diff --git a/DESCRIPTION b/DESCRIPTION
index d7d8e34e1..965bbe820 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Package: spatstat
-Version: 1.46-1.007
-Nickname: Ultracrepidarian
-Date: 2016-07-15
+Version: 1.46-1.008
+Nickname: Pons Asinorum
+Date: 2016-07-16
 Title: Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests
 Author: Adrian Baddeley <Adrian.Baddeley@curtin.edu.au>,
 	Rolf Turner <r.turner@auckland.ac.nz> 
diff --git a/NAMESPACE b/NAMESPACE
index bb0811456..c3ccf74fe 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -456,6 +456,16 @@ export("boundingbox.owin")
 export("boundingbox.ppp")
 export("boundingbox.solist")
 export("bounding.box.xy")
+export("boundingcentre")
+export("boundingcentre.owin")
+export("boundingcentre.ppp")
+export("boundingcircle")
+export("boundingcircle.owin")
+export("boundingcircle.ppp")
+export("boundingradius")
+export("boundingradius.linnet")
+export("boundingradius.owin")
+export("boundingradius.ppp")
 export("box3")
 export("boxx")
 export("branchlabelfun")
@@ -516,12 +526,6 @@ export("chop.tess")
 export("choptext")
 export("circdensity")
 export("circticks")
-export("circumcentre")
-export("circumcentre.owin")
-export("circumcentre.ppp")
-export("circumcircle")
-export("circumcircle.owin")
-export("circumcircle.ppp")
 export("circumradius")
 export("circumradius.linnet")
 export("circumradius.owin")
@@ -1393,6 +1397,7 @@ export("mad.test")
 export("majorminorversion")
 export("make.even.breaks")
 export("makefvlabel")
+export("makeLinnetTolerance")
 export("make.parseable")
 export("makeunits")
 export("mapSparseEntries")
@@ -2841,6 +2846,13 @@ S3method("boundingbox", "im")
 S3method("boundingbox", "owin")
 S3method("boundingbox", "ppp")
 S3method("boundingbox", "solist")
+S3method("boundingcentre", "owin")
+S3method("boundingcentre", "ppp")
+S3method("boundingcircle", "owin")
+S3method("boundingcircle", "ppp")
+S3method("boundingradius", "linnet")
+S3method("boundingradius", "owin")
+S3method("boundingradius", "ppp")
 S3method("by", "im")
  S3method("by", "ppp")
 S3method("cbind", "fv")
@@ -2852,10 +2864,6 @@ S3method("cdf.test", "mppm")
 S3method("cdf.test", "ppm")
 S3method("cdf.test", "ppp")
 S3method("cdf.test", "slrm")
-S3method("circumcentre", "owin")
-S3method("circumcentre", "ppp")
-S3method("circumcircle", "owin")
-S3method("circumcircle", "ppp")
 S3method("circumradius", "linnet")
 S3method("circumradius", "owin")
 S3method("circumradius", "ppp")
diff --git a/NEWS b/NEWS
index e196eb9f5..b419e4060 100644
--- a/NEWS
+++ b/NEWS
@@ -1,21 +1,21 @@
 
-        CHANGES IN spatstat VERSION 1.46-1.007
+        CHANGES IN spatstat VERSION 1.46-1.008
 
 OVERVIEW
 
     o We thank Mehdi Moradi and Jorge Mateu for contributions.
 
-    o Circumcentre and circumcircle.
-
     o Non-Gaussian smoothing kernels.
 
     o Important bug fix in linearK, linearpcf
 
-    o Version nickname: 'Ultracrepidarian'
+    o Bounding circle of a spatial object.
+
+    o Version nickname: 'Pons Asinorum'
 
 NEW FUNCTIONS
 
-    o circumcircle, circumcentre
+    o boundingcircle, boundingcentre
     Find the smallest circle enclosing a window or point pattern.
 
 SIGNIFICANT USER-VISIBLE CHANGES
@@ -26,6 +26,9 @@ SIGNIFICANT USER-VISIBLE CHANGES
     o rcellnumber
     New argument 'mu'.
 
+    o lengths.psp
+    New argument 'squared'.
+
     o density.ppp, Smooth.ppp
     Computation accelerated by about 15% 
     in the case where at='points' and kernel='gaussian'.
@@ -33,6 +36,9 @@ SIGNIFICANT USER-VISIBLE CHANGES
     o linearK, linearpcf
     Accelerated.
 
