R/linim.R

In spatstat.linnet: Linear Networks Functionality of the 'spatstat' Family

#
# linim.R
#
#  $Revision: 1.85 $   $Date: 2023/05/04 01:37:22 $
#
#  Image/function on a linear network
#

linim <- function(L, Z, ..., restrict=TRUE, df=NULL) {
  L <- as.linnet(L)
  stopifnot(is.im(Z))
  class(Z) <- "im"    # prevent unintended dispatch 
  dfgiven <- !is.null(df)
  if(dfgiven) {
    stopifnot(is.data.frame(df))
    neednames <- c("xc", "yc", "x", "y", "mapXY", "tp", "values")
    ok <- neednames %in% names(df)
    dfcomplete <- all(ok)
    if(!dfcomplete) {
      #' omission of "values" column is permissible, but not other columns
      mapnames <- setdiff(neednames, "values")
      if(!all(mapnames %in% names(df))) {
        nn <- sum(!ok)
        stop(paste(ngettext(nn, "A column", "Columns"),
                   "named", commasep(sQuote(neednames[!ok])),
                   ngettext(nn, "is", "are"),
                   "missing from argument", sQuote("df")))
      }
    }
  }
  if(restrict) {
    #' restrict image to pixels actually lying on the network
    M <- psp2mask(as.psp(L), Z)
    if(dfgiven) {
      #' ensure all mapped pixels are untouched
      pos <- nearest.pixel(df$xc, df$yc, Z)
      pos <- cbind(pos$row, pos$col)
      M$m[pos] <- TRUE
    }
    Z <- Z[M, drop=FALSE]
  }
  if(!dfgiven) {
    # compute the data frame of mapping information
    xx <- rasterx.im(Z)
    yy <- rastery.im(Z)
    mm <- !is.na(Z$v)
    xx <- as.vector(xx[mm])
    yy <- as.vector(yy[mm])
    pixelcentres <- ppp(xx, yy, window=as.rectangle(Z), check=FALSE)
    pixdf <- data.frame(xc=xx, yc=yy)
    # project pixel centres onto lines
    p2s <- project2segment(pixelcentres, as.psp(L))
    projloc <- as.data.frame(p2s$Xproj)
    projmap <- as.data.frame(p2s[c("mapXY", "tp")])
    # extract values
    values <- Z[pixelcentres]
    # bundle
    df <- cbind(pixdf, projloc, projmap, data.frame(values=values))
  } else if(!dfcomplete) {
    #' look up values
    pixelcentres <- ppp(df$xc, df$yc, window=as.rectangle(Z), check=FALSE)
    df$values <- safelookup(Z, pixelcentres)
  }
  out <- Z
  attr(out, "L") <- L
  attr(out, "df") <- df
  class(out) <- c("linim", class(out))
  return(out)
}

is.linim <- function(x) { inherits(x, "linim") }

print.linim <- function(x, ...) {
  splat("Image on linear network")
  L <- attr(x, "L")
  Lu <- summary(unitname(L))
  nsample <- nrow(attr(x, "df"))
  print(L)
  NextMethod("print")
  if(!is.null(nsample))
    splat(" Data frame:", nsample, "sample points along network", "\n",
          "Average density: one sample point per",
          signif(volume(L)/nsample, 3),
          Lu$plural, Lu$explain)
  return(invisible(NULL))
}

summary.linim <- function(object, ...) {
  y <- NextMethod("summary")
  if("integral" %in% names(y))
    y$integral <- integral(object)
  y$network <- summary(as.linnet(object))
  class(y) <- c("summary.linim", class(y))
  return(y)
}

print.summary.linim <- function(x, ...) {
  splat(paste0(x$type, "-valued"), "pixel image on a linear network")
  unitinfo <- summary(x$units)
  pluralunits <- unitinfo$plural
  sigdig <- getOption('digits')
  di <- x$dim
  win <- x$window
  splat(di[1L], "x", di[2L], "pixel array (ny, nx)")
  splat("enclosing rectangle:",
        prange(signif(win$xrange, sigdig)),
        "x",
        prange(signif(win$yrange, sigdig)),
        unitinfo$plural,
        unitinfo$explain)
  splat("dimensions of each pixel:",
        signif(x$xstep, 3), "x", signif(x$ystep, sigdig),
        pluralunits)
  if(!is.null(explain <- unitinfo$explain))
    splat(explain)
  splat("Pixel values (on network):")
  switch(x$type,
         integer=,
         real={
           splat("\trange =", prange(signif(x$range, sigdig)))
           splat("\tintegral =", signif(x$integral, sigdig))
           splat("\tmean =", signif(x$mean, sigdig))
         },
         factor={
           print(x$table)
         },
         complex={
           splat("\trange: Real",
                 prange(signif(x$Re$range, sigdig)),
                 "Imaginary",
                 prange(signif(x$Im$range, sigdig)))
           splat("\tintegral =", signif(x$integral, sigdig))
           splat("\tmean =", signif(x$mean, sigdig))
         },
         {
           print(x$summary)
         })
  splat("Underlying network:")
  print(x$network)
  return(invisible(NULL))
}


