R: Polygon Offset

polyoffset {polyclip} | R Documentation

## Polygon Offset

### Description

Given a polygonal region, compute the offset region (aka: guard region, buffer region, morphological dilation) formed by shifting the boundary outwards by a specified distance.

### Usage

     polyoffset(A, delta,
             ...,
             eps, x0, y0,
             miterlim=2, arctol=abs(delta)/100,
             jointype=c("square", "round", "miter"))

### Arguments

`A` | Data specifying polygons. See Details.
`delta` | Distance over which the boundary should be shifted.
`...` | Ignored.
`eps` | Spatial resolution for coordinates.
`x0,y0` | Spatial origin for coordinates.
`miterlim,arctol` | Tolerance parameters: see Details.
`jointype` | Type of join operation to be performed at each vertex. See Details.

### Details

This is part of an interface to the polygon-clipping library `Clipper` written by Angus Johnson.

Given a polygonal region `A`, the function `polyoffset` computes the offset region (also known as the morphological dilation, guard region, buffer region, etc) obtained by shifting the boundary of `A` outward by the distance `delta`.

The argument `A` represents a region in the Euclidean plane bounded by closed polygons. The format is either

- a list containing two components `x` and `y` giving the coordinates of the vertices of a single polygon. The last vertex should not repeat the first vertex.

- a `list` of `list(x,y)` structures giving the coordinates of the vertices of several polygons.

Note that calculations are performed in integer arithmetic: see below.

The argument `jointype` determines what happens at the convex vertices of `A`. See the Examples for illustrations.

- `jointype="round"`: a circular arc is generated.

- `jointype="square"`: the circular arc is replaced by a single straight line.

- `jointype="miter"`: the circular arc is omitted entirely, or replaced by a single straight line.

The arguments `miterlim` and `arctol` are tolerances.

- if `jointype="round"`, then `arctol` is the maximum permissible distance between the true circular arc and its discretised approximation.

- if `jointype="miter"`, then `miterlimit * delta` is the maximum permissible displacement between the original vertex and the corresponding offset vertex if the circular arc were to be omitted entirely. The default is `miterlimit=2` which is also the minimum value.

Calculations are performed in integer arithmetic after subtracting `x0,y0` from the coordinates, dividing by `eps`, and rounding to the nearest 64-bit integer. Thus, `eps` is the effective spatial resolution. The default values ensure reasonable accuracy.

### Value

Data specifying polygons, in the same format as `A`.

### Author(s)

Angus Johnson. Ported to R by Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### References

Clipper Website: http://www.angusj.com

Vatti, B. (1992) A generic solution to polygon clipping. Communications of the ACM 35 (7) 56–63. http://portal.acm.org/citation.cfm?id=129906

Agoston, M.K. (2005) Computer graphics and geometric modeling: implementation and algorithms. Springer-Verlag. http://books.google.com/books?q=vatti+clipping+agoston

Chen, X. and McMains, S. (2005) Polygon Offsetting by Computing Winding Numbers. Paper no. DETC2005-85513 in Proceedings of IDETC/CIE 2005 (ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference), pp. 565–575 http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf

### See Also

`polylineoffset`, `polyclip`, `polysimplify`, `polyminkowski`

### Examples

      A <- list(list(x=c(4,8,8,2,6), y=c(3,3,8,8,6)))
      plot(c(0,10),c(0,10), type="n", main="jointype=square", axes=FALSE, xlab="", ylab="")
      polygon(A[[1]], col="grey")
      C <- polyoffset(A, 1, jointype="square")
      polygon(C[[1]], lwd=3, border="blue")
      plot(c(0,10),c(0,10), type="n", main="jointype=round", axes=FALSE, xlab="", ylab="")
      polygon(A[[1]], col="grey")
      C <- polyoffset(A, 1, jointype="round")
      polygon(C[[1]], lwd=3, border="blue")
      plot(c(0,10),c(0,10), type="n", main="jointype=miter", axes=FALSE, xlab="", ylab="")
      polygon(A[[1]], col="grey")
      C <- polyoffset(A, 1, jointype="miter")
      polygon(C[[1]], lwd=3, border="blue")

[Package polyclip version 1.6-1 Index]