Determines if points are on or in the convex hull of a triangulation object

Given a triangulation object tri.obj of \(n\) points in the plane, this subroutine returns a logical vector indicating if the points \((x_i,y_i)\) lay on or in the convex hull of tri.obj.

on.convex.hull(tri.obj, x, y, eps=1E-16)
in.convex.hull(tri.obj, x, y, eps=1E-16, strict=TRUE)

Arguments

tri.obj

object of class triSht

x

vector of \(x\)-coordinates of points to locate

y

vector of \(y\)-coordinates of points to locate

eps

accuracy for checking the condition

strict

logical, default TRUE. It indicates if the convex hull is treated as an open (strict=TRUE) or closed (strict=FALSE) set. (applies only to in.convex.hull)

Value

Logical vector.

Author

Albrecht Gebhardt <albrecht.gebhardt@aau.at>, Roger Bivand <roger.bivand@nhh.no>

Examples

# use a part of the quakes data set:
data(quakes)
quakes.part<-quakes[(quakes[,1]<=-10.78 & quakes[,1]>=-19.4 &
                     quakes[,2]<=182.29 & quakes[,2]>=165.77),]
q.tri<-tri.mesh(quakes.part$lon, quakes.part$lat, duplicate="remove")
on.convex.hull(q.tri,quakes.part$lon[1:20],quakes.part$lat[1:20])
#>  [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
#> [13] FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE
# Check with part of data set:
# Note that points on the hull (see above) get marked FALSE below:
in.convex.hull(q.tri,quakes.part$lon[1:20],quakes.part$lat[1:20])
#>  [1]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
#> [13]  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE
# If points both on the hull and in the interior of the hull are meant 
# disable strict mode:
in.convex.hull(q.tri,quakes.part$lon[1:20],quakes.part$lat[1:20],strict=FALSE)
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE
# something completely outside:
in.convex.hull(q.tri,c(170,180),c(-20,-10))
#> [1] FALSE FALSE