maxAreaInscribedEllipse {PlaneGeometry}

Maximum area ellipse inscribed in a convex polygon

Description

Computes the ellipse inscribed in a convex polygon with maximum area.

Usage

maxAreaInscribedEllipse(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

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

See Also

maxAreaInscribedCircle

Examples

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)
ell <- maxAreaInscribedEllipse(hexagon)
draw(ell, col = "yellow2", border = "blue", lwd = 2)
par(opar)
# check optimization status:
attr(ell, "status")