+    o circumradius
+    This function is now deprecated, in favour of 'boundingradius'
+
 BUG FIXES
 
     o linearK, linearpcf, and relatives:
diff --git a/R/Kest.R b/R/Kest.R
index 9badd7ea8..a458f7433 100755
--- a/R/Kest.R
+++ b/R/Kest.R
@@ -1,7 +1,7 @@
 #
 #	Kest.R		Estimation of K function
 #
-#	$Revision: 5.118 $	$Date: 2016/04/01 05:55:30 $
+#	$Revision: 5.119 $	$Date: 2016/07/16 03:08:23 $
 #
 #
 # -------- functions ----------------------------------------
@@ -292,7 +292,7 @@ function(X, ..., r=NULL, rmax=NULL, breaks=NULL,
       wh <- whist(DIJ, breaks$val, edgewt)
       numKiso <- cumsum(wh)
       denKiso <- lambda2 * areaW
-      h <- circumradius(W)
+      h <- boundingradius(W)
       numKiso[r >= h] <- NA
       K <- bind.ratfv(K,
                       data.frame(iso=numKiso),
diff --git a/R/boundingcircle.R b/R/boundingcircle.R
new file mode 100644
index 000000000..f3eae6e1b
--- /dev/null
+++ b/R/boundingcircle.R
@@ -0,0 +1,69 @@
+#'
+#'    boundingcircle.R
+#'
+#'  bounding circle and its centre
+#'
+#'  $Revision: 1.5 $ $Date: 2016/07/16 03:07:02 $
+#'
+
+circumradius <- function(x, ...) {
+  .Deprecated(boundingradius)
+  UseMethod("boundingradius")
+}
+circumradius.owin <- function(x, ...) {
+  .Deprecated(boundingradius.owin)
+  boundingradius.owin(x, ...)
+}
+circumradius.ppp <- function(x, ...) {
+  .Deprecated(boundingradius.ppp)
+  boundingradius.ppp(x, ...)
+}
+
+boundingradius <- function(x, ...) {
+  UseMethod("boundingradius")
+}
+
+boundingcentre <- function(x, ...) {
+  UseMethod("boundingcentre")
+}
+
+boundingcircle <- function(x, ...) {
+  UseMethod("boundingcircle")
+}
+
+#' owin
+
+boundingradius.owin <- function(x, ...) {
+  sqrt(min(fardist(x, ..., squared=TRUE)))
+}
+
+boundingcentre.owin <- function(x, ...) {
+  z <- where.min(fardist(x, ..., squared=TRUE))
+  Window(z) <- x
+  return(z)
+}
+
+boundingcircle.owin <- function(x, ...) {
+  d2 <- fardist(x, ..., squared=TRUE)
+  z <- where.min(d2)
+  r <- sqrt(min(d2))
+  w <- disc(centre=z, radius=r) 
+  return(w)
+}
+
+#' ppp
+
+boundingradius.ppp <- function(x, ...) {
+  boundingradius(convexhull(x), ...)
+}
+
+boundingcentre.ppp <- function(x, ...) {
+  z <- boundingcentre(convexhull(x), ...)
+  Window(z) <- Window(x)
+  return(z)
+}
+
+boundingcircle.ppp <- function(x, ...) {
+  boundingcircle(convexhull(x), ...)
+}
+
diff --git a/R/circum.R b/R/circum.R
deleted file mode 100644
index 985ac528f..000000000
--- a/R/circum.R
+++ /dev/null
@@ -1,56 +0,0 @@
-#'
-#'    circum.R
-#'
-#'  circumradius, circumcentre and circumdisc
-#'
-#'  $Revision: 1.2 $ $Date: 2016/07/10 03:22:06 $
-#'
-
-circumradius <- function(x, ...) {
-  UseMethod("circumradius")
-}
-
-circumcentre <- function(x, ...) {
-  UseMethod("circumcentre")
-}
-
-circumcircle <- function(x, ...) {
-  UseMethod("circumcircle")
-}
-
-#' owin
-
-circumradius.owin <- function(x, ...) {
-  sqrt(min(fardist(x, ..., squared=TRUE)))
-}
-
-circumcentre.owin <- function(x, ...) {
-  z <- where.min(fardist(x, ..., squared=TRUE))
-  Window(z) <- x
-  return(z)
-}
-
-circumcircle.owin <- function(x, ...) {
-  d2 <- fardist(x, ..., squared=TRUE)
-  z <- where.min(d2)
-  r <- sqrt(min(d2))
-  w <- disc(centre=z, radius=r) 
-  return(w)
-}
-
-#' ppp
-
-circumradius.ppp <- function(x, ...) {
-  circumradius(convexhull(x), ...)
-}
-
-circumcentre.ppp <- function(x, ...) {
-  z <- circumcentre(convexhull(x), ...)
-  Window(z) <- Window(x)
-  return(z)
-}
-
-circumcircle.ppp <- function(x, ...) {
-  circumcircle(convexhull(x), ...)
-}
-
diff --git a/R/edgeRipley.R b/R/edgeRipley.R
index 0fa1c6a10..e36b8dfad 100755
--- a/R/edgeRipley.R
+++ b/R/edgeRipley.R
@@ -1,7 +1,7 @@
 #
 #        edgeRipley.R
 #
-#    $Revision: 1.13 $    $Date: 2016/04/25 02:34:40 $
+#    $Revision: 1.15 $    $Date: 2016/07/16 03:11:15 $
 #
 #    Ripley isotropic edge correction weights
 #
@@ -173,11 +173,11 @@ edge.Ripley <- local({
 rmax.Ripley <- function(W) {
   W <- as.owin(W)
   if(is.rectangle(W))
-    return(circumradius(W))
+    return(boundingradius(W))
   if(is.polygonal(W) && length(W$bdry) == 1)
-    return(circumradius(W))
+    return(boundingradius(W))
   ## could have multiple connected components
   pieces <- tiles(tess(image=connected(W)))
-  answer <- sapply(pieces, circumradius)
+  answer <- sapply(pieces, boundingradius)
   return(as.numeric(answer))
 }
diff --git a/R/linearK.R b/R/linearK.R
index b86b37e18..24800c4dd 100755
--- a/R/linearK.R
+++ b/R/linearK.R
@@ -1,7 +1,7 @@
 #
 # linearK
 #
-# $Revision: 1.37 $ $Date: 2016/07/15 12:09:15 $
+# $Revision: 1.38 $ $Date: 2016/07/16 03:08:23 $
 #
 # K function for point pattern on linear network
 #
@@ -122,7 +122,7 @@ linearKengine <- function(X, ..., r=NULL, reweight=NULL, denom=1,
   Y <- as.ppp(X)
   W <- Y$window
   # determine r values
-  rmaxdefault <- 0.98 * circumradius(L)
+  rmaxdefault <- 0.98 * boundingradius(L)
   breaks <- handle.r.b.args(r, NULL, W, rmaxdefault=rmaxdefault)
   r <- breaks$r
   rmax <- breaks$max
diff --git a/R/linearKmulti.R b/R/linearKmulti.R
index 3240225e0..580f314d0 100644
--- a/R/linearKmulti.R
+++ b/R/linearKmulti.R
@@ -1,7 +1,7 @@
 #
 # linearKmulti
 #
-# $Revision: 1.8 $ $Date: 2016/07/15 12:09:29 $
+# $Revision: 1.9 $ $Date: 2016/07/16 03:08:23 $
 #
 # K functions for multitype point pattern on linear network
 #
@@ -199,7 +199,7 @@ linearKmultiEngine <- function(X, I, J, ..., r=NULL, reweight=NULL, denom=1,
   XP <- as.ppp(X)
   W <- as.owin(XP)
   # determine r values
-  rmaxdefault <- 0.98 * circumradius(L)
+  rmaxdefault <- 0.98 * boundingradius(L)
   breaks <- handle.r.b.args(r, NULL, W, rmaxdefault=rmaxdefault)
   r <- breaks$r
   rmax <- breaks$max
diff --git a/R/lineardisc.R b/R/lineardisc.R
index 85d9d7f9c..b89e6680a 100755
--- a/R/lineardisc.R
+++ b/R/lineardisc.R
@@ -209,10 +209,21 @@ countends <- function(L, x=locator(1), r, toler=NULL) {
 }
 
