#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

library(DAAG)

funRel = function(x=leafshape$logpet, y=leafshape$loglen, scale=c(1,1)){
  ## Find principal components rotation; see section 11.1
  xy.pcr = prcomp( cbind(x,y), scale=scale )
  b = xy.pcr$rotation[,2]/scale
  bxy = -b[1]/b[2] # slope - functional eqn line
  bint = mean(y) - bxy * mean(x) # intercept - functional eqn line 
  c(bint,bxy)
}

x = leafshape$logpet
y = leafshape$loglen

x = softbacks$volume
y = softbacks$weight

x = elastic2$stretch
y = elastic2$distance

#postscript("../../WriteUp/Graphics/Chapter5/prob_12_plot.eps", onefile=FALSE, horizontal=FALSE)

res1 = funRel(x,y,scale=c(1,1))
plot( x, y, xlab="logpet", ylab="loglen" )
abline( a=res1[1], b=res1[2], col="red" )

res2 = funRel(x,y,scale=c(1,10))
abline( a=res2[1], b=res2[2], col="blue" )

res3 = funRel(x,y,scale=c(10,1))
abline( a=res3[1], b=res3[2], col="green" )

#dev.off()