ads (version 1.5-5)

triangulate: Triangulate polygon

Description

Function triangulate decomposes a simple polygon (optionally having holes) into contiguous triangles.

Usage

triangulate(outer.poly, holes)

Arguments

outer.poly

a list with two component vectors x and y giving vertex coordinates of the polygon or a vector (xmin,ymin,xmax,ymax) giving coordinates \((ximn,ymin)\) and \((xmax,ymax)\) of the origin and the opposite corner of a rectangle sampling window (see swin).

holes

(optional) a list (or a list of list) with two component vectors x and y giving vertices coordinates of inner polygon(s) delineating hole(s) within the outer.poly.

Value

A list of 6 variables, suitable for using in swin and spp, and giving the vertices coordinates \((ax,ay,bx,by,cx,cy)\) of the triangles that pave the polygon. For a polygon with t holes totaling \(n\) vertices (outer contour + holes), the number of triangles produced is \((n-2)+2t\), with \(n<200\) in this version of the program.

Details

In argument outer.poly, the vertices must be listed following boundary of the polygon without any repetition (i.e. do not repeat the first vertex). Argument holes may be a list of vertices coordinates of a single hole (i.e. with \(x\) and \(y\) component vectors) or a list of list for multiple holes, where each holes[[i]] is a list with \(x\) and \(y\) component vectors. Holes' vertices must all be inside the outer.poly boundary (vertices on the boundary are considered outside). Multiple holes do not overlap each others.

References

Goreaud, F. and P?Pelissier, R. 1999. On explicit formula of edge effect correction for Ripley's K-function. Journal of Vegetation Science, 10:433-438. Narkhede, A. & Manocha, D. 1995. Fast polygon triangulation based on Seidel's algorithm. Pp 394-397 In A.W. Paeth (Ed.) Graphics Gems V. Academic Press. http://www.cs.unc.edu/~dm/CODE/GEM/chapter.html.

See Also

spp, swin

Examples

# NOT RUN {
  data(BPoirier)
  BP <- BPoirier
  plot(BP$poly1$x, BP$poly1$y)
  
  
# }
# NOT RUN {
a single polygon triangulation
# }
# NOT RUN {
  tri1 <- triangulate(BP$poly1)
  plot(swin(BP$rect, tri1))
  
  
# }
# NOT RUN {
a single polygon with a hole
# }
# NOT RUN {
  
# }
# NOT RUN {
tri2 <- triangulate(c(-10,-10,120,100), BP$poly1)
  plot(swin(c(-10,-10,120,100), tri2))
# }
# NOT RUN {
  
  
# }
# NOT RUN {
the same with narrower outer polygon
# }
# NOT RUN {
  
# }
# NOT RUN {
tri3 <- lapply(BP$poly2,triangulate)
  tri3<-do.call(rbind,tri3)
  xr<-range(tri3$ax,tri3$bx,tri3$cx)
  yr<-range(tri3$ay,tri3$by,tri3$cy)
  plot(swin(c(xr[1],yr[1],xr[2],yr[2]), tri3))
# }