 default.linnet.tolerance <- function(L) {
+  # L could be a linnet or psp
   if(!is.null(toler <- L$toler)) return(toler)
-  lenfs <- lengths.psp(as.psp(L))
-  toler <- 0.001 * min(lenfs[lenfs > 0])
-  toler <- max(sqrt(.Machine$double.xmin),
-               toler[is.finite(toler)], na.rm=TRUE)
+  len2 <- lengths.psp(as.psp(L), squared=TRUE)
+  len2pos <- len2[len2 > 0]
+  toler <- if(length(len2pos) == 0) 0 else (0.001 * sqrt(min(len2pos)))
+  toler <- makeLinnetTolerance(toler)
   return(toler)
 }
+
+makeLinnetTolerance <- function(toler) {
+  max(sqrt(.Machine$double.xmin),
+      toler[is.finite(toler)], na.rm=TRUE)
+}
+
+
+
+
+  
diff --git a/R/linearpcf.R b/R/linearpcf.R
index f0a7137e5..621f9f101 100755
--- a/R/linearpcf.R
+++ b/R/linearpcf.R
@@ -1,7 +1,7 @@
 #
 # linearpcf.R
 #
-# $Revision: 1.15 $ $Date: 2016/07/15 12:08:39 $
+# $Revision: 1.16 $ $Date: 2016/07/16 03:08:23 $
 #
 # pair correlation function for point pattern on linear network
 #
@@ -91,7 +91,7 @@ linearpcfengine <- function(X, ..., r=NULL,
   Y <- as.ppp(X)
   W <- Y$window
   # determine r values
-  rmaxdefault <- 0.98 * circumradius(L)
+  rmaxdefault <- 0.98 * boundingradius(L)
   breaks <- handle.r.b.args(r, NULL, W, rmaxdefault=rmaxdefault)
   r <- breaks$r
   rmax <- breaks$max
diff --git a/R/linearpcfmulti.R b/R/linearpcfmulti.R
index 42f97de46..d8f3c4c2b 100644
--- a/R/linearpcfmulti.R
+++ b/R/linearpcfmulti.R
@@ -1,7 +1,7 @@
 #
 # linearpcfmulti.R
 #
-# $Revision: 1.7 $ $Date: 2016/07/15 12:08:51 $
+# $Revision: 1.8 $ $Date: 2016/07/16 03:08:23 $
 #
 # pair correlation functions for multitype point pattern on linear network
 #
@@ -198,7 +198,7 @@ linearPCFmultiEngine <- function(X, I, J, ..., r=NULL, reweight=NULL, denom=1,
   XP <- as.ppp(X)
   W <- as.owin(XP)
   # determine r values
-  rmaxdefault <- 0.98 * circumradius(L)
+  rmaxdefault <- 0.98 * boundingradius(L)
   breaks <- handle.r.b.args(r, NULL, W, rmaxdefault=rmaxdefault)
   r <- breaks$r
   rmax <- breaks$max
diff --git a/R/linnet.R b/R/linnet.R
index d8e4eaf18..04bd45517 100755
--- a/R/linnet.R
+++ b/R/linnet.R
@@ -3,7 +3,7 @@
 #    
 #    Linear networks
 #
-#    $Revision: 1.50 $    $Date: 2016/04/25 02:34:40 $
+#    $Revision: 1.54 $    $Date: 2016/07/16 02:38:47 $
 #
 # An object of class 'linnet' defines a linear network.
 # It includes the following components
@@ -84,9 +84,12 @@ linnet <- function(vertices, m, edges, sparse=FALSE, warn=TRUE) {
   yy   <- vertices$y
   lines <- psp(xx[from], yy[from], xx[to], yy[to], window=vertices$window,
                check=FALSE)
+  # tolerance
+  toler <- default.linnet.tolerance(lines)
   ## pack up
   out <- list(vertices=vertices, m=m, lines=lines, from=from, to=to,
-              sparse=sparse, window=vertices$window)
+              sparse=sparse, window=vertices$window,
+              toler=toler)
   class(out) <- c("linnet", class(out))
   ## finish ?
   if(sparse)
@@ -100,9 +103,8 @@ linnet <- function(vertices, m, edges, sparse=FALSE, warn=TRUE) {
   out$dpath <- dpath <- dist2dpath(d)
   if(warn && any(is.infinite(dpath)))
     warning("Network is not connected", call.=FALSE)
-  # pre-compute circumradius and tolerance
-  out$circumradius <- circumradius(out)
-  out$toler <- default.linnet.tolerance(out)
+  # pre-compute bounding radius 
+  out$boundingradius <- boundingradius(out)
   return(out)  
 }
 