plot.linim <- local({

  plot.linim <- function(x, ..., style=c("colour", "width"),
                         scale, adjust=1, fatten=0, 
                         negative.args=list(col=2),
                         legend=TRUE,
                         leg.side=c("right", "left", "bottom", "top"),
                         leg.sep=0.1,
                         leg.wid=0.1,
                         leg.args=list(),
                         leg.scale=1,
                         zlim,
                         box=FALSE,
                         do.plot=TRUE) {
    xname <- short.deparse(substitute(x))
    style <- match.arg(style)
    leg.side <- match.arg(leg.side)
    check.1.real(leg.scale)
    force(x)

    if(!missing(fatten)) {
      check.1.real(fatten)
      if(fatten != 0 && style == "width")
        warning("Argument 'fatten' is ignored when style='width'", call.=FALSE)
      stopifnot(fatten >= 0)
    }
    
    if(missing(zlim) || is.null(zlim)) {
      zlim <- NULL
      zliminfo <- list()
    } else {
      check.range(zlim)
      stopifnot(all(is.finite(zlim)))
      zliminfo <- list(zlim=zlim)
    }
    
    ribstuff <- list(ribbon   = legend,
                     ribside  = leg.side,
                     ribsep   = leg.sep,
                     ribwid   = leg.wid,
                     ribargs  = leg.args,
                     ribscale = leg.scale)
    
