R/plot.shapes.R

In igraph: Network Analysis and Visualization

#   IGraph R package
#   Copyright (C) 2003-2012  Gabor Csardi <csardi.gabor@gmail.com>
#   334 Harvard street, Cambridge, MA 02139 USA
#
#   This program is free software; you can redistribute it and/or modify
#   it under the terms of the GNU General Public License as published by
#   the Free Software Foundation; either version 2 of the License, or
#   (at your option) any later version.
#
#   This program is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#   GNU General Public License for more details.
#
#   You should have received a copy of the GNU General Public License
#   along with this program; if not, write to the Free Software
#   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
#   02110-1301 USA
#
###################################################################

###################################################################
## API design
##
## A vertex shape is defined by two functions: the clipping function and
## the plotting function.
##
## The clipping function is called to determine where to put the
## arrowhead of a potential (incoming) incident edge. Its signature is
##    function(coords, el, params, end=c("both", "from", "to"))
## where the arguments are:
##    coords    A matrix with one row for each edge, and four columns.
##              It contains the coordinates of the end points of all
##              edges. The first two columns are the coordinates of the
##              first end points (sources, if the graph is directed),
##              the last two columns are for the other end points
##              (targets if the graph is directed).
##    el        The edge list itself, with vertex ids.
##    params    A function object to query plotting parameters.
##    end       Which end points to calculate. "both" means both,
##              "from" means the first end point, "to" the second.
## The clipping function must return the new version of "coords",
## modified according to the vertex sizes/shapes, with proper positions
## for the potential arrow heads. The positions are for the tips of the
## arrows.
##
## The plotting function plots the vertex. Its signature is
##    function(coords, v=NULL, params)
## where the arguments are
##    coords    Two column matrix, the coordinates for the vertices to draw.
##    v         The vertex ids of the vertices to draw. If NULL, then all
##              vertices are drawn.
##    params    A function object to query plotting parameters.
##
## shapes()         - lists all vertex shapes
## shapes(shape)    - returns the clipping and plotting functions
##                           for a given vertex shape
## add_shape()             - adds a new vertex shape, the clipping and
##                           plotting functions must be given, and
##                           optionally the newly introduced plotting
##                           parameters. This function can also be used
##                           to overwrite a given vertex shape.
##
## Examples:
## add_shape("image", clip=image.clip, plot=image.plot,
##                   parameters=list(filename=NA))
##
## add_shape("triangle", clip=shapes("circle")$clip,
##                   plot=triangle.plot)
##
## add_shape("polygon", clip=shapes("circle")$clip,
##                   plot=polygon.plot)
##
###################################################################