@@ -130,8 +132,9 @@ summary.linnet <- function(object, ...) {
                  sparse = sparse)
   if(!sparse) {
     result$diam <- diameter(object)
-    result$circrad <- circumradius(object)
+    result$boundrad <- boundingradius(object)
   }
+  result$toler <- object$toler
   class(result) <- c("summary.linnet", class(result))
   result
 }
@@ -148,8 +151,10 @@ print.summary.linnet <- function(x, ...) {
     splat("Maximum vertex degree:", maxdegree)
     if(sparse) splat("[Sparse matrix representation]") else {
       splat("Diameter:", signif(diam, dig), unitinfo$plural)
-      splat("Circumradius:", signif(circrad, dig), unitinfo$plural)
+      splat("Bounding radius:", signif(boundrad, dig), unitinfo$plural)
     }
+    if(!is.null(toler))
+      splat("Numerical tolerance:", signif(toler, dig), unitinfo$plural)
     print(win, prefix="Enclosing window: ")
   })
   return(invisible(NULL))
@@ -248,11 +253,13 @@ as.linnet.linnet <- function(X, ..., sparse) {
     d[edges] <- sqrt(rowSums((coo[from, 1:2] - coo[to, 1:2])^2))
     # compute shortest path distance matrix
     X$dpath <- dist2dpath(d)
-    # compute circumradius
-    X$circumradius <- circumradius(X)
+    # compute bounding radius
+    X$boundingradius <- boundingradius(X)
     X$m <- m
     X$sparse <- FALSE
   }
+  X$circumradius <- NULL
+  X$toler <- default.linnet.tolerance(X)
   return(X)
 }
 
@@ -318,8 +325,13 @@ vertexdegree <- function(x) {
 }
 
 circumradius.linnet <- function(x, ...) {
+  .Deprecated("boundingradius.linnet")
+  boundingradius.linnet(x, ...)
+}
+
+boundingradius.linnet <- function(x, ...) {
   stopifnot(inherits(x, "linnet"))
-  cr <- x$circumradius
+  cr <- x$boundingradius %orifnull% x$circumradius
   if(!is.null(cr))
     return(cr)
   dpath <- x$dpath
@@ -382,8 +394,11 @@ scalardilate.linnet <- function(X, f, ...) {
   Y$window       <- scalardilate(X$window, f=f)
   if(!is.null(X$dpath)) {
     Y$dpath        <- f * X$dpath
-    Y$circumradius <- f * X$circumradius
+    Y$boundingradius <- f * (X$boundingradius %orifnull% X$circumradius)
+    Y$circumradius <- NULL
   }
+  if(!is.null(X$toler))
+    X$toler <- makeLinnetTolerance(f * X$toler)
   return(Y)
 }
 
