Converting 4-d Cartesian vectors to 3-d Barycentric vectors

Hello,

I am unable to determine how to use the cartesianToBarycentric function to convert a matrix 4-dimensional probability vectors into a matrix of 3-dimensional Barycentric vectors (with the final aim of plotting the 3-dimensional vectors as a line plot using plot3 ). My desired input is a matrix like

P =

    0.2500    0.2500    0.2500    0.2500
    0.7955    0.0682    0.0682    0.0682
    0.2706    0.0232    0.0232    0.6830
    0.7357    0.0084    0.0084    0.2475
    0.2724    0.0031    0.0031    0.7213
    0.7284    0.0012    0.0012    0.2692
    0.2727    0.0004    0.0004    0.7264
    0.7274    0.0002    0.0002    0.2722
    0.2727    0.0001    0.0001    0.7272
    0.7273    0.0000    0.0000    0.2727
    0.2727    0.0000    0.0000    0.7273

I am unable to determine the other required inputs. (The relevant MatLab documentation I can find so far has no examples of 3-dimensional Barycentric coordinates so I am unable to determine the required representation of a tetrahedron (which I'd simply like to be an equilateral tetrahedron) or the required id's.)

The corresponding tetrahedron would be defined by [0 0 0 1] -> [0 0 0] [1 0 0 0] -> [1 0 0] and the remaining [0 1 0 0] and [0 0 1 0] vertices defined by the 3d-vertices to the equilateral tetrahedrom with one edge along [0 0 0] and [1 0 0].

Thanks ahead of time for any help on this!