Appendix A
Practical recipes
A.1 Plotting a ternary diagram
Denote the three vertices of the ternary diagram counterclockwise from the upper vertex as 
, 
, and 
(see Figure A.1). The scale of the plot is arbitrary and a unitary equilateral triangle can be chosen. Assume that 
are the plotting coordinates of the 
vertex. The 
vertex is then 
and the vertex 
has abscissa 
; the square-height is obtained using Pythagoras' theorem: 
. Thus, . These are the vertices of the triangle shown in Figure A.1
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