@@ -398,8 +413,11 @@ affine.linnet <- function(X,  mat=diag(c(1,1)), vec=c(0,0), ...) {
     Y$window       <- affine(X$window,   mat=mat, vec=vec, ...)
     if(!is.null(X$dpath)) {
       Y$dpath        <- scal * X$dpath
-      Y$circumradius <- scal * X$circumradius
+      Y$boundingradius <- scal * (X$boundingradius %orifnull% X$circumradius)
+      X$circumradius <- NULL
     }
+    if(!is.null(Y$toler))
+      Y$toler <- makeLinnetTolerance(scal * Y$toler)
   } else {
     # general case
     vertices <- affine(X$vertices, mat=mat, vec=vec, ...)
diff --git a/R/psp.R b/R/psp.R
index af5a30eaf..4cb9b807d 100755
--- a/R/psp.R
+++ b/R/psp.R
@@ -1,7 +1,7 @@
 #
 #  psp.R
 #
-#  $Revision: 1.83 $ $Date: 2016/07/15 10:21:33 $
+#  $Revision: 1.84 $ $Date: 2016/07/16 01:13:41 $
 #
 # Class "psp" of planar line segment patterns
 #
@@ -531,9 +531,10 @@ midpoints.psp <- function(x) {
   ppp(x=xm, y=ym, window=win, check=FALSE)
 }
 
-lengths.psp <- function(x) {
+lengths.psp <- function(x, squared=FALSE) {
   verifyclass(x, "psp")
-  eval(expression(sqrt((x1-x0)^2 + (y1-y0)^2)), envir=x$ends)
+  lengths2 <- eval(expression((x1-x0)^2 + (y1-y0)^2), envir=x$ends)
+  return(if(squared) lengths2 else sqrt(lengths2))
 }
 
 angles.psp <- function(x, directed=FALSE) {
diff --git a/R/treebranches.R b/R/treebranches.R
index 8958b47d4..ed5e3db40 100644
--- a/R/treebranches.R
+++ b/R/treebranches.R
@@ -3,7 +3,7 @@
 #'
 #'  Label branches in a tree
 #'
-#'  $Revision: 1.3 $ $Date: 2015/10/21 09:06:57 $
+#'  $Revision: 1.4 $ $Date: 2016/07/16 03:14:51 $
 
