diff --git a/DESCRIPTION b/DESCRIPTION
index e184b67..e105fe9 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -8,7 +8,7 @@ Authors@R: c(person("Paul", "Murrell", role = c("aut", "cre"),
 Description: Functions for performing polygon geometry with 'grid' grobs.
              This allows complex shapes to be defined by combining simpler
              shapes.  
-URL: https://github.com/pmur002/gridgeometry, https://stattech.wordpress.fos.auckland.ac.nz/2019/03/04/2019-01-a-geometry-engine-interface-for-grid/, https://stattech.blogs.auckland.ac.nz/2022/06/01/2022-02-constructive-geometry-for-complex-grobs
+URL: https://github.com/pmur002/gridgeometry, https://stattech.wordpress.fos.auckland.ac.nz/2019/03/04/2019-01-a-geometry-engine-interface-for-grid/, https://stattech.blogs.auckland.ac.nz/2022/06/01/2022-02-constructive-geometry-for-complex-grobs/
 Depends: R (>= 3.6.0), grid
 Imports: grDevices, polyclip (>= 1.10-0)
 Suggests: graphics, lattice
diff --git a/R/minkowski.R b/R/minkowski.R
index 6400db0..fe02f99 100644
--- a/R/minkowski.R
+++ b/R/minkowski.R
@@ -10,62 +10,84 @@ polyminkowski.default <- function(A, B, ...) {
     polyclip::polyminkowski(A, B, ...)
 }
 
-polyminkowskiGrob <- function(A, B, reduceA, reduceB, ...) {
-    if (inherits(B, "gPath") || is.character(B)) {
-        B <- grid.get(B, ...)
-    }
+polyminkowskiGridGrob <- function(A, B, closed, reduceA, reduceB, ...) {
     if (!(inherits(B, "grob") || inherits(B, "gList")))
         stop("Argument 'B' must be a grob")
     polyA <- xyListFromGrob(A, op = reduceA, closed = TRUE, ...)
-    polyB <- xyListFromGrob(B, op = reduceB, closed = TRUE, ...)
-    polyclip::polyminkowski(polyA, polyB, ...)
+    polyB <- xyListFromGrob(B, op = reduceB, closed = closed, ...)
+    polyclip::polyminkowski(polyA, polyB, closed = closed, ...)
 }
 
-polyminkowski.grob <- function(A, B, 
+polyminkowski.grob <- function(A, B, closed=isClosedShape(B),
                                reduceA = "union",
                                reduceB = "union",
                                ...) {
-    polyminkowskiGrob(A, B, reduceA, reduceB, ...)
+    polyminkowskiGridGrob(A, B, closed, reduceA, reduceB, ...)
 }
 
-polyminkowski.gList <- function(A, B,
+polyminkowski.gList <- function(A, B, closed=isClosedShape(B),
                                 reduceA = "union",
                                 reduceB = "union",
                                 ...) {
-    polyminkowskiGrob(A, B, reduceA, reduceB, ...)
+    polyminkowskiGridGrob(A, B, closed, reduceA, reduceB, ...)
 }
 
-polyminkowski.gPath <- function(A, B, 
+polyminkowski.gPath <- function(A, B, closed,
                                 strict=FALSE, grep=FALSE, global=FALSE,
                                 reduceA = "union",
                                 reduceB = "union",
                                 ...) {
     A <- grid.get(A, strict, grep, global)
-    polyminkowskiGrob(A, B, reduceA, reduceB, ...)
+    if (inherits(B, "gPath") || is.character(B)) {
+        B <- grid.get(B, ...)
+    }
+    if (missing(closed))
+        closed <- isClosedShape(B)
+    polyminkowskiGridGrob(A, B, closed, reduceA, reduceB, ...)
 }
 
