Toan Hoang

Creating Ternary Plots in Tableau

Toan Hoang

This is my last tutorial until I go on my August Tableau Magic break, and as such, I want to finish with a comprehensive tutorial on creating Ternary Plots in Tableau; going step-by-step, talking about the theory, and more importantly, going through the maths required. I hope you all enjoy this.

Note: This is an alternative type of data visualisation, and sometimes pushed for by clients. Please always look at best practices for data visualisations before deploying this into production.

Data

Load the following data into Tableau Desktop / Tableau Public.

OrdersDownload

Note: If you have Tableau Desktop. please use the Sample Superstore Data Source.

Ternary Plots

According to Wikipedia, a ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. In population genetics, it is often called a de Finetti diagram. In-game theory, it is often called a simplex plot. Ternary plots are tools for analyzing compositional data in the three-dimensional case.

In a ternary plot, the values of the three variables a, b, and c must sum to some constant, K. Usually, this constant is represented as 1.0 or 100%. Because a + b + c = K for all substances being graphed, any one variable is not independent of the others, so only two variables must be known to find a sample’s point on the graph: for instance, c must be equal to K − a − b. 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.

How I translate this, is that we have dimensions which comprise of three metrics, a, b and c, and the dimension is plotted based on the degree of relative impact that these values have on the dimension.

Implementation Theory

We are going to build a Data Visualisation which will use City as our Dimension and the following three Metrics: Total Sales, Total Quantity and Total Number of Orders.

For each City:

We will now get started by creating our Calculated Fields.

Calculated Fields

With the Orders data loaded, let us create the following Calculated Fields:

Percentage of Total Orders

COUNTD([Order ID])/TOTAL(COUNTD([Order ID]))

Percentage of Total Quantity

SUM([Quantity]) / TOTAL(SUM([Quantity]))

Percentage of Total Sales

SUM([Sales]) / TOTAL(SUM([Sales]))

Total Percentages

[Percentage of Total Orders]+[Percentage of Total Quantity]+[Percentage of Total Sales]

Ternary Value: Quantity

[Percentage of Quantity]/[Total Percentages]

Ternary Value: Orders

[Percentage of Orders]/[Total Percentages]

Ternary Value: Sales

[Percentage of Sales]/[Total Percentages]

So far we have not done anything too crazy, but we have built out our required values, and will now get to the trick stuff.

Y

SIN(RADIANS(60))*[Ternary Value: Quantity]

The right side of the triangle will represent Quantity, and because this value is along a slope, we will use the above formula to Calculate the Y position.

X

[Ternary Value: Orders]+([Y]/TAN(RADIANS(60)))

We used the Ternary Value for Quantity to work out the height (or Y). the bottom of the triangle will represent the Ternary Value for Orders. But let us have a look at the diagram again:

You can see that the value along the bottom, the red line goes off at an angle, so to adjust our X value, we will use the Y value, and a 60-degree angle (angle of an equilateral triangle).

So for example, if you look at the Comp1 value of 0.6, it maps to 0.1 for Comp2 and 0.3 for Comp3 (this gives us a total of 1.0); now if we map this to X and Y absolute coordinates, you can see that the value for the dot is not actually 0.6 but slightly adjusted, and it is this value that we work out using the [Y]*TAN(RADIANS(60)) calculation.

Note: If you fancy a primer on Trigonometry, check out: https://www.mathsisfun.com/algebra/trigonometry.html

These are actually the only Calculated Fields that we need to create our Ternary Chart, however, we will also create the following:

Parameter Called Metric Parameter

Metric

IF [Metric Parameter] = "Sales" THEN
    SUM([Sales])
ELSEIF [Metric Parameter] = "Quantity" THEN
    SUM([Quantity])
ELSE
    COUNTD([Order ID])
END

Note: this will allow us to have a selector and to utilise the Metric value for Color or Size etc…

Color

IF [Ternary Value: Quantity]>[Ternary Value: Orders] AND [Ternary Value: Quantity]> [Ternary Value: Sales] THEN
    "Quantity"
ELSEIF [Ternary Value: Orders]> [Ternary Value: Quantity] AND [Ternary Value: Orders] >[Ternary Value: Sales] THEN
    "Orders"
ELSE
    "Sales"
END

With this done, let us create our worksheet:

Worksheet

With all the calculations created, the Worksheet is actually pretty simple:

It is simple as that and you should now have the following:

Now let us adjust the Visualisation:

If all goes well, you should now have the following:

Now will create our triangle background worksheet, and will start by loading the following into Tableau Desktop / Tableau Public:

Metric,Path,X,Y
Sales,1,0,0
Quantity,2,0.5,0.866025404
Orders,3,1,0
Sales,4,0,0

In a New Worksheet:

You should now see the following:

Now we will drag both of these onto a dashboard and place them on top of each other, Ternary Chart on top of the Triangle Shape, add some labels, and we should now have the following:

and with that said, we are done with creating this very cool looking Data Visualisation, and on a personal note, it is extremely rewarding to create such a data visualisation without the need to perform any data preparation, but out of the box Calculations. You can find this Data Visualisation on my Tableau Public Profile https://public.tableau.com/profile/toan.hoang#!/vizhome/TernaryChart_15628715360680/TernaryPlot

Summary

I hope you all enjoyed this article as much as I enjoyed writing it and as always do share the love. Do let me know if you experienced any issues recreating this Visualisation, and as always, please leave a comment below or reach out to me on Twitter @Tableau_Magic.

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