 #' compute branch labels for each *vertex* in the tree L
 
@@ -114,9 +114,10 @@ extractbranch.linnet <- function(X, code, labels, ..., which=NULL) {
               sparse=sparse,
               window=V$window)
   class(out) <- c("linnet", class(out))
-  #' pre-compute circumradius
+  #' pre-compute bounding radius
   if(sparse)
-    out$circumradius <- circumradius(out)
+    out$boundingradius <- boundingradius(out)
+  out$toler <- default.linnet.tolerance(out)
   attr(out, "which") <- vin
   return(out)  
 }
@@ -169,9 +170,10 @@ deletebranch.linnet <- function(X, code, labels, ...) {
               sparse=sparse,
               window=V$window)
   class(out) <- c("linnet", class(out))
-  #' recompute circumradius
+  #' recompute bounding radius
   if(sparse)
-    out$circumradius <- circumradius(out)
+    out$boundingradius <- boundingradius(out)
+  out$toler <- default.linnet.tolerance(out)
   attr(out, "which") <- vkeep
   return(out)  
 }
diff --git a/data/chicago.rda b/data/chicago.rda
index 98e80999a..19fc0e9ee 100644
Binary files a/data/chicago.rda and b/data/chicago.rda differ
diff --git a/data/dendrite.rda b/data/dendrite.rda
index 718f70145..fdfed9749 100644
Binary files a/data/dendrite.rda and b/data/dendrite.rda differ
diff --git a/data/simplenet.rda b/data/simplenet.rda
index daff8cb63..5d0e34258 100755
Binary files a/data/simplenet.rda and b/data/simplenet.rda differ
diff --git a/data/spiders.rda b/data/spiders.rda
index ac406746c..4eb9be8db 100644
Binary files a/data/spiders.rda and b/data/spiders.rda differ
diff --git a/man/boundingcircle.Rd b/man/boundingcircle.Rd
new file mode 100644
index 000000000..6d597cd80
--- /dev/null
+++ b/man/boundingcircle.Rd
@@ -0,0 +1,85 @@
+\name{boundingcircle}
+\alias{boundingradius}
+\alias{boundingradius.owin}
+\alias{boundingradius.ppp}
+\alias{boundingcentre}
+\alias{boundingcircle}
+\alias{boundingcentre.owin}
+\alias{boundingcircle.owin}
+\alias{boundingcentre.ppp}
+\alias{boundingcircle.ppp}
+\title{
+  Smallest Enclosing Circle
+}
+\description{
+  Find the smallest circle enclosing a spatial window
+  or other object. Return its radius, or the location of its centre,
+  or the circle itself.
+}
+\usage{
+boundingradius(x, \dots)
+
+boundingcentre(x, \dots)
+
+boundingcircle(x, \dots)
+
+\method{boundingradius}{owin}(x, \dots)
+
+\method{boundingcentre}{owin}(x, \dots)
+
+\method{boundingcircle}{owin}(x, \dots)
+
+\method{boundingradius}{ppp}(x, \dots)
+
+\method{boundingcentre}{ppp}(x, \dots)
+
+\method{boundingcircle}{ppp}(x, \dots)
+}
+\arguments{
+  \item{x}{
+    A window (object of class \code{"owin"}), or another spatial object. 
+  }
+  \item{\dots}{
+    Arguments passed to \code{\link{as.mask}} to determine the
+    pixel resolution for the calculation.
+  }
+}
+\details{
+  The \code{boundingcircle} of a spatial region \eqn{W} is the smallest circle
+  that contains \eqn{W}. The \code{boundingradius} is the radius of this circle,
+  and the \code{boundingcentre} is the centre of the circle.
+  
+  The functions \code{boundingcircle}, \code{boundingcentre} and
+  \code{boundingradius} are generic. There are methods
+  for objects of class \code{"owin"}, \code{"ppp"} and \code{"linnet"}.
+}
+\value{
+  The result of \code{boundingradius} is a single numeric value.
+
+  The result of \code{boundingcentre} is a point pattern containing a
+  single point.
+
+  The result of \code{boundingcircle} is a window representing the
+  boundingcircle.
+}
+\author{
+  \adrian 
+}
+\seealso{
+ \code{\link{boundingradius.linnet}}
+}
+\examples{
+  boundingradius(letterR)
+
+  plot(grow.rectangle(Frame(letterR), 0.2), main="", type="n")
+  plot(letterR, add=TRUE, col="grey")
+  plot(boundingcircle(letterR), add=TRUE, border="green", lwd=2)
+  plot(boundingcentre(letterR), pch="+", cex=2, col="blue", add=TRUE)
+
+  X <- runifpoint(5)
+  plot(X)
+  plot(boundingcircle(X), add=TRUE)
+  plot(boundingcentre(X), pch="+", cex=2, col="blue", add=TRUE)
+}
+\keyword{spatial}
+\keyword{math}
diff --git a/man/circumradius.Rd b/man/circumradius.Rd
deleted file mode 100644
index d6ba4b3be..000000000
--- a/man/circumradius.Rd
+++ /dev/null
@@ -1,85 +0,0 @@
-\name{circumradius}
-\alias{circumradius}
-\alias{circumcentre}
-\alias{circumcircle}
-\alias{circumradius.owin}
-\alias{circumcentre.owin}
-\alias{circumcircle.owin}
-\alias{circumradius.ppp}
-\alias{circumcentre.ppp}
-\alias{circumcircle.ppp}
-\title{
-  Smallest Enclosing Circle
-}
-\description{
-  Find the smallest circle enclosing a spatial window
-  or other object. Return its radius, or the location of its centre,
-  or the circle itself.
-}
-\usage{
-circumradius(x, \dots)
-
-circumcentre(x, \dots)
-
-circumcircle(x, \dots)
-
-\method{circumradius}{owin}(x, \dots)
-
-\method{circumcentre}{owin}(x, \dots)
-
-\method{circumcircle}{owin}(x, \dots)
-
-\method{circumradius}{ppp}(x, \dots)
-
-\method{circumcentre}{ppp}(x, \dots)
-
-\method{circumcircle}{ppp}(x, \dots)
-}
-\arguments{
-  \item{x}{
-    A window (object of class \code{"owin"}), or another spatial object. 
-  }
-  \item{\dots}{
-    Arguments passed to \code{\link{as.mask}} to determine the
-    pixel resolution for the calculation.
-  }
-}
-\details{
-  The circumcircle of a spatial region \eqn{W} is the smallest circle
-  that contains \eqn{W}. The circumradius is the radius of this circle,
-  and the circumcentre is the centre of the circle.
-  
-  The functions \code{circumcircle}, \code{circumcentre} and
-  \code{circumradius} are generic. There are methods
-  for objects of class \code{"owin"}, \code{"ppp"} and \code{"linnet"}.
-}
-\value{
-  The result of \code{circumradius} is a single numeric value.
-
-  The result of \code{circumcentre} is a point pattern containing a
-  single point.
-
-  The result of \code{circumcircle} is a window representing the
-  circumcircle.
-}
-\author{
-  \adrian 
-}
-\seealso{
- \code{\link{circumradius.linnet}}
-}
-\examples{
-  circumradius(letterR)
-
-  plot(grow.rectangle(Frame(letterR), 0.2), main="", type="n")
-  plot(letterR, add=TRUE, col="grey")
-  plot(circumcircle(letterR), add=TRUE, border="green", lwd=2)
-  plot(circumcentre(letterR), pch="+", cex=2, col="blue", add=TRUE)
-
-  X <- runifpoint(5)
-  plot(X)
-  plot(circumcircle(X), add=TRUE)
-  plot(circumcentre(X), pch="+", cex=2, col="blue", add=TRUE)
-}
-\keyword{spatial}
-\keyword{math}
diff --git a/man/diameter.linnet.Rd b/man/diameter.linnet.Rd
index 349fef634..0b1892cd6 100644
--- a/man/diameter.linnet.Rd
+++ b/man/diameter.linnet.Rd
@@ -1,17 +1,17 @@
 \name{diameter.linnet}
-\alias{circumradius.linnet}
+\alias{boundingradius.linnet}
 \alias{diameter.linnet}
 \title{
-  Circumradius and Diameter of a Linear Network
+  Diameter and Bounding Radius of a Linear Network
 }
 \description{
-  Compute the circumradius or diameter of a linear network
+  Compute the diameter or bounding radius of a linear network
   measured using the shortest path distance.
 }
 \usage{
-\method{circumradius}{linnet}(x, \dots)
-
 \method{diameter}{linnet}(x)
+
+\method{boundingradius}{linnet}(x, \dots)
 }
 \arguments{
   \item{x}{
@@ -24,30 +24,29 @@
   is the maximum value of the shortest-path distance between any
   two points \eqn{u} and \eqn{v} on the network.
 
