Compute Radially Equispaced Points on Ellipse

Compute points on (the boundary of) an ellipse which is given by elementary geometric parameters.

ellipsePoints(a, b, alpha = 0, loc = c(0, 0), n = 201, keep.ab.order=FALSE)

Arguments

a,b

length of half axes in (x,y) direction. Note that \((a,b)\) is equivalent to \((b,a)\) unless keep.ab.order=TRUE.

alpha

angle (in degrees) giving the orientation of the ellipse, i.e., the original (x,y)-axis ellipse is rotated by angle.

loc

center (LOCation) of the ellipse.

n

number of points to generate.

keep.ab.order

logical indicating if \((a,b)\) should be considered ordered. When FALSE, as per default, the orientation of the ellipse is solely determined by alpha.

Note that keep.ab.order = TRUE seems a more natural default, but FALSE is there for back-compatibility.

Value

A numeric matrix of dimension n x 2, each row containing the (x,y) coordinates of a point.

Author

Martin Maechler, March 2002.

See also

the ellipse package and ellipsoidhull and ellipsoidPoints in the cluster package.

Examples

## Simple Ellipse, centered at (0,0), x-/y- axis parallel:
ep <- ellipsePoints(5,2)
str(ep)
#>  num [1:201, 1:2] 5 4.98 4.94 4.87 4.77 ...
plot(ep, type="n",asp=1) ; polygon(ep, col = 2)
## (a,b) = (2,5)  is equivalent to (5,2) :
lines(ellipsePoints(2,5), lwd=2, lty=3)
## keep.order=TRUE : Now, (2,5) are axes in x- respective y- direction:
lines(ellipsePoints(2,5, keep.ab.order=TRUE), col="blue")


## rotate by 30 degrees :
plot(ellipsePoints(5,2, alpha = 30), asp=1)
abline(h=0,v=0,col="gray")
abline(a=0,b= tan( 30 *pi/180), col=2, lty = 2)
abline(a=0,b= tan(120 *pi/180), col=3, lty = 2)


## NB: use x11(type = "Xlib") for the following if you can
if(dev.interactive(TRUE)) {
  ## Movie : rotating ellipse  :
  nTurns <- 4 # #{full 360 deg turns}
  for(al in 1:(nTurns*360)) {
      ep <- ellipsePoints(3,6, alpha=al, loc = c(5,2))
      plot(ep,type="l",xlim=c(-1,11),ylim=c(-4,8),
     asp=1, axes = FALSE, xlab="", ylab="")
  }

  ## Movie : rotating _filled_ ellipse {less nice to look at}
  for(al in 1:180) {
      ep <- ellipsePoints(3,6, alpha=al, loc = c(5,2))
      plot(ep,type="n",xlim=c(-1,11),ylim=c(-4,8),
     asp=1, axes = FALSE, xlab="", ylab="")
      polygon(ep,col=2,border=3,lwd=2.5)
  }
}# only if interactive