Ternary plot

Ternary plots are tools for analyzing compositional data in the three-dimensional case.

In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram.

In game theory[2] and convex optimization,[3] it is often called a simplex plot.

Because the three numerical values cannot vary independently—there are only two degrees of freedom—it is possible to graph the combinations of all three variables in only two dimensions.

Motion along a line through a corner preserves the ratio of the other two values.Figure (1) shows an oblique projection of point P(a,b,c) in a 3-dimensional Cartesian space with axes a, b and c, respectively.

For any line l = s + t n̂ in vector form (n̂ is a unit vector) and a point p, the perpendicular distance from p to l is In this case, point P is at Line BC has Using the perpendicular distance formula, Substituting K = a + b + c, Similar calculation on lines AC and AB gives This shows that the distance of the point from the respective lines is linearly proportional to the original values a, b and c.[4] Cartesian coordinates are useful for plotting points in the triangle.

A ternary flammability diagram , showing which mixtures of methane , oxygen gas , and inert nitrogen gas will burn
Derivation of a ternary plot from Cartesian coordinates
Analogue on a Cartesian grid by adding lines of slope −1. The scale of the c axis is that of the a and b axes. The cross denotes the point a = b = c .
A colorized soil textural triangle from the United States Department of Agriculture