-  The circumradius of a linear network (in the shortest path distance)
+  The bounding radius of a linear network (in the shortest path distance)
   is the minimum value, over all points \eqn{u} on the network,
   of the maximum shortest-path distance from \eqn{u} to another point
   \eqn{v} on the network.
   
-  The functions \code{\link{circumradius}} and
+  The functions \code{\link{boundingradius}} and
   \code{\link{diameter}} are generic;
-  the functions \code{circumradius.linnet} and \code{diameter.linnet}
+  the functions \code{boundingradius.linnet} and \code{diameter.linnet}
   are the methods for objects of class \code{linnet}.
 }
 \value{
   A single numeric value.
 }
 \author{
-  \adrian 
-  
+  \adrian
 }
 \seealso{
- \code{\link{circumradius}}, \code{\link{diameter}}, 
+ \code{\link{boundingradius}}, \code{\link{diameter}}, 
  \code{\link{linnet}}
 }
 \examples{
    diameter(simplenet)
-   circumradius(simplenet)
+   boundingradius(simplenet)
 }
 \keyword{spatial}
 \keyword{math}
diff --git a/man/lengths.psp.Rd b/man/lengths.psp.Rd
index 668387b70..fd4d18c04 100644
--- a/man/lengths.psp.Rd
+++ b/man/lengths.psp.Rd
@@ -6,12 +6,17 @@
   in a line segment pattern.
 }
 \usage{
-  lengths.psp(x)
+  lengths.psp(x, squared=FALSE)
 }
 \arguments{
   \item{x}{
     A line segment pattern (object of class \code{"psp"}).
   }
+  \item{squared}{
+    Logical value indicating whether to return
+    the squared lengths (\code{squared=TRUE})
+    or the lengths themselves (\code{squared=FALSE}, the default).
+  }
 }
 \value{
   Numeric vector.
@@ -19,6 +24,11 @@
 \details{
   The length of each line segment is computed
   and the lengths are returned as a numeric vector.
+
+  Using squared lengths may be more efficient for some purposes,
+  for example, to find the length of the shortest segment,
+  \code{sqrt(min(lengths.psp(x, squared=TRUE)))}
+  is faster than \code{min(lengths.psp(x))}.
 }
 \seealso{
   \code{\link{summary.psp}},
diff --git a/man/spatstat-deprecated.Rd b/man/spatstat-deprecated.Rd
index 618eabacf..0efd0282d 100644
--- a/man/spatstat-deprecated.Rd
+++ b/man/spatstat-deprecated.Rd
@@ -19,6 +19,10 @@
 \alias{dirichlet.network}
 \alias{dirichlet.vertices}
 \alias{dirichlet.weights}
+\alias{circumradius}
+\alias{circumradius.owin}
+\alias{circumradius.ppp}
+\alias{circumradius.linnet}
 \title{Deprecated spatstat functions}
 \description{
   Deprecated spatstat functions.
@@ -47,6 +51,10 @@ dirichlet.edges(\dots)
 dirichlet.network(\dots)
 dirichlet.vertices(\dots)
 dirichlet.weights(\dots)
+circumradius(x, \dots)
+\method{circumradius}{owin}(x, \dots)
+\method{circumradius}{ppp}(x, \dots)
+\method{circumradius}{linnet}(x, \dots)
 }
 
 \details{
@@ -95,5 +103,8 @@ dirichlet.weights(\dots)
   \code{dirichlet.vertices} is replaced by \code{dirichletVertices}.
   
