Fitting a Circle
Fitting a circle from points in the plane
circlefit(xp, yp, fast = TRUE)
xp, yp |
Vectors representing the x and y coordinates of plane points |
fast |
deprecated; will not be used. |
This routine finds an ‘algebraic’ solution based on a linear fit. The value to be minimized is the distance of the given points to the nearest point on the circle along a radius.
Returns x- and y-coordinates of the center and the radius as a vector of length 3.
Writes the RMS error of the (radial) distance of the original points to the circle directly onto the console.
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.
# 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)
circe <- circlefit(xp, yp) #=> 0.9899628 1.0044920 1.0256633
# RMS error: 0.07631986
## Not run:
x0 <- circe[1]; y0 <- circe[2]; r0 <- circe[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")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.