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

In circular: Circular Statistics

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 class 'lsfit.circle'
print(x, digits = max(3, getOption("digits") - 3), ...)

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.

Details

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

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.

Author(s)

Claudio Agostinelli and Ulric Lund

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)

circular documentation built on Sept. 11, 2024, 8:21 p.m.