#' Various vertex shapes when plotting igraph graphs
#'
#' Starting from version 0.5.1 igraph supports different
#' vertex shapes when plotting graphs.
#'
#' @details
#' In igraph a vertex shape is defined by two functions: 1) provides
#' information about the size of the shape for clipping the edges and 2)
#' plots the shape if requested. These functions are called \dQuote{shape
#'   functions} in the rest of this manual page. The first one is the
#' clipping function and the second is the plotting function.
#'
#' The clipping function has the following arguments:
#' \describe{
#'   \item{coords}{A matrix with four columns, it contains the
#'     coordinates of the vertices for the edge list supplied in the
#'     `el` argument.}
#'   \item{el}{A matrix with two columns, the edges of which some end
#'     points will be clipped. It should have the same number of rows as
#'     `coords`.}
#'   \item{params}{This is a function object that can be called to query
#'     vertex/edge/plot graphical parameters. The first argument of the
#'     function is \dQuote{`vertex`}, \dQuote{`edge`} or
#'     \dQuote{`plot`} to decide the type of the parameter, the
#'     second is a character string giving the name of the
#'     parameter. E.g.
#'     \preformatted{
#' 	params("vertex", "size")
#'     }
#'   }
#'   \item{end}{Character string, it gives which end points will be
#'     used. Possible values are \dQuote{`both`},
#'     \dQuote{`from`} and \dQuote{`to`}. If
#'     \dQuote{`from`} the function is expected to clip the
#'     first column in the `el` edge list, \dQuote{`to`}
#'     selects the second column, \dQuote{`both`} selects both.}
#' }
#'
#' The clipping function should return a matrix
#' with the same number of rows as the `el` arguments.
#' If `end` is `both` then the matrix must have four
#' columns, otherwise two. The matrix contains the modified coordinates,
#' with the clipping applied.
#'
#' The plotting function has the following arguments:
#' \describe{
#'   \item{coords}{The coordinates of the vertices, a matrix with two
#'     columns.}
#'   \item{v}{The ids of the vertices to plot. It should match the number
#'     of rows in the `coords` argument.}
#'   \item{params}{The same as for the clipping function, see above.}
#' }
#'
#' The return value of the plotting function is not used.
#'
#' `shapes()` can be used to list the names of all installed
#' vertex shapes, by calling it without arguments, or setting the
#' `shape` argument to `NULL`. If a shape name is given, then
#' the clipping and plotting functions of that shape are returned in a
#' named list.
#'
#' `add_shape()` can be used to add new vertex shapes to
#' igraph. For this one must give the clipping and plotting functions of
#' the new shape. It is also possible to list the plot/vertex/edge
#' parameters, in the `parameters` argument, that the clipping
#' and/or plotting functions can make use of. An example would be a
#' generic regular polygon shape, which can have a parameter for the
#' number of sides.
#'
#' `shape_noclip()` is a very simple clipping function that the
#' user can use in their own shape definitions. It does no clipping, the
#' edges will be drawn exactly until the listed vertex position
#' coordinates.
#'
#' `shape_noplot()` is a very simple (and probably not very
#' useful) plotting function, that does not plot anything.
#'
#' @aliases add.vertex.shape igraph.shape.noclip igraph.shape.noplot
#'   vertex.shapes igraph.vertex.shapes
#'
#' @param shape Character scalar, name of a vertex shape. If it is
#'    `NULL` for `shapes()`, then the names of all defined
#'    vertex shapes are returned.
#' @param clip An R function object, the clipping function.
#' @param plot An R function object, the plotting function.
#' @param parameters Named list, additional plot/vertex/edge
#'    parameters. The element named define the new parameters, and the
#'    elements themselves define their default values.
#'    Vertex parameters should have a prefix
#'    \sQuote{`vertex.`}, edge parameters a prefix
#'    \sQuote{`edge.`}. Other general plotting parameters should have
#'    a prefix \sQuote{`plot.`}. See Details below.
#' @param coords,el,params,end,v See parameters of the clipping/plotting
#'    functions below.
#' @return `shapes()` returns a character vector if the
#'    `shape` argument is `NULL`. It returns a named list with
#'    entries named \sQuote{clip} and \sQuote{plot}, both of them R
#'    functions.
#'
#'    `add_shape()` returns `TRUE`, invisibly.
#'
#'    `shape_noclip()` returns the appropriate columns of its
#'    `coords` argument.
#' @family plot.shapes
#' @export
#'
#' @examples
#' # all vertex shapes, minus "raster", that might not be available
#' shapes <- setdiff(shapes(), "")
#' g <- make_ring(length(shapes))
#' set.seed(42)
#' plot(g,
#'   vertex.shape = shapes, vertex.label = shapes, vertex.label.dist = 1,
#'   vertex.size = 15, vertex.size2 = 15,
#'   vertex.pie = lapply(shapes, function(x) if (x == "pie") 2:6 else 0),
#'   vertex.pie.color = list(heat.colors(5))
#' )
#'
#' # add new vertex shape, plot nothing with no clipping
#' add_shape("nil")
#' plot(g, vertex.shape = "nil")
#'
#' #################################################################
#' # triangle vertex shape
#' mytriangle <- function(coords, v = NULL, params) {
#'   vertex.color <- params("vertex", "color")
#'   if (length(vertex.color) != 1 && !is.null(v)) {
#'     vertex.color <- vertex.color[v]
#'   }
#'   vertex.size <- 1 / 200 * params("vertex", "size")
#'   if (length(vertex.size) != 1 && !is.null(v)) {
#'     vertex.size <- vertex.size[v]
#'   }
#'
#'   symbols(
#'     x = coords[, 1], y = coords[, 2], bg = vertex.color,
#'     stars = cbind(vertex.size, vertex.size, vertex.size),
#'     add = TRUE, inches = FALSE
#'   )
#' }
#' # clips as a circle
#' add_shape("triangle",
#'   clip = shapes("circle")$clip,
#'   plot = mytriangle
#' )
#' plot(g,
#'   vertex.shape = "triangle", vertex.color = rainbow(vcount(g)),
#'   vertex.size = seq(10, 20, length.out = vcount(g))
#' )
#'
#' #################################################################
#' # generic star vertex shape, with a parameter for number of rays
#' mystar <- function(coords, v = NULL, params) {
#'   vertex.color <- params("vertex", "color")
#'   if (length(vertex.color) != 1 && !is.null(v)) {
#'     vertex.color <- vertex.color[v]
#'   }
#'   vertex.size <- 1 / 200 * params("vertex", "size")
#'   if (length(vertex.size) != 1 && !is.null(v)) {
#'     vertex.size <- vertex.size[v]
#'   }
#'   norays <- params("vertex", "norays")
#'   if (length(norays) != 1 && !is.null(v)) {
#'     norays <- norays[v]
#'   }
#'
#'   mapply(coords[, 1], coords[, 2], vertex.color, vertex.size, norays,
#'     FUN = function(x, y, bg, size, nor) {
#'       symbols(
#'         x = x, y = y, bg = bg,
#'         stars = matrix(c(size, size / 2), nrow = 1, ncol = nor * 2),
#'         add = TRUE, inches = FALSE
#'       )
#'     }
#'   )
#' }
#' # no clipping, edges will be below the vertices anyway
#' add_shape("star",
#'   clip = shape_noclip,
#'   plot = mystar, parameters = list(vertex.norays = 5)
#' )
#' plot(g,
#'   vertex.shape = "star", vertex.color = rainbow(vcount(g)),
#'   vertex.size = seq(10, 20, length.out = vcount(g))
#' )
#' plot(g,
#'   vertex.shape = "star", vertex.color = rainbow(vcount(g)),
#'   vertex.size = seq(10, 20, length.out = vcount(g)),
#'   vertex.norays = rep(4:8, length.out = vcount(g))
#' )
shapes <- function(shape = NULL) {
  if (is.null(shape)) {
    ls(.igraph.shapes)
  } else {
    ## checkScalarString(shape)
    .igraph.shapes[[shape]]
  }
}

