pracma (version 1.8.6)

circlefit: Fitting a Circle

Description

Fitting a circle from points in the plane

Usage

circlefit(xp, yp, fast = FALSE)

Arguments

xp, yp

Vectors representing the x and y coordinates of plane points

fast

logical; shall a fast, non-optimized solution be returned?

Value

• Returns x- and y-coordinates of the center and the radius as a vector of length 3.

  Writes the RMS error of the distance of the original points to the circle directly onto the console.

encoding

utf8

Details

This routine first finds an `algebraic' solution based on a linear fit and then calls optim with this solution as starting point. If fast is TRUE the algebraic solution will not be improved.

The value to be minimized is the distance of the given points to the nearest point on the circle.

References

Gander, W., G. H. Golub, and R. Strebel (1994). Fitting of Circles and Ellipses --- Least Squares Solutions. ETH Zürich, Technical Report 217, Institut für Wissenschaftliches Rechnen.

Examples

# set.seed(8421)
n  <- 20
w  <- 2*pi*runif(n)
xp <- cos(w) + 1 + 0.25 * (runif(n) - 0.5)
yp <- sin(w) + 1 + 0.25 * (runif(n) - 0.5)

circlefit(xp, yp, fast = TRUE)  #=> 0.9899628 1.0044920 1.0256633
                                # RMS error: 0.07631986 
rslt <- circlefit(xp, yp)       #=> 0.9965782 1.0009066 1.0240452
                                # RMS error: 0.07611598
x0 <- rslt[1]; y0 <- rslt[2]; r0 <- rslt[3]
plot(c(-0.2, 2.2), c(-0.2, 2.2), type="n", asp=1)
grid()
abline(h=0, col="gray"); abline(v=0, col="gray")
points(xp, yp, col="darkred")

w  <- seq(0, 2*pi, len=100)
xx <- r0 * cos(w) + x0
yy <- r0 * sin(w) + y0
lines(xx, yy, col="blue")