    if(style == "colour" || !do.plot) {
      #' colour style: plot as pixel image
      if(fatten > 0) {
        #' first fatten the lines 
        L <- attr(x, "L")
        S <- as.psp(L)
        D <- distmap(psp2mask(S, xy=x))
        fatwin <- levelset(D, fatten)
        x <- nearestValue(x)[fatwin, drop=FALSE]
      }
      return(do.call(plot.im,
                     resolve.defaults(list(quote(x)),
                                      list(...),
                                      ribstuff,
                                      zliminfo, 
                                      list(main=xname,
                                           legend=legend,
                                           do.plot=do.plot,
                                           box=box))))
    }
    #' width style
    L <- attr(x, "L")
    df <- attr(x, "df")
    Llines <- as.psp(L)
    W <- as.owin(L)
    #' ensure function values are numeric
    vals <- try(as.numeric(df$values))
    if(inherits(vals, "try-error")) 
      stop("Function values should be numeric: unable to convert them",
           call.=FALSE)
    #' convert non-finite values to zero width
    vals[!is.finite(vals)] <- 0
    df$values <- vals
    #' plan layout
    if(legend) {
      #' use layout procedure in plot.im
      z <- do.call(plot.im,
                   resolve.defaults(list(quote(x), do.plot=FALSE, ribbon=TRUE),
                                    list(...),
                                    ribstuff,
                                    list(main=xname, valuesAreColours=FALSE)))
      bb.all <- attr(z, "bbox")
      bb.leg <- attr(z, "bbox.legend")
    } else {
      bb.all <- Frame(W)
      bb.leg <- NULL
    }
    legend <- !is.null(bb.leg)
    if(legend) {
      #' expand plot region to accommodate text annotation in legend
      if(leg.side %in% c("left", "right")) {
        delta <- 2 * sidelengths(bb.leg)[1]
        xmargin <- if(leg.side == "right") c(0, delta) else c(delta, 0)
        bb.all <- grow.rectangle(bb.all, xmargin=xmargin)
      }
    }
    #' initialise plot
    bb <- do.call.matched(plot.owin,
                          resolve.defaults(list(x=quote(bb.all), type="n"),
                                           list(...), list(main=xname)),
                          extrargs="type")
    if(box)
      plot(Frame(W), add=TRUE)
    #' resolve graphics parameters for polygons
    names(negative.args) <- paste0(names(negative.args), ".neg")
    grafpar <- resolve.defaults(negative.args,
                                list(...),
                               list(col=1),
                                .MatchNull=FALSE)
    #' rescale values to a plottable range
    if(is.null(zlim)) zlim <- range(x, finite=TRUE)
    vr <- range(0, zlim)
    if(missing(scale)) {
      maxsize <- mean(distmap(Llines))/2
      scale <- maxsize/max(abs(vr))
    } 
    df$values <- adjust * scale * df$values/2
    #' examine sign of values
    signtype <- if(vr[1] >= 0) "positive" else
                if(vr[2] <= 0) "negative" else "mixed"
    #' split data by segment
    mapXY <- factor(df$mapXY, levels=seq_len(Llines$n))
    dfmap <- split(df, mapXY, drop=TRUE)
    #' sort each segment's data by position along segment
    dfmap <- lapply(dfmap, sortalongsegment)
    #' plot each segment's data
    Lperp <- angles.psp(Llines) + pi/2
    Lfrom <- L$from
    Lto   <- L$to
    Lvert <- L$vertices
    Ljoined  <- (vertexdegree(L) > 1)
    #' precompute coordinates of dodecagon
    dodo <- disc(npoly=12)$bdry[[1L]]
    #'
    for(i in seq(length(dfmap))) {
      z <- dfmap[[i]]
      segid <- unique(z$mapXY)[1L]
      xx <- z$x
      yy <- z$y
      vv <- z$values
      #' add endpoints of segment
      ileft <- Lfrom[segid]
      iright <- Lto[segid]
      leftend <- Lvert[ileft]
      rightend <- Lvert[iright]
      xx <- c(leftend$x, xx, rightend$x)
      yy <- c(leftend$y, yy, rightend$y)
      vv <- c(vv[1L],     vv, vv[length(vv)])
      rleft <- vv[1L]
      rright <- vv[length(vv)]
      ## first add dodecagonal 'joints'
      if(Ljoined[ileft] && rleft != 0) 
        drawSignedPoly(x=rleft * dodo$x + leftend$x,
                      y=rleft * dodo$y + leftend$y,
                      grafpar, sign(rleft))
      if(Ljoined[iright] && rright != 0)
        drawSignedPoly(x=rright * dodo$x + rightend$x,
                      y=rright * dodo$y + rightend$y,
                      grafpar, sign(rright))
      ## Now render main polygon
      ang <- Lperp[segid]
      switch(signtype,
             positive = drawseg(xx, yy, vv, ang, grafpar),
             negative = drawseg(xx, yy, vv, ang, grafpar),
             mixed = {
               ## find zero-crossings
               xing <- (diff(sign(vv)) != 0)
               ## excursions
               excu <- factor(c(0, cumsum(xing)))
               elist <- split(data.frame(xx=xx, yy=yy, vv=vv), excu)
               ## plot each excursion
               for(e in elist) 
                 with(e, drawseg(xx, yy, vv, ang, grafpar))
             })
    }
    result <- adjust * scale
    attr(result, "bbox") <- bb
    if(legend) {
      attr(result, "bbox.legend") <- bb.leg
      plotWidthMap(bb.leg     = bb.leg,
                   zlim       = zlim,
                   phys.scale = adjust * scale, 
                   leg.scale  = leg.scale,
                   leg.side   = leg.side,
                   leg.args   = leg.args,
                   grafpar    = grafpar)
    }
    return(invisible(result))
  }

  drawseg <- function(xx, yy, vv, ang, pars) {
    ## draw polygon around segment
    sgn <- sign(mean(vv))
    xx <- c(xx, rev(xx))
    yy <- c(yy, rev(yy))
    vv <- c(vv, -rev(vv))
    xx <- xx + cos(ang) * vv
    yy <- yy + sin(ang) * vv
    drawSignedPoly(xx, yy, pars, sgn)
    invisible(NULL)
  }

  plot.linim
})


sortalongsegment <- function(df) {
  df[fave.order(df$tp), , drop=FALSE]
}

as.im.linim <- function(X, ...) {
  attr(X, "L") <- attr(X, "df") <- NULL
  class(X) <- "im"
  if(length(list(...)) > 0)
    X <- as.im(X, ...)
  return(X)
}

