maxAreaInscribedCircle {PlaneGeometry}

Maximum area circle inscribed in a convex polygon

Description

Computes the circle inscribed in a convex polygon with maximum area. This is the so-called Chebyshev circle.

Usage

maxAreaInscribedCircle(points, verbose = FALSE)

Arguments

points

the vertices of the polygon in a two-columns matrix; their order has no importance, since the procedure takes the convex hull of these points (and does not check the convexity)

verbose

argument passed to psolve

Value

A Circle object. The status of the optimization problem is given as an attribute of this circle. A warning is thrown if it is not optimal.

See Also

maxAreaInscribedEllipse

Examples

library(PlaneGeometry)
hexagon <- rbind(
  c(-1.7, -1),
  c(-1.4, 0.4),
  c(0.3, 1.3),
  c(1.7, 0.6),
  c(1.3, -0.3),
  c(-0.4, -1.8)
)
opar <- par(mar = c(2, 2, 1, 1))
plot(NULL, xlim=c(-2, 2), ylim=c(-2, 2), xlab = NA, ylab = NA, asp = 1)
points(hexagon, pch = 19)
polygon(hexagon)
circ <- maxAreaInscribedCircle(hexagon)
draw(circ, col = "yellow2", border = "blue", lwd = 2)
par(opar)
# check optimization status:
attr(circ, "status")