, Mehdi Moradi, Virginia Morera Pujol, Erika Mudrak, Gopalan Nair, Nader Najari, Nicoletta Nava, Linda Stougaard Nielsen, Felipe Nunes, Jens Randel Nyengaard, Jens \Oehlschlaegel, Thierry Onkelinx, Sean O'Riordan, Evgeni Parilov, Jeff Picka, Nicolas Picard, Tim Pollington, Mike Porter, Sergiy Protsiv, Adrian Raftery, Suman Rakshit, Ben Ramage, Pablo Ramon, Xavier Raynaud, Nicholas Read, Matt Reiter, Ian Renner, Tom Richardson, Brian Ripley, Ted Rosenbaum, Barry Rowlingson, Jason Rudokas, Tyler Rudolph, John Rudge, Christopher Ryan, Farzaneh Safavimanesh, Aila \Sarkka, Cody Schank, Katja Schladitz, Sebastian Schutte, Bryan Scott, Olivia Semboli, Francois Semecurbe, Vadim Shcherbakov, Shen Guochun, Shi Peijian, Harold-Jeffrey Ship, Tammy L Silva, Ida-Maria Sintorn, Yong Song, Malte Spiess, Mark Stevenson, Kaspar Stucki, Jan Sulavik, Michael Sumner, P. Surovy, Ben Taylor, Thordis Linda Thorarinsdottir, Leigh Torres, Berwin Turlach, Torben Tvedebrink, Kevin Ummer, Medha Uppala, Andrew van Burgel, Tobias Verbeke, Mikko Vihtakari, Alexendre Villers, Fabrice Vinatier, Maximilian Vogtland, Sasha Voss, Sven Wagner, Hao Wang, H. Wendrock, Jan Wild, Carl G. Witthoft, Selene Wong, Maxime Woringer, Luke Yates, Mike Zamboni and Achim Zeileis.




spatstat.geom documentation built on Oct. 20, 2023, 9:06 a.m.