as.linim <- function(X, ...) {
  UseMethod("as.linim")
}

as.linim.default <- function(X, L, ..., eps = NULL, dimyx = NULL, xy = NULL,
                             rule.eps=c("adjust.eps",
                                        "grow.frame", "shrink.frame"),
                             delta = NULL, nd = NULL) {
  stopifnot(inherits(L, "linnet"))
  rule.eps <- match.arg(rule.eps)
  Y <- as.im(X, W=Frame(L), ..., eps=eps, dimyx=dimyx, xy=xy, rule.eps=rule.eps)
  M <- psp2mask(as.psp(L), as.owin(Y))
  Y[complement.owin(M)] <- NA
  df <- NULL
  if(!is.null(delta) || !is.null(nd)) {
    if(is.null(delta)) delta <- volume(L)/nd
    df <- pointsAlongNetwork(L, delta)
    pix <- nearest.valid.pixel(df$x, df$y, Y)
    df$xc <- Y$xcol[pix$col]
    df$yc <- Y$yrow[pix$row]
    df$values <- Y$v[cbind(pix$row, pix$col)]
    df <- df[,c("xc", "yc", "x", "y", "seg", "tp", "values")]
    names(df)[names(df) == "seg"] <- "mapXY"
  }
  if(is.mask(WL <- Window(L)) && !all(sapply(list(eps, dimyx, xy), is.null))) {
    Window(L, check=FALSE) <- as.mask(WL,
                              eps=eps, dimyx=dimyx, xy=xy, rule.eps=rule.eps)
  }
  out <- linim(L, Y, df=df, restrict=FALSE)
  return(out)
}

pointsAlongNetwork <- function(L, delta) {
  #' sample points evenly spaced along each segment
  stopifnot(inherits(L, "linnet"))
  S <- as.psp(L)
  ns <- nsegments(S)
  seglen <- lengths_psp(S)
  ends <- as.data.frame(S)
  nsample <- pmax(1, ceiling(seglen/delta))
  df <- NULL
  x0 <- ends$x0
  y0 <- ends$y0
  x1 <- ends$x1
  y1 <- ends$y1
  for(i in seq_len(ns)) {
    nn <- nsample[i] + 1L
    tcut <- seq(0, 1, length.out=nn)
    tp <- (tcut[-1] + tcut[-nn])/2
    x <- x0[i] * (1-tp) + x1[i] * tp
    y <- y0[i] * (1-tp) + y1[i] * tp
    df <- rbind(df, data.frame(x=x, y=y, seg=i, tp=tp))
  }
  return(df)          
}

as.linim.linim <- function(X, ...) {
  if(length(list(...)) == 0)
    return(X)
  Y <- as.linim.default(X, as.linnet(X), ...)
  return(Y)
}

# analogue of eval.im

eval.linim <- function(expr, envir, harmonize=TRUE, warn=TRUE) {
  sc <- sys.call()
  # Get names of all variables in the expression
  e <- as.expression(substitute(expr))
  varnames <- all.vars(e)
  allnames <- all.names(e, unique=TRUE)
  funnames <- allnames[!(allnames %in% varnames)]
  if(length(varnames) == 0)
    stop("No variables in this expression")
  # get the values of the variables
  if(missing(envir)) {
    envir <- parent.frame() # WAS: sys.parent()
  } else if(is.list(envir)) {
    envir <- list2env(envir, parent=parent.frame())
  }
  vars <- mget(varnames, envir=envir, inherits=TRUE, ifnotfound=list(NULL))
  funs <- mget(funnames, envir=envir, inherits=TRUE, ifnotfound=list(NULL))
  # Find out which variables are (linear) images
  islinim <- unlist(lapply(vars, inherits, what="linim"))
  if(!any(islinim))
    stop("There are no linear images (class linim) in this expression")
  # ....................................
  # Evaluate the pixel values using eval.im
  # ....................................
  sc[[1L]] <- as.name('eval.im')
  sc$envir <- envir
  Y <- eval(sc)
  # .........................................
  # Then evaluate data frame entries if feasible
  # .........................................
  dfY <- NULL
  linims <- vars[islinim]
  nlinims <- length(linims)
  dframes <- lapply(linims, attr, which="df")
  nets <- lapply(linims, attr, which="L")
  isim <- unlist(lapply(vars, is.im))
  if(!any(isim & !islinim)) {
    # all images are 'linim' objects
    # Check that the images refer to the same linear network
    if(nlinims > 1) {
      agree <- unlist(lapply(nets[-1L], identical, y=nets[[1L]]))
      if(!all(agree))
        stop(paste("Images do not refer to the same linear network"))
    }
    dfempty <- unlist(lapply(dframes, is.null))
    if(!any(dfempty)) {
      # ensure data frames are compatible
      if(length(dframes) > 1 && (
          length(unique(nr <- sapply(dframes, nrow))) > 1   ||
           !allElementsIdentical(dframes, "seg")            ||
   	   !allElementsIdentical(dframes, "tp")
	)) {
        # find the one with finest spacing
	imax <- which.max(nr)
	# resample the others
	dframes[-imax] <- lapply(dframes[-imax],
	                         resampleNetworkDataFrame,
	                         template=dframes[[imax]])
      }
      # replace each image variable by its data frame column of values
      vars[islinim] <- lapply(dframes, getElement, "values")
      # now evaluate expression
      Yvalues <- eval(e, append(vars, funs))
      # pack up
      dfY <- dframes[[1L]]
      dfY$values <- Yvalues
    }
  }
  result <- linim(nets[[1L]], Y, df=dfY, restrict=FALSE)
  return(result)
}