#' @rdname shapes
#' @family plot.shapes
#' @export
shape_noclip <- function(coords, el, params,
                         end = c("both", "from", "to")) {
  end <- igraph.match.arg(end)

  if (end == "both") {
    coords
  } else if (end == "from") {
    coords[, 1:2, drop = FALSE]
  } else {
    coords[, 3:4, drop = FALSE]
  }
}

#' @rdname shapes
#' @family plot.shapes
#' @export
shape_noplot <- function(coords, v = NULL, params) {
  invisible(NULL)
}

#' @rdname shapes
#' @family plot.shapes
#' @export
add_shape <- function(shape, clip = shape_noclip,
                      plot = shape_noplot,
                      parameters = list()) {
  ## TODO
  ## checkScalarString(shape)
  ## checkFunction(clip)
  ## checkFunction(plot)
  ## checkList(parameters, named=TRUE)

  assign(shape, value = list(clip = clip, plot = plot), envir = .igraph.shapes)
  do.call(igraph.options, parameters)
  invisible(TRUE)
}

## These are the predefined shapes

.igraph.shape.circle.clip <- function(coords, el, params,
                                      end = c("both", "from", "to")) {
  end <- match.arg(end)

  if (length(coords) == 0) {
    return(coords)
  }

  vertex.size <- 1 / 200 * params("vertex", "size")

  if (end == "from") {
    phi <- atan2(coords[, 4] - coords[, 2], coords[, 3] - coords[, 1])
    vsize.from <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    res <- cbind(
      coords[, 1] + vsize.from * cos(phi),
      coords[, 2] + vsize.from * sin(phi)
    )
  } else if (end == "to") {
    phi <- atan2(coords[, 4] - coords[, 2], coords[, 3] - coords[, 1])
    r <- sqrt((coords[, 3] - coords[, 1])^2 + (coords[, 4] - coords[, 2])^2)
    vsize.to <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    res <- cbind(
      coords[, 1] + (r - vsize.to) * cos(phi),
      coords[, 2] + (r - vsize.to) * sin(phi)
    )
  } else if (end == "both") {
    phi <- atan2(coords[, 4] - coords[, 2], coords[, 3] - coords[, 1])
    r <- sqrt((coords[, 3] - coords[, 1])^2 + (coords[, 4] - coords[, 2])^2)
    vsize.from <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    vsize.to <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    res <- cbind(
      coords[, 1] + vsize.from * cos(phi),
      coords[, 2] + vsize.from * sin(phi),
      coords[, 1] + (r - vsize.to) * cos(phi),
      coords[, 2] + (r - vsize.to) * sin(phi)
    )
  }
  res
}

#' @importFrom graphics symbols
.igraph.shape.circle.plot <- function(coords, v = NULL, params) {
  vertex.color <- params("vertex", "color")
  if (length(vertex.color) != 1 && !is.null(v)) {
    vertex.color <- vertex.color[v]
  }
  vertex.frame.color <- params("vertex", "frame.color")
  if (length(vertex.frame.color) != 1 && !is.null(v)) {
    vertex.frame.color <- vertex.frame.color[v]
  }
  vertex.frame.width <- params("vertex", "frame.width")
  if (length(vertex.frame.width) != 1 && !is.null(v)) {
    vertex.frame.width <- vertex.frame.width[v]
  }
  vertex.size <- 1 / 200 * params("vertex", "size")
  if (length(vertex.size) != 1 && !is.null(v)) {
    vertex.size <- vertex.size[v]
  }
  vertex.size <- rep(vertex.size, length.out = nrow(coords))