-polyminkowski.character <- function(A, B,
+polyminkowski.character <- function(A, B, closed,
                                     strict=FALSE, grep=FALSE, global=FALSE,
                                     reduceA = "union",
                                     reduceB = "union",
                                     ...) {
     A <- grid.get(A, strict, grep, global)
-    polyminkowskiGrob(A, B, reduceA, reduceB, ...)
+    if (inherits(B, "gPath") || is.character(B)) {
+        B <- grid.get(B, ...)
+    }
+    if (missing(closed))
+        closed <- isClosedShape(B)
+    polyminkowskiGridGrob(A, B, closed, reduceA, reduceB, ...)
 }
 
 ################################################################################
 ## High level grob interface
 makeContent.minkowskiGrob <- function(x) {
-    offsetpts <- do.call(polyminkowski, c(list(A=x$A, B=x$B), x$minkowskiArgs))
-    setChildren(x, gList(xyListToPath(offsetpts)))
+    children <- vector("list", 2)
+    closedPaths <- do.call(polyminkowski,
+                           c(list(A=x$A, B=x$B, closed=TRUE),
+                             x$polyclipArgs))
+    if (length(closedPaths)) {
+        children[[1]] <- x$grobFn(closedPaths,
+                                  name=paste0(x$name, ".closed"))
+    }
+    openPaths <- do.call(polyminkowski,
+                         c(list(A=x$A, B=x$B, closed=FALSE),
+                           x$polyclipArgs))
+    if (length(openPaths)) {
+        children[[2]] <- x$grobFn(openPaths, 
+                                  name=paste0(x$name, ".open"))
+    }
+    setChildren(x, do.call(gList, children[!is.null(children)]))
 }
 
 minkowskiGrob <- function(A, B, 
+                          grobFn=xyListToPath,
                           name=NULL, gp=gpar(),
                           ...) {
     if (!(grobArg(A) && grobArg(B)))
         stop("Invalid argument")
-    gTree(A=A, B=B, 
+    gTree(A=A, B=B, grobFn=grobFn,
           polyclipArgs=list(...),
           gp=gp, name=name, cl="minkowskiGrob")
 }
diff --git a/inst/NEWS.Rd b/inst/NEWS.Rd
index 6e79a02..50e68da 100755
--- a/inst/NEWS.Rd
+++ b/inst/NEWS.Rd
@@ -5,7 +5,10 @@
 \section{Changes in version 0.4-0}{
   \itemize{
     \item New functions \code{grid.polyoffset()} and
-    \code{grid.polylineoffset()}.
+    \code{grid.polylineoffset()} for generating offset regions.
+    
+    \item New function \code{grid.minkowski()} for generating
+    Minkowski sums of grobs.
   }
 }
 
