circular (version 0.3-7)

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 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)

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.

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 . radius{the distance between the observations and the center coordinate} convergence{value from the function optim.} optim{the output from the function optim.} call{match.call().}
• Coope, I. (1993). Circle fitting by linear and non-linear least squares. Journal of Optimization Theory and Applications, 76, 381-388. [object Object],[object Object]

  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 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)

  models

Details

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