  # Handle vertex.frame.width <= 0 by hiding the border
  vertex.frame.color[vertex.frame.width <= 0] <- NA
  vertex.frame.width[vertex.frame.width <= 0] <- 1

  if (length(vertex.frame.width) == 1) {
    symbols(
      x = coords[, 1], y = coords[, 2], bg = vertex.color, fg = vertex.frame.color,
      circles = vertex.size, lwd = vertex.frame.width, add = TRUE, inches = FALSE
    )
  } else {
    mapply(coords[, 1], coords[, 2], vertex.color, vertex.frame.color,
      vertex.size, vertex.frame.width,
      FUN = function(x, y, bg, fg, size, lwd) {
        symbols(
          x = x, y = y, bg = bg, fg = fg, lwd = lwd,
          circles = size, add = TRUE, inches = FALSE
        )
      }
    )
  }
}

.igraph.shape.square.clip <- function(coords, el, params,
                                      end = c("both", "from", "to")) {
  end <- match.arg(end)

  if (length(coords) == 0) {
    return(coords)
  }

  vertex.size <- 1 / 200 * params("vertex", "size")

  square.shift <- function(x0, y0, x1, y1, vsize) {
    m <- (y0 - y1) / (x0 - x1)
    l <- cbind(
      x1 - vsize / m, y1 - vsize,
      x1 - vsize, y1 - vsize * m,
      x1 + vsize / m, y1 + vsize,
      x1 + vsize, y1 + vsize * m
    )

    v <- cbind(
      x1 - vsize <= l[, 1] & l[, 1] <= x1 + vsize &
        y1 - vsize <= l[, 2] & l[, 2] <= y1 + vsize,
      x1 - vsize <= l[, 3] & l[, 3] <= x1 + vsize &
        y1 - vsize <= l[, 4] & l[, 4] <= y1 + vsize,
      x1 - vsize <= l[, 5] & l[, 5] <= x1 + vsize &
        y1 - vsize <= l[, 6] & l[, 6] <= y1 + vsize,
      x1 - vsize <= l[, 7] & l[, 7] <= x1 + vsize &
        y1 - vsize <= l[, 8] & l[, 8] <= y1 + vsize
    )

    d <- cbind(
      (l[, 1] - x0)^2 + (l[, 2] - y0)^2,
      (l[, 3] - x0)^2 + (l[, 4] - y0)^2,
      (l[, 5] - x0)^2 + (l[, 6] - y0)^2,
      (l[, 7] - x0)^2 + (l[, 8] - y0)^2
    )

    t(sapply(seq(length.out = nrow(l)), function(x) {
      d[x, ][!v[x, ]] <- Inf
      m <- which.min(d[x, ])
      l[x, c(m * 2 - 1, m * 2)]
    }))
  }

  if (end %in% c("from", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    res <- res1 <- square.shift(
      coords[, 3], coords[, 4], coords[, 1], coords[, 2],
      vsize
    )
  }
  if (end %in% c("to", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    res <- res2 <- square.shift(
      coords[, 1], coords[, 2], coords[, 3], coords[, 4],
      vsize
    )
  }
  if (end == "both") {
    res <- cbind(res1, res2)
  }

  res
}

#' @importFrom graphics symbols
.igraph.shape.square.plot <- function(coords, v = NULL, params) {
  vertex.color <- params("vertex", "color")
  if (length(vertex.color) != 1 && !is.null(v)) {
    vertex.color <- vertex.color[v]
  }
  vertex.frame.color <- params("vertex", "frame.color")
  if (length(vertex.frame.color) != 1 && !is.null(v)) {
    vertex.frame.color <- vertex.frame.color[v]
  }
  vertex.frame.width <- params("vertex", "frame.width")
  if (length(vertex.frame.width) != 1 && !is.null(v)) {
    vertex.frame.width <- vertex.frame.width[v]
  }
  vertex.size <- 1 / 200 * params("vertex", "size")
  if (length(vertex.size) != 1 && !is.null(v)) {
    vertex.size <- vertex.size[v]
  }
  vertex.size <- rep(vertex.size, length.out = nrow(coords))

  # Handle vertex.frame.width <= 0 by hiding the border
  vertex.frame.color[vertex.frame.width <= 0] <- NA
  vertex.frame.width[vertex.frame.width <= 0] <- 1

  if (length(vertex.frame.width) == 1) {
    symbols(
      x = coords[, 1], y = coords[, 2], bg = vertex.color, fg = vertex.frame.color,
      squares = 2 * vertex.size, lwd = vertex.frame.width, add = TRUE, inches = FALSE
    )
  } else {
    mapply(coords[, 1], coords[, 2], vertex.color, vertex.frame.color,
      vertex.size, vertex.frame.width,
      FUN = function(x, y, bg, fg, size, lwd) {
        symbols(
          x = x, y = y, bg = bg, fg = fg, lwd = lwd,
          squares = 2 * size, add = TRUE, inches = FALSE
        )
      }
    )
  }
}

