Converting in R cartesian coordinates to barycentric ones

Question

I have three reference vectors

a ( 0, 0, 1 )
b ( 0, 1, 0 )
c ( 1, 0, 0 )

and will have measurements such as

x( 0, 0.5, 0.3 )

which I want to plot in a 2D figure as a triangle, who edges would correspond to a, b and c.

In Matlab there is a straighforward function to do that

http://fr.mathworks.com/help/matlab/ref/triangulation.cartesiantobarycentric.html?s_tid=gn_loc_drop

does anyone know an equivalent in R or should I implement the maths?

Answer 1

Sure, you can go back and forth between cartesian and barycentric.

Bary to Cart:

library(geometry)

## Define simplex in 2D (i.e. a triangle)
X <- rbind(
            c( 0, 0, 1 ),
            c( 0, 1, 0 ),
            c( 1, 0, 0 ))

## Cartesian cooridinates of points
beta <- rbind(c( 0, 0.5, 0.3 ),
              c(0.1, 0.8, 0.1),
              c(0.1, 0.8, 0.1))

## Plot triangle and points
trimesh(rbind(1:3), X)
text(X[,1], X[,2], 1:3) # Label vertices
P <- bary2cart(X, beta)

Cart to Bary:

## Define simplex in 2D (i.e. a triangle)
X <- rbind(c(0, 0),
           c(0, 1),
           c(1, 0))
## Cartesian cooridinates of points
P <- rbind(c(0.5, 0.5),
           c(0.1, 0.8))
## Plot triangle and points
trimesh(rbind(1:3), X)
text(X[,1], X[,2], 1:3) # Label vertices
points(P)
cart2bary(X, P)