sl.polygon.mergehole: Merge Hole in Polygon

In helgegoessling/spheRlab: Spherical Geometry, Analysis, and Plotting of Geoscientific Data on Arbitrary Grids

Merge Hole in Polygon

Description

Merge a hole ('inverse') polygon with a larger polygon that encompasses the hole, on a sphere, returning either a single merged polygon (with duplicate points at a single connecting segment) or two polygons where a second connecting segment is used to obtain two polygons, each of which individually being free of duplicate points. Additional arguments allow some control over the way how the connecting segments are constructed.

Usage

sl.polygon.mergehole(poly, poly.hole, connect.maxstep=Inf, checkcross=TRUE, split.poly=FALSE, split.costexp=2)

Arguments

poly	a list with two elements lon and lat, which are numeric vectors of length N1 specifying the longitudes and latitudes of the outer polygon.
poly.hole	a list with two elements lon and lat, which are numeric vectors of length N2 specifying the longitudes and latitudes of the inner polygon.
connect.maxstep	either a numeric scalar (in radians) specifying an upper bound for the step length used to subdivide the connecting segment(s), or a function that determines this upper bound based on the length of all segments comprising poly and poly.hole (e.g. max). Default is connect.maxstep=Inf, in which case no points are added. See details below.
checkcross	a logical value specifying whether or not (i) to check the two input polygons for integrity, meaning that no intersections between the segments comprising each polygon are present, and (ii) to make sure that the connection(s) do not intesect with any polygon segment. Default is TRUE.
split.poly	a logical value specifying whether two polygons (using a second connecting segment), both individually being free of duplicate points, shall be returned. If FALSE (default), a single merged polygon with duplicate points at a single connecting segment is returned.
split.costexp	a numeric scalar specifying a parameter in the cost function used to determine the location of the second connection, used only if split.poly=TRUE, see details below. Default is split.costexp=2.

Details

The first connection between the outer and inner polygons is determined simply by minimizing the distances between the connected points. If checkcross=TRUE and the connection over the shortest distance would cross other polygon segments, those two points with the second-shortest distance are tried, and so forth. The first connection is determined independently of the optional second connection to split the polygon in two pieces.

The cost function used to determine the second connection (if split.poly=TRUE) favours a small distance between the connected points, too, but now it also favours a long minimum distance along the polygon boundaries between the first and second connections (minimum over the four polygon boundary pieces, two inner and two outer). The cost function to be minimized reads COST = length_second_connection / min(inter_connection_distance_along_polygon_boundary)^split.costexp. A larger value for split.costexp thus means that a large (minimum) along-boundary distance is considered relatively more important compared to a short connection distance, leading tendentially to more equally-sized polygons.

If a connection is longer than connect.maxstep, the minimum number of points required to obtain sub-segments shorter than (or as long as) the upper bound are added in an equidistant manner along the connection using sl.fillequidist(...,method="gc"). For example, connect.maxstep=max will make sure that individual segments of the connection(s) will not be longer than the longest segment of the two input polygons. This can be useful if the resulting polygons are to be split further, e.g., with sl.polygon.split.

Value

If split.poly=FALSE, a list with the following two elements is returned (where C1 is the number of points inserted into the connecting segment):

lon	a vector of length N1+N2+2*C1 with the longitude(s) of the merged polygon.
lat	a vector of length N1+N2+2*C1 with the latitude(s) of the merged polygon.

If split.poly=TRUE, a list with the following two elements is returned (where N3+N4 = N1+N2+2*(C1+C2) and C1 and C2 are the numbers of points inserted into the first and second connecting segments):

polygon1	a list with elements lon and lat, each a vector of length N3, that provide the longitudes and latitudes of the first polygon.
polygon2	a list with elements lon and lat, each a vector of length N4, that provide the longitudes and latitudes of the second polygon.

Author(s)

Helge Goessling

See Also

sl.finddist, sl.intersect

Examples

lon1 = c(5,0,9,0.5,0,10,10)
lat1 = c(10,9.8,9.6,9.2,0,0,9.9)
lon2 = c(2,5,8)
lat2 = c(3,9,4)

res.nosplit = sl.polygon.mergehole(poly=list(lon=lon1,lat=lat1), poly.hole=list(lon=lon2,lat=lat2), split.poly=FALSE)
str(res.nosplit)
## Should return:
## List of 2
##  $ lon: num [1:12] 0 10 10 5 0 9 0.5 0 2 5 ...
##  $ lat: num [1:12] 0 0 9.9 10 9.8 9.6 9.2 0 3 9 ...

res.split = sl.polygon.mergehole(poly=list(lon=lon1,lat=lat1), poly.hole=list(lon=lon2,lat=lat2), split.poly=TRUE, connect.maxstep=function(x){min(x)/2})
str(res.split)
## Should return:
## List of 2
##  $ polygon1:List of 2
##   ..$ lon: num [1:6] 0 10 9 8 2 ...
##   ..$ lat: num [1:6] 0 0 2 4 3 ...
##  $ polygon2:List of 2
##   ..$ lon: num [1:12] 10 10 5 0 9 ...
##   ..$ lat: num [1:12] 0 9.9 10 9.8 9.6 ...

plot(NA, xlim=range(c(lon1,lon2)), ylim=range(c(lat1,lat2)))
polygon(res.split$polygon1$lon, res.split$polygon1$lat, col="red", border=NA)
polygon(res.split$polygon2$lon, res.split$polygon2$lat, col="blue", border=NA)
polygon(lon1, lat1, lwd=2)
polygon(lon2, lat2, lwd=2, lty=2)

helgegoessling/spheRlab documentation built on April 8, 2024, 8:34 a.m.