diff --git a/man/grid.minkowski.Rd b/man/grid.minkowski.Rd
new file mode 100644
index 0000000..049f664
--- /dev/null
+++ b/man/grid.minkowski.Rd
@@ -0,0 +1,71 @@
+\name{grid.minkowski}
+\alias{grid.minkowski}
+\alias{minkowskiGrob}
+\title{
+  Generate Minkowski Sums of Grobs
+}
+\description{
+  Given a polygonal \dfn{pattern} and a polygonal \dfn{path},
+  generate the Minkowski Sum by adding the pattern to the path.
+}
+\usage{
+minkowskiGrob(A, B, 
+              grobFn=xyListToPath,
+              name=NULL, gp=gpar(), ...) 
+grid.minkowski(A, B, ...)
+}
+\arguments{
+  \item{A}{
+    A grob, gList, or gTree, or a gPath or a character value
+    identifying a grob that has already been drawn.  This is known as the
+    \dfn{pattern} grob.
+  }
+  \item{B}{
+    A grob, gList, or gTree, or a gPath or a character value
+    identifying a grob that has already been drawn.  This is known as the
+    \dfn{path} grob.
+  }
+  \item{grobFn}{
+    The function that is used to create the final grob result.
+    Predefined options are:  \code{\link{xyListToPath}},
+    \code{\link{xyListToPolygon}}, and
+    \code{\link{xyListToLine}}.
+  }
+  \item{name}{
+    A name for the resulting grob.
+  }
+  \item{gp}{
+    Graphical parameter settings for the resulting grob.
+  }
+  \item{\dots}{
+    For \code{minkowskiGrob}, arguments passed on to
+    \code{polyclip::polyminkowski}.
+  }
+}
+\details{
+  Both \code{A} and \code{B} should not contain self-intersections,
+  though they can be non-convex.
+}
+\value{
+  \code{minkowskiGrob} returns a gTree.
+  
+  \code{grid.minkowski} is only used for its side-effect of drawing
+  on the current graphics device.
+}
+\author{
+  Jack Wong
+}
+\seealso{
+  \code{\link{xyListToPath}},
+  \code{\link{xyListToPolygon}},
+  \code{\link{xyListToLine}},
+  \code{\link{polyminkowski}}
+}
+\examples{
+pattern <- circleGrob(x = 0, y = 0, r = .1)
+path <- rectGrob(width = 0.5, height = 0.5)
+minkowski <- minkowskiGrob(pattern, path)
+grid.draw(minkowski)
+}
+\keyword{ dplot }
+\keyword{ aplot }
diff --git a/man/polyminkowski.Rd b/man/polyminkowski.Rd
new file mode 100644
index 0000000..686e5ab
--- /dev/null
+++ b/man/polyminkowski.Rd
@@ -0,0 +1,89 @@
+\name{polyminkowski}
+\alias{polyminkowski}
+\alias{polyminkowski.grob}
+\alias{polyminkowski.gList}
+\alias{polyminkowski.gPath}
+\alias{polyminkowski.character}
+\title{
+  Generate Minkowski Sums on Coordinates
+}
+\description{
+  This function generates the Minkowski Sum of two sets of coordinates.  
+}
+\usage{
+polyminkowski(A, B, ...)
+\method{polyminkowski}{grob}(A, B, closed=isClosedShape(B),
+         reduceA = "union",
+         reduceB = "union",
+         ...)
+\method{polyminkowski}{gList}(A, B, closed=isClosedShape(B),
+         reduceA = "union",
+         reduceB = "union",
+         ...)
+\method{polyminkowski}{gPath}(A, B, closed,
+                         strict=FALSE, grep=FALSE, global=FALSE,
+         reduceA = "union",
+         reduceB = "union",
+         ...)
+\method{polyminkowski}{character}(A, B, closed,
+                             strict=FALSE, grep=FALSE, global=FALSE,
+         reduceA = "union",
+         reduceB = "union",
+         ...)
+}
+\arguments{
+  \item{A}{
+    A set of coordinates describing a
+    \dfn{pattern} shape.
+    Or a grob, gList, or a gPath (or a character value)
+    identifying a grob that has already been drawn from which
+    coordinates are generated.  
+  }
+  \item{B}{
+    A set of coordinates describing a
+    \dfn{path} shape.
+    Or a grob, gList, or a gPath (or a character value)
+    identifying a grob that has already been drawn from which
+    coordinates are generated.  
+  }
+  \item{closed}{
+    A logical value indicating whether the \code{B} coordinates describe
+    a closed shape or an open shape.
+  }
+  \item{reduceA, reduceB}{
+    A character value describing the operation to be used if either
+    \code{A} or \code{B} need to be reduced to a single set of
+    coordinates.   One of
+    \code{"intersection"}, \code{"minus"}, \code{"union"}, or
+    \code{"xor"}, in which case \code{polyminkowski} is used to
+    reduce multiple shapes, or \code{"flatten"}, in which case
+    coordinates for all shapes are returned.  
+  }
+  \item{strict, grep, global}{
+    Arguments controlling the interpretation of the gPath
+    (passed to \code{grid.get}).
+  }
+  \item{\dots}{
+    Arguments used by methods.
+  }
+}
+\details{
+  The shape described by the pattern coordinates is added
+  to the shape described by the path coordinates.
+}
+\value{
+  The result is a new set of coordinates.  
+}
+\author{
+  Paul Murrell
+}
+\seealso{
+  \code{\link{grid.minkowski}}
+}
+\examples{
+c <- circleGrob(x=0, y=0, r=.1)
+r <- rectGrob(width=.5, height=.5)
+polyminkowski(c, r)
+}
+\keyword{ dplot }
+\keyword{ aplot }