resampleNetworkDataFrame <- function(df, template) {
  # resample 'df' at the points of 'template'
  invalues  <- df$values
  insegment <- df$mapXY
  inteepee  <- df$tp
  out <- template
  n <- nrow(out)
  outvalues <- vector(mode = typeof(invalues), length=n)
  outsegment <- out$mapXY
  outteepee  <- out$tp
  for(i in seq_len(n)) {
    relevant <- which(insegment == outsegment[i])
    if(length(relevant) > 0) {
      j <- which.min(abs(inteepee[relevant] - outteepee[i]))
      outvalues[i] <- invalues[relevant[j]]
    }
  }
  out$values <- outvalues
  return(out)
}

as.linnet.linim <- function(X, ...) {
  attr(X, "L")
}

"[.linim" <- function(x, i, ..., drop=TRUE) {
  if(!missing(i) && is.lpp(i)) {
    n <- npoints(i)
    result <- vector(mode=typeof(x$v), length=n)
    if(is.factor(x$v)) {
      lev <- levels(x$v)
      result <- factor(result, levels=seq_along(lev), labels=lev)
    }
    if(n == 0) return(result)
    if(!is.null(df <- attr(x, "df"))) {
      #' use data frame of sample points along network
      knownseg <- df$mapXY
      knowntp  <- df$tp
      knownval <- df$values
      #' extract local coordinates of query points
      coo <- coords(i)
      queryseg <- coo$seg
      querytp  <- coo$tp
      #' match to nearest sample point
      for(j in 1:n) {
        relevant <- (knownseg == queryseg[j])
        if(!any(relevant)) {
          result[j] <- NA
        } else {
          k <- which.min(abs(knowntp[relevant] - querytp[j]))
          result[j] <- knownval[relevant][k]
        }
      }
      if(drop && anyNA(result))
        result <- result[!is.na(result)]
      return(result)
    }
    #' give up and use pixel image
  }
  #' apply subset method for 'im'
  y <- NextMethod("[")
  if(!is.im(y)) return(y) # vector of pixel values
  class(y) <- unique(c("linim", class(y)))
  #' handle linear network info
  L <- attr(x, "L")
  df <- attr(x, "df")
  #' clip to new window
  W <- if(!missing(i) && is.owin(i)) i else Window(y)
  LW <- L[W]
  df <- df[inside.owin(df$xc, df$yc, W), , drop=FALSE]
  #' update local coordinates in data frame
  samplepoints <- ppp(df$x, df$y, window=Frame(W), check=FALSE)
  a <- project2segment(samplepoints, as.psp(LW))
  df$mapXY <- a$mapXY
  df$tp    <- a$tp
  #' wrap up
  attr(y, "L") <- LW
  attr(y, "df") <- df
  return(y)
}