.igraph.shape.csquare.clip <- function(coords, el, params,
                                       end = c("both", "from", "to")) {
  end <- match.arg(end)

  if (length(coords) == 0) {
    return(coords)
  }

  vertex.size <- 1 / 200 * params("vertex", "size")

  square.shift <- function(x0, y0, x1, y1, vsize) {
    l <- cbind(
      x1, y1 - vsize,
      x1 - vsize, y1,
      x1, y1 + vsize,
      x1 + vsize, y1
    )

    d <- cbind(
      (l[, 1] - x0)^2 + (l[, 2] - y0)^2,
      (l[, 3] - x0)^2 + (l[, 4] - y0)^2,
      (l[, 5] - x0)^2 + (l[, 6] - y0)^2,
      (l[, 7] - x0)^2 + (l[, 8] - y0)^2
    )

    t(sapply(seq(length.out = nrow(l)), function(x) {
      m <- which.min(d[x, ])
      l[x, c(m * 2 - 1, m * 2)]
    }))
  }

  if (end %in% c("from", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    res <- res1 <- square.shift(
      coords[, 3], coords[, 4], coords[, 1], coords[, 2],
      vsize
    )
  }
  if (end %in% c("to", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    res <- res2 <- square.shift(
      coords[, 1], coords[, 2], coords[, 3], coords[, 4],
      vsize
    )
  }
  if (end == "both") {
    res <- cbind(res1, res2)
  }

  res
}

.igraph.shape.csquare.plot <- .igraph.shape.square.plot

.igraph.shape.rectangle.clip <- function(coords, el, params,
                                         end = c("both", "from", "to")) {
  end <- match.arg(end)

  if (length(coords) == 0) {
    return(coords)
  }

  vertex.size <- 1 / 200 * params("vertex", "size")
  vertex.size2 <- 1 / 200 * params("vertex", "size2")

  rec.shift <- function(x0, y0, x1, y1, vsize, vsize2) {
    m <- (y0 - y1) / (x0 - x1)
    l <- cbind(
      x1 - vsize / m, y1 - vsize2,
      x1 - vsize, y1 - vsize * m,
      x1 + vsize2 / m, y1 + vsize2,
      x1 + vsize, y1 + vsize * m
    )

    v <- cbind(
      x1 - vsize <= l[, 1] & l[, 1] <= x1 + vsize &
        y1 - vsize2 <= l[, 2] & l[, 2] <= y1 + vsize2,
      x1 - vsize <= l[, 3] & l[, 3] <= x1 + vsize &
        y1 - vsize2 <= l[, 4] & l[, 4] <= y1 + vsize2,
      x1 - vsize <= l[, 5] & l[, 5] <= x1 + vsize &
        y1 - vsize2 <= l[, 6] & l[, 6] <= y1 + vsize2,
      x1 - vsize <= l[, 7] & l[, 7] <= x1 + vsize &
        y1 - vsize2 <= l[, 8] & l[, 8] <= y1 + vsize2
    )

    d <- cbind(
      (l[, 1] - x0)^2 + (l[, 2] - y0)^2,
      (l[, 3] - x0)^2 + (l[, 4] - y0)^2,
      (l[, 5] - x0)^2 + (l[, 6] - y0)^2,
      (l[, 7] - x0)^2 + (l[, 8] - y0)^2
    )

    t(sapply(seq(length.out = nrow(l)), function(x) {
      d[x, ][!v[x, ]] <- Inf
      m <- which.min(d[x, ])
      l[x, c(m * 2 - 1, m * 2)]
    }))
  }

  if (end %in% c("from", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    vsize2 <- if (length(vertex.size2) == 1) {
      vertex.size2
    } else {
      vertex.size2[el[, 1]]
    }
    res <- res1 <- rec.shift(
      coords[, 3], coords[, 4], coords[, 1], coords[, 2],
      vsize, vsize2
    )
  }
  if (end %in% c("to", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    vsize2 <- if (length(vertex.size2) == 1) {
      vertex.size2
    } else {
      vertex.size2[el[, 2]]
    }
    res <- res2 <- rec.shift(
      coords[, 1], coords[, 2], coords[, 3], coords[, 4],
      vsize, vsize2
    )
  }
  if (end == "both") {
    res <- cbind(res1, res2)
  }

