polygon-operations {bivrp}

Polygon operations

Description

Convex polygon operations - determination of area, centre of mass, and area reduction

Usage

polygon_area(P)
get_k(P, conf)
get_newpolygon(conf, P, method)
get_reduced_bag(x, y, conf)
compute_bagplot(x, y, conf)

Arguments

P

2-column matrix or data.frame with the coordinates of the vertices of the convex polygon

conf

proportion of the area of polygon P

method

method used to reduce the area of the polygon. Use method = "proportional" to scale the distances between the centroid and the vertices by sqrt(conf); use method = "get_k" to subtract the same distance k from the centroid to each vertex.

x

x coordinates (of raw data) used to obtain the reduced bag

y

y coordinates (of raw data) used to obtain the reduced bag

Details

The function compute_bagplot uses an adapted version of the code written by P. Segaert to obtain the bagplot, that uses the Fortran subroutine written by P.J. Rousseeuw, I. Ruts and A. Struyf.

Author(s)

Rafael A. Moral <[e-mail]> and John Hinde

References

Rousseeuw P.J., Ruts I., Tukey J.W. (1999). The bagplot: A bivariate boxplot. The American Statistician, 53, 382–387.

See Also

is_point_inside polygon

Examples

  oldPolygon <- data.frame(x=c(2,1,3,4.5,5), y=c(1,3,5,4.5,2))
  
  # area
  polygon_area(oldPolygon)$area
  # centre of mass
  polygon_area(oldPolygon)$centre
  
  # get a new polygon with 50% of the area of the old one
  newPolygon <- get_newpolygon(conf=.5, P=oldPolygon, method="proportional")
  polygon_area(newPolygon)$area/polygon_area(oldPolygon)$area
  
  # second method
  newPolygon2 <- get_newpolygon(conf=.5, P=oldPolygon, method="get.k")
  polygon_area(newPolygon2)$area/polygon_area(oldPolygon)$area
  
  # illustration
  plot(oldPolygon, xlim=c(0,6), ylim=c(0,6), main="(a)", pch=16)
  polygon(oldPolygon, lwd=2, col="#00000033")
  text(oldPolygon, c(expression(P[1]), expression(P[2]),
                     expression(P[3]), expression(P[4]),
                     expression(P[5])), pos=c(1,2,3,4,4), cex=2)
  polygon(newPolygon, border=4, lwd=2, col="#52A3E199")
  points(newPolygon, pch=16, col=4)
  text(newPolygon, c(expression(paste(P[1],minute)), expression(paste(P[2],minute)),
             expression(paste(P[3],minute)), expression(paste(P[4],minute)),
             expression(paste(P[5],minute))), pos=c(1,3,2,4,4), col=4, cex=2)

  C <- polygon_area(oldPolygon)$centre
  text(C[1], C[2], "C", pos=4, cex=2)
  for(i in 1:5) lines(c(C[1], oldPolygon[i,1]), 
                      c(C[2], oldPolygon[i,2]), lty=2, lwd=2, type="b")