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

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. https://dl.acm.org/doi/10.1145/129902.129906

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 https://mcmains.me.berkeley.edu/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")