  res
}

#' @importFrom graphics symbols
.igraph.shape.rectangle.plot <- function(coords, v = NULL, params) {
  vertex.color <- params("vertex", "color")
  if (length(vertex.color) != 1 && !is.null(v)) {
    vertex.color <- vertex.color[v]
  }
  vertex.frame.color <- params("vertex", "frame.color")
  if (length(vertex.frame.color) != 1 && !is.null(v)) {
    vertex.frame.color <- vertex.frame.color[v]
  }
  vertex.frame.width <- params("vertex", "frame.width")
  if (length(vertex.frame.width) != 1 && !is.null(v)) {
    vertex.frame.width <- vertex.frame.width[v]
  }
  vertex.size <- 1 / 200 * params("vertex", "size")
  if (length(vertex.size) != 1 && !is.null(v)) {
    vertex.size <- vertex.size[v]
  }
  vertex.size <- rep(vertex.size, length.out = nrow(coords))
  vertex.size2 <- 1 / 200 * params("vertex", "size2")
  if (length(vertex.size2) != 1 && !is.null(v)) {
    vertex.size2 <- vertex.size2[v]
  }
  vertex.size <- cbind(vertex.size, vertex.size2)

  # Handle vertex.frame.width <= 0 by hiding the border
  vertex.frame.color[vertex.frame.width <= 0] <- NA
  vertex.frame.width[vertex.frame.width <= 0] <- 1

  if (length(vertex.frame.width) == 1) {
    symbols(
      x = coords[, 1], y = coords[, 2], bg = vertex.color, fg = vertex.frame.color,
      rectangles = 2 * vertex.size, lwd = vertex.frame.width, add = TRUE, inches = FALSE
    )
  } else {
    mapply(coords[, 1], coords[, 2], vertex.color, vertex.frame.color,
      vertex.size[, 1], vertex.size[, 2], vertex.frame.width,
      FUN = function(x, y, bg, fg, size, size2, lwd) {
        symbols(
          x = x, y = y, bg = bg, fg = fg, lwd = lwd,
          rectangles = 2 * cbind(size, size2), add = TRUE, inches = FALSE
        )
      }
    )
  }
}

.igraph.shape.crectangle.clip <- function(coords, el, params,
                                          end = c("both", "from", "to")) {
  end <- match.arg(end)

  if (length(coords) == 0) {
    return(coords)
  }

  vertex.size <- 1 / 200 * params("vertex", "size")
  vertex.size2 <- 1 / 200 * params("vertex", "size2")

  rec.shift <- function(x0, y0, x1, y1, vsize, vsize2) {
    l <- cbind(
      x1, y1 - vsize2,
      x1 - vsize, y1,
      x1, y1 + vsize2,
      x1 + vsize, y1
    )

    d <- cbind(
      (l[, 1] - x0)^2 + (l[, 2] - y0)^2,
      (l[, 3] - x0)^2 + (l[, 4] - y0)^2,
      (l[, 5] - x0)^2 + (l[, 6] - y0)^2,
      (l[, 7] - x0)^2 + (l[, 8] - y0)^2
    )

    t(sapply(seq(length.out = nrow(l)), function(x) {
      m <- which.min(d[x, ])
      l[x, c(m * 2 - 1, m * 2)]
    }))
  }

  if (end %in% c("from", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    vsize2 <- if (length(vertex.size2) == 1) {
      vertex.size2
    } else {
      vertex.size2[el[, 1]]
    }
    res <- res1 <- rec.shift(
      coords[, 3], coords[, 4], coords[, 1], coords[, 2],
      vsize, vsize2
    )
  }
  if (end %in% c("to", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    vsize2 <- if (length(vertex.size2) == 1) {
      vertex.size2
    } else {
      vertex.size2[el[, 2]]
    }
    res <- res2 <- rec.shift(
      coords[, 1], coords[, 2], coords[, 3], coords[, 4],
      vsize, vsize2
    )
  }
  if (end == "both") {
    res <- cbind(res1, res2)
  }

  res
}

.igraph.shape.crectangle.plot <- .igraph.shape.rectangle.plot

.igraph.shape.vrectangle.clip <- function(coords, el, params,
                                          end = c("both", "from", "to")) {
  end <- match.arg(end)

  if (length(coords) == 0) {
    return(coords)
  }

  vertex.size <- 1 / 200 * params("vertex", "size")
  vertex.size2 <- 1 / 200 * params("vertex", "size2")

  rec.shift <- function(x0, y0, x1, y1, vsize, vsize2) {
    l <- cbind(x1 - vsize, y1, x1 + vsize, y1)

    d <- cbind(
      (l[, 1] - x0)^2 + (l[, 2] - y0)^2,
      (l[, 3] - x0)^2 + (l[, 4] - y0)^2
    )

    t(sapply(seq(length.out = nrow(l)), function(x) {
      m <- which.min(d[x, ])
      l[x, c(m * 2 - 1, m * 2)]
    }))
  }