"[<-.linim" <- function(x, i, j, value) {
  y <- NextMethod("[<-")
  #' extract linear network info
  L <- attr(x, "L")
  df <- attr(x, "df")
  #' propagate *changed* pixel values to sample points
  pos <- nearest.pixel(df$xc, df$yc, y)
  pos <- cbind(pos$row, pos$col)
  yvalue <- y$v[pos]
  xvalue <- x$v[pos]
  okx <- !is.na(xvalue)
  oky <- !is.na(yvalue)
  changed <- (okx != oky) | (okx & oky & yvalue != xvalue)
  df$values[changed] <- yvalue[changed]
  #' restrict main pixel image to network
  m <- psp2mask(L, as.mask(y))$m
  m[pos] <- TRUE
  y$v[!m] <- NA
  #' package up
  attr(y, "L") <- L
  attr(y, "df") <- df
  class(y) <- unique(c("linim", class(y)))
  return(y)
}

integral.linim <- function(f, domain=NULL, weight=NULL, ...){
  verifyclass(f, "linim")
  if(!is.null(weight))
    weight <- as.linim(weight, domain(f))
  if(is.tess(domain)) {
    result <- sapply(tiles(domain), integral.linim, f = f)
    if(length(dim(result)) > 1) result <- t(result)
    return(result)
  }
  if(!is.null(domain)) {
    f <- f[domain]
    if(!is.null(weight)) weight <- weight[domain]
  }
  #' extract data
  L <- as.linnet(f)
  ns <- nsegments(L)
  df <- attr(f, "df")
  vals <- df$values
  seg <- factor(df$mapXY, levels=1:ns)
  #' weight
  if(!is.null(weight)) {
    samplepoints <- ppp(df$xc, df$yc, window=Frame(L), check=FALSE)
    vals <- vals * safelookup(weight, samplepoints)
  }
  #' ensure each segment has at least one sample point
  nper <- table(seg)
  if(any(missed <- (nper == 0))) {
    missed <- unname(which(missed))
    mp <- midpoints.psp(as.psp(L)[missed])
    #' nearest pixel value
    valmid <- safelookup(f, mp)
    if(!is.null(weight))
      valmid <- valmid * safelookup(weight, mp)
    #' concatenate factors
    seg <- unlist(list(seg, factor(missed, levels=1:ns)))
    vals <- c(vals, valmid)
    #' update
    nper <- table(seg)
  }
  #' take average of data on each segment
  if(!is.complex(vals)) vals <- as.numeric(vals)
  num <- tapplysum(vals, list(seg), na.rm=TRUE)
  mu <- num/nper
  #' weighted sum
  len <- lengths_psp(as.psp(L))
  if(anyNA(vals)) {
    ##    p <- as.numeric(by(!is.na(vals), seg, mean, ..., na.rm=TRUE))
    ##    p[is.na(p)] <- 0
    defined <- as.numeric(!is.na(vals))
    pnum <- tapplysum(defined, list(seg), na.rm=FALSE)
    p <- pnum/nper
    len <- len * p
  }
  return(sum(mu * len))
}

mean.linim <- function(x, ...) {
  trap.extra.arguments(...)
  integral(x)/sum(lengths_psp(as.psp(as.linnet(x))))
}

quantile.linim <- function(x, probs = seq(0,1,0.25), ...) {
  verifyclass(x, "linim")
  #' extract data
  df <- attr(x, "df")
  L <- as.linnet(x)
  vals <- df$values
  #' count sample points on each segment
  seg <- factor(df$mapXY, levels=1:nsegments(L))
  nvals <- as.integer(table(seg))
  #' calculate weights
  len <- lengths_psp(as.psp(L))
  iseg <- as.integer(seg)
  wts <- len[iseg]/nvals[iseg]
  return(weighted.quantile(vals, wts, probs))
}

quantilefun.linim <- function(x, ..., type=1) {
  verifyclass(x, "linim")
  #' extract data
  df <- attr(x, "df")
  L <- as.linnet(x)
  vals <- df$values
  #' count sample points on each segment
  seg <- factor(df$mapXY, levels=1:nsegments(L))
  nvals <- as.integer(table(seg))
  #' calculate weights
  len <- lengths_psp(as.psp(L))
  iseg <- as.integer(seg)
  wts <- len[iseg]/nvals[iseg]
  #' form weighted CDF
  FZ <- ewcdf(vals, wts)
  #' quantile function
  return(quantilefun(FZ, type=type))
}

median.linim <- function(x, ...) {
  trap.extra.arguments(...)
  return(unname(quantile(x, 0.5)))
}

shift.linim <- function (X, ...) {
  verifyclass(X, "linim")
  Z <- shift(as.im(X), ...)
  L <- shift(as.linnet(X), ...)
  v <- getlastshift(L)
  df <- attr(X, "df")
  df[,c("xc","yc")] <- shiftxy(df[,c("xc", "yc")], v)
  df[,c("x","y")]   <- shiftxy(df[,c("x", "y")],   v)
  Y <- linim(L, Z, df=df, restrict=FALSE)
  return(putlastshift(Y, v))
}

