On 03/14/2014 08:19 PM, al Vel wrote:
Hi,
Exactly the matrix transformation is the one that pasted in my first
mail. That is here:
new_point <- function(x1, x2, y1, y2, grad=1.73206){
b1 <- y1-(grad*x1)
b2 <- y2-(-grad*x2)
M <- matrix(c(grad, -grad, -1,-1), ncol=2)
intercepts <- as.matrix(c(b1,b2))
t_mat <- -solve(M) %*% intercepts
data.frame(x=t_mat[1,1], y=t_mat[2,1])
}
The problem is: the points are going out of the rhombus.
Well, there must be something wrong with it then. I think that the
matrix is:
pmat<-matrix(c(cos(pp),-2*sin(pp),0,sin(pp),2*cos(pp),0,0,0,1),
nrow=3)
and as the upper angle of the rhombus is pi/3, I think pp should be:
pp<-pi/6
and the transformation is something like:
xymat<-matrix(c(0.5,0.3,0.5,0.3,1,1),nrow=3,byrow=TRUE)
pmat%*%xymat
[,1] [,2]
[1,] 0.6830127 0.4098076
[2,] 0.3660254 0.2196152
[3,] 1.0000000 1.0000000
Unfortunately, the hydrogeo package does not reveal the formula used for
transforming the two ternary diagrams into the rhomboidal one. It does
seem to work, however. I do recall trying to contact the maintainer when
attempting to sort out the Piper diagram problem we had and getting no
response.
Jim
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