Conventions in mpltern

Axes and Ticks

In a ternary plot, three variables which sum to a constant t + l + r = ternary_scale (= 1 in mpltern by default) are projected onto a two-dimensional triangle. Each variable is associated with each corner of the triangle, and the value is represented by the scaled distance to the corner from its opposite side.

There may be two kinds of perspectives to read a ternary plot; the “corner-based” and the “side-based” perspectives. Mpltern adopts the “corner-based” perspective. In this perspective, each of the three variables is associated with a corner of the triangle, and the position in the triangle is given as the scaled distance to the corner from its opposite side, as already written above. In mpltern, the order of the variables is T (top) → L (left) → R (right) (counterclockwise).

In mpltern, by default, the ticks are shown to the right side of the triangle with seeing the corresponding corner upward. You can put the ticks to the opposite sides by ax.opposite_ticks(True). Notice that, although the tick positions are changed, still a point in the triangle corresponds to the same composition (see the red point).

Some people read a ternary plot with the “side-based” perspective like the figure below. In this perspective, we must also specify if the ticks proceed in a clockwise or a counterclockwise manner. Be careful that, in the “side-based” perspective, a point in the triangle corresponds to different compositions between the clockwise and the counterclockwise tick progresses, which may be confusing (see the red point). This also means that a position for a side is not immediately associated with the value of the corresponding variable in the “side-based” perspective. To avoid such confusions, in mpltern, the “corner-based” perspective is adopted.

The discussions here and here may be also helpful to understand.

Convention in Other Software

In the corner-based perspective, existing codes for ternary plots give the following orders by default:

Code	Order of triangle corners	Ticks
Plotly	T → L → R (CCW)	CW
python-ternary	R → T → L (CCW)	CCW
ggtern	L → R → T (CCW)	CCW
Ternary (R)	T → R → L (CW)	CW
d3-ternary	L → R → T (CCW)	CW
PGFPlots	T → L → R (CCW)	CCW
Veusz	R → L → T (CW)	CCW
ternaryplot.com	T → L → R (CCW)	CW
Delta Plotware	T → R → L (CW)	CCW
Dplot	R → T → L (CW)	CW
Grapher	R → T → L (CCW)	CCW
JMP	L → T → R (CW)	CW
Origin	R → T → L (CCW)	CCW
Statgraphics	T → L → R (CCW)	CCW

In mpltern by default:

• T → L → R (CCW) for the order of triangle corners

• CCW for the ticks progress

Normalization in Ternary Plots

In most plotting methods in mpltern, the given three variables are automatically normalized by ternary_scale. By this convention, the three variables can be treated on an equal footing. The exceptions are the span-plots like ax.axtline. Since in these methods only one of the variables is given, in principle it is not possible whether the given value is already normalized or not. To avoid confusions, it is strongly suggested to normalize the three variables beforehand outside mpltern.