affine.linim <- function(X, mat = diag(c(1, 1)), vec = c(0, 0), ...) {
  Z <- affine(as.im(X), mat=mat, vec=vec, ...)
  L <- affine(as.linnet(X), mat=mat, vec=vec, ...)
  df <- attr(X, "df")
  df[,c("xc","yc")] <- affinexy(df[,c("xc", "yc")], mat=mat, vec=vec)
  df[,c("x","y")]   <- affinexy(df[,c("x", "y")],   mat=mat, vec=vec)
  Y <- linim(L, Z, df=df, restrict=FALSE)
  return(Y)
}

scalardilate.linim <- function(X, f, ..., origin=NULL) {
  trap.extra.arguments(..., .Context = "In scalardilate(X,f)")
  check.1.real(f, "In scalardilate(X,f)")
  stopifnot(is.finite(f) && f > 0)
  if (!is.null(origin)) {
    X <- shift(X, origin = origin)
    negorig <- getlastshift(X)
  }
  else negorig <- c(0, 0)
  Y <- affine(X, mat = diag(c(f, f)), vec = -negorig)
  return(Y)
}

as.data.frame.linim <- function(x, ...) {
  df <- attr(x, "df")
  if(!is.na(m <- match("mapXY", colnames(df))))
    colnames(df)[m] <- "seg"
  return(df)
}

pairs.linim <- function(..., plot=TRUE, eps=NULL) {
  argh <- list(...)
  cl <- match.call()
  ## unpack single argument which is a list of images
  if(length(argh) == 1) {
    arg1 <- argh[[1L]]
    if(is.list(arg1) && all(sapply(arg1, is.im)))
      argh <- arg1
  }
  ## identify which arguments are images
  isim <- sapply(argh, is.im)
  nim <- sum(isim)
  if(nim == 0) 
    stop("No images provided")
  ## separate image arguments from others
  images <- argh[isim]
  rest   <- argh[!isim]
  ## identify which arguments are images on a network
  islinim <- sapply(images, inherits, what="linim")
  if(!any(islinim)) # shouldn't be here
    return(pairs.im(argh, plot=plot))
  ## determine image names for plotting
  imnames <- argh$labels %orifnull% names(images)
  if(length(imnames) != nim || !all(nzchar(imnames))) {
    #' names not given explicitly
    callednames <- paste(cl)[c(FALSE, isim, FALSE)]
    backupnames <- paste0("V", seq_len(nim))
    if(length(callednames) != nim) {
      callednames <- backupnames
    } else if(any(toolong <- (nchar(callednames) > 15))) {
      callednames[toolong] <- backupnames[toolong]
    }
    imnames <- good.names(imnames, good.names(callednames, backupnames))
  }
  names(images) <- imnames
  ## choose resolution
  if(is.null(eps)) {
    xstep <- min(sapply(images, getElement, name="xstep"))
    ystep <- min(sapply(images, getElement, name="ystep"))
    eps <- min(xstep, ystep)
  }
  ## extract linear network
  Z1 <- images[[min(which(islinim))]]
  L <- as.linnet(Z1)
  ## construct equally-spaced sample points
  X <- pointsOnLines(as.psp(L), eps=eps)
  ## sample each image
  pixvals <- lapply(images, "[", i=X, drop=FALSE)
  pixdf <- as.data.frame(pixvals)
  dont.complain.about(pixdf)
  ## pairs plot
  if(plot) {
    if(nim > 1) {
      do.call(pairs.default, resolve.defaults(list(x=quote(pixdf)),
                                              rest,
                                              list(labels=imnames, pch=".")))
      labels <- resolve.defaults(rest, list(labels=imnames))$labels
      colnames(pixdf) <- labels
    } else {
      xname <- imnames[1L]
      pixdf1 <- pixdf[,1L]
      dont.complain.about(pixdf1)
      do.call(hist.default,
              resolve.defaults(list(x=quote(pixdf1)),
                               rest,
                               list(main=paste("Histogram of", xname),
                                    xlab=xname)))
    }
  }
  class(pixdf) <- unique(c("plotpairsim", class(pixdf)))
  attr(pixdf, "eps") <- eps
  return(invisible(pixdf))
}