Polygon Offset
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.
polyoffset(A, delta,
...,
eps, x0, y0,
miterlim=2, arctol=abs(delta)/100,
jointype=c("square", "round", "miter"))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. |
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.
Data specifying polygons, in the same format as A.
Angus Johnson. Ported to R by Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
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
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")
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