polyclip {polyclip}

Polygon Clipping

Description

Find intersection, union or set difference of two polygonal regions or polygonal lines.

Usage

 polyclip(A, B, op=c("intersection", "union", "minus", "xor"),
         ...,
         eps, x0, y0,
         fillA=c("evenodd", "nonzero", "positive", "negative"),
         fillB=c("evenodd", "nonzero", "positive", "negative"),
         closed = TRUE)

Arguments

A, B

Data specifying polygons. See Details.

op

Set operation to be performed to combine A and B. One of the character strings "intersection", "union", "minus" or "xor" (partially matched).

...

Ignored.

eps

Spatial resolution for coordinates. A single positive numeric value.

x0, y0

Spatial origin for coordinates. Numeric values.

fillA, fillB

Polygon-filling rules for A and B. Each argument is one of the character strings "evenodd", "nonzero", "positive" or "negative" (partially matched).

closed

Logical value specifying whether A is a closed polygon (closed=TRUE, the default) or an open polyline (closed=FALSE).

Details

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

Given two polygonal regions A and B the function polyclip performs one of the following geometrical operations:

• op="intersection": set intersection of A and B.

• op="union": set union of A and B.

• op="minus": set subtraction (sometimes called set difference): the region covered by A that is not covered by B.

• op="xor": exclusive set difference (sometimes called exclusive-or): the region covered by exactly one of the sets A and B.

Each of the arguments A and B represents a region in the Euclidean plane bounded by closed polygons. The format of these arguments 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 interpretation of the polygons depends on the polygon-filling rule for A and B that is specified by the arguments fillA and fillB respectively.

Even-Odd:

The default rule is even-odd filling, in which every polygon edge demarcates a boundary between the inside and outside of the region. It does not matter whether a polygon is traversed in clockwise or anticlockwise order. Holes are determined simply by their locations relative to other polygons such that outers contain holes and holes contain outers.

Non-Zero:

Under the nonzero filling rule, an outer boundary must be traversed in clockwise order, while a hole must be traversed in anticlockwise order.

Positive:

Under the positive filling rule, the filled region consists of all points with positive winding number.

Negative:

Under the negative filling rule, the filled region consists of all points with negative winding number.

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

Value

Data specifying polygons, in the same format as A and B.

Author(s)

Angus Johnson. Ported to R by Adrian Baddeley [e-mail]. Additional modification by Paul Murrell.

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

polysimplify, polyoffset, polylineoffset, polyminkowski

Examples

  A <- list(list(x=1:10, y=c(1:5,5:1)))
  B <- list(list(x=c(2,8,8,2),y=c(0,0,10,10)))

  plot(c(0,10),c(0,10), type="n", axes=FALSE,
    xlab="", ylab="", main="intersection of closed polygons")
  invisible(lapply(A, polygon))
  invisible(lapply(B, polygon))
  C <- polyclip(A, B)
  polygon(C[[1]], lwd=3, col=3)

  plot(c(0,10),c(0,10), type="n", axes=FALSE,
    xlab="", ylab="", main="intersection of open polyline and closed polygon")
  invisible(lapply(A, polygon))
  invisible(lapply(B, polygon))
  E <- polyclip(A, B, closed=FALSE)
  invisible(lapply(E, lines, col="purple", lwd=5))