  if (end %in% c("from", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    vsize2 <- if (length(vertex.size2) == 1) {
      vertex.size2
    } else {
      vertex.size2[el[, 1]]
    }
    res <- res1 <- rec.shift(
      coords[, 3], coords[, 4], coords[, 1], coords[, 2],
      vsize, vsize2
    )
  }
  if (end %in% c("to", "both")) {
    vsize <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    vsize2 <- if (length(vertex.size2) == 1) {
      vertex.size2
    } else {
      vertex.size2[el[, 2]]
    }
    res <- res2 <- rec.shift(
      coords[, 1], coords[, 2], coords[, 3], coords[, 4],
      vsize, vsize2
    )
  }
  if (end == "both") {
    res <- cbind(res1, res2)
  }

  res
}

.igraph.shape.vrectangle.plot <- .igraph.shape.rectangle.plot

.igraph.shape.none.clip <- .igraph.shape.circle.clip

.igraph.shape.none.plot <- function(coords, v = NULL, params) {
  ## does not plot anything at all
  invisible(NULL)
}

#' @importFrom graphics par polygon
mypie <- function(x, y, values, radius, edges = 200, col = NULL, angle = 45,
                  density = NULL, border = NULL, lty = NULL, init.angle = 90, ...) {
  values <- c(0, cumsum(values) / sum(values))
  dx <- diff(values)
  nx <- length(dx)
  twopi <- 2 * pi
  if (is.null(col)) {
    col <- if (is.null(density)) {
      c(
        "white", "lightblue", "mistyrose", "lightcyan",
        "lavender", "cornsilk"
      )
    } else {
      par("fg")
    }
  }
  col <- rep(col, length.out = nx)
  border <- rep(border, length.out = nx)
  lty <- rep(lty, length.out = nx)
  angle <- rep(angle, length.out = nx)
  density <- rep(density, length.out = nx)
  t2xy <- function(t) {
    t2p <- twopi * t + init.angle * pi / 180
    list(x = radius * cos(t2p), y = radius * sin(t2p))
  }
  for (i in 1:nx) {
    n <- max(2, floor(edges * dx[i]))
    P <- t2xy(seq.int(values[i], values[i + 1], length.out = n))
    polygon(x + c(P$x, 0), y + c(P$y, 0),
      density = density[i], angle = angle[i],
      border = border[i], col = col[i], lty = lty[i], ...
    )
  }
}

.igraph.shape.pie.clip <- function(coords, el, params,
                                   end = c("both", "from", "to")) {
  end <- match.arg(end)

  if (length(coords) == 0) {
    return(coords)
  }

  vertex.size <- 1 / 200 * params("vertex", "size")

  if (end == "from") {
    phi <- atan2(coords[, 4] - coords[, 2], coords[, 3] - coords[, 1])
    vsize.from <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    res <- cbind(
      coords[, 1] + vsize.from * cos(phi),
      coords[, 2] + vsize.from * sin(phi)
    )
  } else if (end == "to") {
    phi <- atan2(coords[, 4] - coords[, 2], coords[, 3] - coords[, 1])
    r <- sqrt((coords[, 3] - coords[, 1])^2 + (coords[, 4] - coords[, 2])^2)
    vsize.to <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    res <- cbind(
      coords[, 1] + (r - vsize.to) * cos(phi),
      coords[, 2] + (r - vsize.to) * sin(phi)
    )
  } else if (end == "both") {
    phi <- atan2(coords[, 4] - coords[, 2], coords[, 3] - coords[, 1])
    r <- sqrt((coords[, 3] - coords[, 1])^2 + (coords[, 4] - coords[, 2])^2)
    vsize.from <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 1]]
    }
    vsize.to <- if (length(vertex.size) == 1) {
      vertex.size
    } else {
      vertex.size[el[, 2]]
    }
    res <- cbind(
      coords[, 1] + vsize.from * cos(phi),
      coords[, 2] + vsize.from * sin(phi),
      coords[, 1] + (r - vsize.to) * cos(phi),
      coords[, 2] + (r - vsize.to) * sin(phi)
    )
  }

  res
}

#' @importFrom stats na.omit
.igraph.shape.pie.plot <- function(coords, v = NULL, params) {
  getparam <- function(pname) {
    p <- params("vertex", pname)
    if (length(p) != 1 && !is.null(v)) {
      p <- p[v]
    }
    p
  }
  vertex.color <- getparam("color")
  vertex.frame.color <- getparam("frame.color")
  vertex.size <- rep(1 / 200 * getparam("size"), length.out = nrow(coords))
  vertex.pie <- getparam("pie")
  vertex.pie.color <- getparam("pie.color")
  vertex.pie.angle <- getparam("pie.angle")
  vertex.pie.density <- getparam("pie.density")
  vertex.pie.lty <- getparam("pie.lty")