   \code{dirichlet.weights} is replaced by \code{dirichletWeights}.
+
+  \code{circumradius} is replaced by the more appropriately named
+  \code{boundingradius}.
 }
 \keyword{internal}
diff --git a/man/spatstat-internal.Rd b/man/spatstat-internal.Rd
index 5f18898b0..0786da90c 100644
--- a/man/spatstat-internal.Rd
+++ b/man/spatstat-internal.Rd
@@ -350,6 +350,7 @@
 \alias{logi.engine}
 \alias{logLik.vblogit}
 \alias{lty2char}
+\alias{makeLinnetTolerance}
 \alias{maskLaslett}
 \alias{matsqrt}
 \alias{matchNameOrPosition}
@@ -1220,6 +1221,7 @@ logi.engine(Q, trend, interaction, \dots,
             VB)
 \method{logLik}{vblogit}(object, \dots) 
 lty2char(i)
+makeLinnetTolerance
 maskLaslett(X, \dots, eps, dimyx, xy, oldX, verbose, plotit)
 matsqrt(x)
 matchNameOrPosition(expected, avail)
diff --git a/tests/testsAtoN.R b/tests/testsAtoN.R
index 96481451e..e5eceb054 100644
--- a/tests/testsAtoN.R
+++ b/tests/testsAtoN.R
@@ -933,7 +933,7 @@ local({
 #
 # Tests for lpp code
 #
-#  $Revision: 1.6 $  $Date: 2016/02/01 09:44:54 $
+#  $Revision: 1.7 $  $Date: 2016/07/16 03:59:27 $
 
 
 require(spatstat)
@@ -1023,6 +1023,27 @@ local({
   B <- owin(c(0.1,0.7),c(0.19,0.6))
   XB <- X[B]
   validate.lpp.coords(XB, context="returned by [.lpp")
+
+  ## Tests related to linearK, etc
+  testcountends <- function(X, r=100, s=1) {
+    if(s != 1) {
+      X <- rescale(X, s)
+      r <- r/s
+    }
+    L <- as.linnet(X)
+    n1 <- countends(L, X[1], r)
+    n2 <- npoints(lineardisc(L, X[1], r, plotit=FALSE)$endpoints)
+    if(n1 != n2)
+      stop(paste("Incorrect result from countends:",
+                 n1, "!=", n2, 
+                 paren(paste("scale=", 1/s))),
+           call.=FALSE)
+  }
+  # original scale
+  X <- unmark(chicago)
+  testcountends(X)
+  # finer scale
+  testcountends(X, s=1000)
 })
 
 ##
diff --git a/vignettes/packagesizes.txt b/vignettes/packagesizes.txt
index 428d9797b..2bf0d742a 100644
--- a/vignettes/packagesizes.txt
+++ b/vignettes/packagesizes.txt
@@ -182,4 +182,4 @@ date version nhelpfiles nobjects ndatasets Rlines srclines
 "2016-05-09" "1.45-2" 977 2478 54 101981 28124
 "2016-07-06" "1.46-0" 981 2490 54 102484 28310
 "2016-07-08" "1.46-1" 981 2491 54 102573 28310
-"2016-07-15" "1.46-1.007" 981 2505 54 102899 28334
+"2016-07-16" "1.46-1.008" 981 2510 54 102944 28334
diff --git a/vignettes/updates.Rnw b/vignettes/updates.Rnw
index cd1c2877d..3b662ba15 100644
--- a/vignettes/updates.Rnw
+++ b/vignettes/updates.Rnw
@@ -211,6 +211,9 @@ Following is a list of all the functions that have been added.
 
 \begin{itemize}
 
+ \item \texttt{boundingcircle}, \texttt{boundingcentre}:
+   Smallest circle enclosing a spatial object.
+
  \item \texttt{split.msr}:
     Decompose a measure into parts.
 
@@ -613,6 +616,8 @@ listed alphabetically.
    \item A non-Gaussian kernel can now be specified
    using the argument \texttt{kernel}.
    \item Accelerated by about 15\%
+     in the case where \texttt{at="points"}
+     and \texttt{kernel="gaussian"}.
    \end{itemize}
 
  
@@ -724,10 +729,14 @@ listed alphabetically.
     a fitted point process model.
     New arguments \texttt{update}, \texttt{leaveoneout}, \texttt{lambdaX}.
 
+ \item \texttt{lengths.psp}: New argument \texttt{squared}.
+   
  \item \texttt{leverage.ppm}:
     For Gibbs models, memory usage has been dramatically reduced, 
     so the code can handle larger datasets and finer quadrature schemes.
 
+ \item \texttt{linearK}, \texttt{linearpcf} and relatives: Accelerated.
+   
  \item \texttt{linnet}:
    \begin{itemize}
    \item 
@@ -977,8 +986,13 @@ listed alphabetically.
    New argument \texttt{verbose}.
    
  \item \texttt{Smooth.ppp}:
-   A non-Gaussian kernel can now be specified
+   \begin{itemize}
+   \item A non-Gaussian kernel can now be specified
    using the argument \texttt{kernel}.
+   \item Accelerated by about 15\% in the case where \texttt{at="points"}
+     and \texttt{kernel="gaussian"}.
+   \end{itemize}
+
  
    \item \texttt{spatstat.options}
    New options \texttt{fastthin} and \texttt{fastpois}