circular (version 0.5-1)

lsfit.circle: Fit a 2D circle to an (x,y) dataset

Description

Fit a 2D circle to an (x,y) dataset using LS.

Usage

lsfit.circle(x, y, init = NULL, units = c("radians", "degrees"), 
  template = c("none", "geographics"),
  modulo = c("asis", "2pi", "pi"), zero = 0, 
  rotation = c("counter", "clock"), ...)
# S3 method for lsfit.circle
print(x, digits = max(3, getOption("digits") - 3), ...)

Value

An object of class lsfit.circle.

coefficients

a vector of length 3 with the estimated radius and coordinate of the center of the fitted circle.

x

the x-coordinate.

y

the y-coordinate.

x.centered

the x-coordinate re-centered at the center of the circle.

y.centered

the y-coordinate re-centered at the center of the circle.

angles

angles of the observations with respect to the center coordinate of class circular.

radius

the distance between the observations and the center coordinate

convergence

value from the function optim.

optim

the output from the function optim.

call

the match.call result.

Arguments

x

either a matrix with two columns or a vector.

y

if x is a vector then y must be a vector with the same length.

init

initial values of the parameters. A vector of length 3 with the following components: radius of the circle, x-coordinate of the center, y-coordinate of the center. If NULL the vector is set to c(max(c(abs(x-mean(x)), abs(y-mean(y)))), mean(x), mean(y).

units

the units used in defining the angles between observations and the center of the circle. See circular.

template

the template used in defining the angles between observations and the center of the circle. See circular.

modulo

the modulo used in defining the angles between observations and the center of the circle. See circular.

zero

the zero used in defining the angles between observations and the center of the circle. See circular.

rotation

the rotation used in defining the angles between observations and the center of the circle. See circular.

...

further parameters passed to the optim function.

digits

the number of digits to be printed.

Author

Claudio Agostinelli and Ulric Lund

Details

lsfit.circle uses the optim function to minimize the sum of the squared residuals between the observations and the optimally fitting circle.

References

Coope, I. (1993). Circle fitting by linear and non-linear least squares. Journal of Optimization Theory and Applications, 76, 381-388.

Examples

data(coope)
res <- lsfit.circle(x=x.coope, y=y.coope)
res

plot(res)

par(mfcol=c(1,2))
plot(res$angles)
hist(res$radius)

plot(circular(0), type="n", xlim=c(-5.2, 5.2), ylim=c(-5.2, 5.2), 
  xlab="The Radius of the circle \n is measured from the base line of the axes.")
lines(x=res$angles, y=res$radius, join=TRUE, type="b")
ff <- function(x) sqrt((res$coefficients[1]*cos(x))^2+(res$coefficients[1]*sin(x))^2)
curve.circular(ff, add=TRUE, join=TRUE, nosort=FALSE, col=2)

windrose(x=res$angles, y=res$radius)