  for (i in seq_len(nrow(coords))) {
    pie <- if (length(vertex.pie) == 1) {
      vertex.pie[[1]]
    } else {
      vertex.pie[[i]]
    }
    col <- if (length(vertex.pie.color) == 1) {
      vertex.pie.color[[1]]
    } else {
      vertex.pie.color[[i]]
    }
    mypie(
      x = coords[i, 1], y = coords[i, 2], pie,
      radius = vertex.size[i], edges = 200, col = col,
      angle = na.omit(vertex.pie.angle[c(i, 1)])[1],
      density = na.omit(vertex.pie.density[c(i, 1)])[1],
      border = na.omit(vertex.frame.color[c(i, 1)])[1],
      lty = na.omit(vertex.pie.lty[c(i, 1)])[1]
    )
  }
}

.igraph.shape.sphere.clip <- .igraph.shape.circle.clip

#' @importFrom graphics rasterImage
#' @importFrom grDevices col2rgb as.raster
.igraph.shape.sphere.plot <- function(coords, v = NULL, params) {
  getparam <- function(pname) {
    p <- params("vertex", pname)
    if (length(p) != 1 && !is.null(v)) {
      p <- p[v]
    }
    p
  }
  vertex.color <- rep(getparam("color"), length.out = nrow(coords))
  vertex.size <- rep(1 / 200 * getparam("size"), length.out = nrow(coords))

  ## Need to create a separate image for every different vertex color
  allcols <- unique(vertex.color)
  images <- lapply(allcols, function(col) {
    img <- .Call(R_igraph_getsphere,
      pos = c(0.0, 0.0, 10.0), radius = 7.0,
      color = col2rgb(col) / 255, bgcolor = c(0, 0, 0),
      lightpos = list(c(-2, 2, 2)), lightcolor = list(c(1, 1, 1)),
      width = 100L, height = 100L
    )
    as.raster(img)
  })
  whichImage <- match(vertex.color, allcols)

  for (i in seq_len(nrow(coords))) {
    vsp2 <- vertex.size[i]
    rasterImage(
      images[[whichImage[i]]],
      coords[i, 1] - vsp2, coords[i, 2] - vsp2,
      coords[i, 1] + vsp2, coords[i, 2] + vsp2
    )
  }
}

.igraph.shape.raster.clip <- .igraph.shape.rectangle.clip

#' @importFrom graphics rasterImage
.igraph.shape.raster.plot <- function(coords, v = NULL, params) {
  getparam <- function(pname) {
    p <- params("vertex", pname)
    if (is.list(p) && length(p) != 1 && !is.null(v)) {
      p <- p[v]
    }
    p
  }

  size <- rep(1 / 200 * getparam("size"), length.out = nrow(coords))
  size2 <- rep(1 / 200 * getparam("size2"), length.out = nrow(coords))
  raster <- getparam("raster")

  for (i in seq_len(nrow(coords))) {
    ras <- if (!is.list(raster) || length(raster) == 1) raster else raster[[i]]
    rasterImage(
      ras, coords[i, 1] - size[i], coords[i, 2] - size2[i],
      coords[i, 1] + size[i], coords[i, 2] + size2[i]
    )
  }
}

.igraph.shapes <- new.env()
.igraph.shapes[["circle"]] <- list(
  clip = .igraph.shape.circle.clip,
  plot = .igraph.shape.circle.plot
)
.igraph.shapes[["square"]] <- list(
  clip = .igraph.shape.square.clip,
  plot = .igraph.shape.square.plot
)
.igraph.shapes[["csquare"]] <- list(
  clip = .igraph.shape.csquare.clip,
  plot = .igraph.shape.csquare.plot
)
.igraph.shapes[["rectangle"]] <- list(
  clip = .igraph.shape.rectangle.clip,
  plot = .igraph.shape.rectangle.plot
)
.igraph.shapes[["crectangle"]] <- list(
  clip = .igraph.shape.crectangle.clip,
  plot = .igraph.shape.crectangle.plot
)
.igraph.shapes[["vrectangle"]] <- list(
  clip = .igraph.shape.vrectangle.clip,
  plot = .igraph.shape.vrectangle.plot
)
.igraph.shapes[["none"]] <- list(
  clip = .igraph.shape.none.clip,
  plot = .igraph.shape.none.plot
)
.igraph.shapes[["pie"]] <- list(
  clip = .igraph.shape.pie.clip,
  plot = .igraph.shape.pie.plot
)
.igraph.shapes[["sphere"]] <- list(
  clip = .igraph.shape.sphere.clip,
  plot = .igraph.shape.sphere.plot
)
.igraph.shapes[["raster"]] <- list(
  clip = .igraph.shape.raster.clip,
  plot = .igraph.shape.raster.plot
)