Generate ellipses
Given the axes a, b (major and minor) and angle phi (in radian, counter clockwise from x-axis), and the midpoint c(0,0), points on a rotated ellipse will be generated. The major axis is rotated from the positive x-axis by the angle phi.
ellipseC(mid, a, b=a, ra=c(-1,361), phi=0, k=a*100 ) ellipse1( a, b=a, ra=c(-1,361), phi=0, k=a*100 ) conf.ellipse( a, b, phi, df1, df2, level = 0.95, k)
mid |
Complex, center of ellipse |
b |
Real > 0, minor axis |
a |
Real > 0, major axis |
ra |
Integer, range of arc [deg] |
phi |
Real, angle in radian describing the counter clockwise rotation |
k |
Integer, the number of generated points on the ellipse. |
df1, df2, level |
degrees of freedom and probability level |
ellipseC complex coordinates of the ellipse.
ellipse1 (x,y)-coordinates of the ellipse.
conf.ellipse (x,y)-coordinates of the confidence ellipse according to qf(level, df1, df2), see qf.
Christian W. Hoffmann <christian@echoffmann.ch>
opar <- par(mfrow=c(1,1))
k <- 60; m <- c(0,0); a <- 2; b <- 1; phi <- pi/7
df1 <- 2; df2 <- 20
# show F for different confidence levels:
p <- c(0.5, 0.75, 0.8, 0.95)
qf(p, df1, df2) # 0.717735 1.486984 1.746189 3.492828
el7 <- conf.ellipse(a,b,phi,df1,df2,p[2], k) + m
plot(el7*1.8,type="n",xlab="Different confidence ellipses",ylab="")
lines(conf.ellipse(a,b,phi,df1,df2,p[1],60) + m,lty=2,col="red")
lines(conf.ellipse(a,b,phi,df1,df2,p[3],60) + m,lty=2,col="green")
lines(conf.ellipse(a,b,phi,df1,df2,p[4],60) + m,lty=2,col="blue")
lines(el7,lty=2,col="orange")
leg1 <- paste(as.character(p*100),rep("percent",length(p)),sep="")
# leg1 <- paste(as.character(p*100),rep("%",length(p)),sep="")
col1 <- c("red", "orange","green","blue")
legend(x="bottom",leg1,col=col1,
text.col="black",lty=c(2,2,2,2), merge=TRUE, bg='white', cex=0.9)
par(opar)
for(ii in 0:15){ x <- ellipseC(40,1,2,phi=pi/15*ii);lines(x,col=ii%%3+1)}Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.