# Create Ternary Plots in R

#### Martin R. Smith

#### 2025-09-03

“Ternary” is an R package to allow the creation of ternary plots in the standard R graphics environment. I hope that it proves simple to use.

For simple use cases, generate Ternary plots using the point-and-click Shiny app:

    install.packages("Ternary")
    Ternary::TernaryApp()

For greater control over your plots, use the full R implementation.

Install the package with:

    install.packages("Ternary")

Or if you want the latest development version of the package:

    if (!require("devtools")) install.packages("devtools")
    install_github("ms609/Ternary", args = "--recursive")

Once the package is installed, load it into the current R session with

    library("Ternary")

There are two stages to creating a ternary plot: first, rendering the plot, styled as you like it and pointing in any of the four compass directions; secondly, adding data.

## Create a blank plot

At its simplest, all you need to do is type

    TernaryPlot()

The following charts show which corners are which, under different orientations:

    par(mfrow = c(2, 2), mar = rep(0.5, 4))
    for (dir in c("up", "right", "down", "le")) {
      TernaryPlot(point = dir, atip = "A", btip = "B", ctip = "C",
                  alab = "Aness", blab = "Bness", clab = "Cness")
      TernaryText(list(A = c(10, 1, 1), B = c(1, 10, 1), C = c(1, 1, 10)),
                  labels = c("P1", "P2", "P3"),
                  col = cbPalette8[4], font = 2)
    }

## Plot two stylised plots side by side, and plot data

First we will define some data that we wish to plot:

    # Define data points
    data_points <- list(
      R = c(255, 0, 0),
      O = c(240, 180, 52),
      Y = c(210, 222, 102),
      G = c(111, 222, 16),
      B = c(25, 160, 243),
      I = c(92, 12, 243),
      V = c(225, 24, 208)
    )

    # Compute RGB colours based on point values
    PointColour <- function(x) {
      rgb(x[1], x[2], x[3], maxColorValue = 255, # Use point values for RGB
          alpha = 128 # Semitransparency
          )
    }

    # Precompute the colour for each point
    data_col <- sapply(data_points, PointColour)

Now we set up our plotting area to display two plots side by side, and produce the plots.

    par(                          # Configure plotting area
      mfrow = c(1, 2),            # Plot one row of panels in two columns
      mar = c(0.3, 0.3, 1.3, 0.3) # Set margins for each plot
    )

    # Initial plot
    TernaryPlot(alab = "Redder \u2192", blab = "\u2190 Greener", clab = "Bluer \u2192",
                lab.col = c("red", "darkgreen", "blue"),
                main = "Colours", # Title
                point = "right", lab.cex = 0.8, grid.minor.lines = 0,
                grid.lty = "solid", col = rgb(0.9, 0.9, 0.9), grid.col = "white",
                axis.col = rgb(0.6, 0.6, 0.6), ticks.col = rgb(0.6, 0.6, 0.6),
                axis.rotate = FALSE,
                padding = 0.08)

    # Colour the background:
    cols <- TernaryPointValues(rgb)
    ColourTernary(cols, spectrum = NULL)

    # Add the data to the plot
    AddToTernary(graphics::points, data_points, pch = 21, cex = 2.8, bg = data_col)
    AddToTernary(text, data_points, names(data_points), cex = 0.8, font = 2)
    legend("bottomright",
           legend = c("Red", "Orange", "Yellow", "Green"),
           cex = 0.8, bty = "n", pch = 21, pt.cex = 1.8,
           pt.bg = c(rgb(255,   0,   0, 128, NULL, 255),
                     rgb(240, 180,  52, 128, NULL, 255),
                     rgb(210, 222, 102, 128, NULL, 255),
                     rgb(111, 222,  16, 128, NULL, 255)),
           )

    ###
    # Next plot:
    ###
    TernaryPlot("Steam", "Ice", "Water",
                grid.lines = 5, grid.lty = "dotted",
                grid.minor.lines = 1, grid.minor.lty = "dotted",
                point = "West")

    # Another way to add a title
    title("Water phases", cex.main = 0.8)

    # Add horizontal grid lines
    HorizontalGrid()

    # Define a polygon
    middle_triangle <- matrix(c(
      30, 40, 30,
      30, 30, 40,
      55, 20, 25
    ), ncol = 3, byrow = TRUE)

    # Add polygon to plot
    TernaryPolygon(middle_triangle, col = "#aaddfa", border = "grey")

    # Connect corners of polygon to plot corners
    TernaryLines(list(c(0, 100, 0), middle_triangle[1, ]), col = "grey")
    TernaryLines(list(c(0, 0, 100), middle_triangle[2, ]), col = "grey")
    TernaryLines(list(c(100, 0, 0), middle_triangle[3, ]), col = "grey")

    # Add an arrow
    TernaryArrows(c(20, 20, 60), c(30, 30, 40), length = 0.2, col = "darkblue")

### Styling points

More sophisticated plots can be created, for example styling each point according to additional properties of the data, in a manner analogous to the standard plotting functions:

    # Configure plotting area
    par(mar = rep(0.3, 4))

    # Example data object
    dat <- data.frame(sio2 = c(2, 4, 10, 20),
                      fe2o3 = c(5, 6, 7, 8),
                      al2o3 = c(12, 11, 10, 9),
                      grain_size = c(20, 16, 12, 8),
                      reflectance = c(80, 63, 51, 20))

    # Define a colour spectrum
    spectrumBins <- 255 # Number of bins to use
    mySpectrum <- rowCol <- hcl.colors(spectrumBins, palette = "viridis")

    # Cut our reflectance data into categories
    binnedReflectance <- cut(dat$reflectance, spectrumBins)

    # Assign each data point a colour from the spectrum
    pointCol <- mySpectrum[binnedReflectance]

    # Define a size range
    maxSize <- 2.4 # Size of largest point, in plotting units
    sizes <- dat$grain_size
    pointSize <- sizes * maxSize / max(sizes)

    # Initialize the plot
    TernaryPlot(atip = expression(SiO[2]),
                btip = expression(paste(Fe[2], O[3], " (wt%)")),
                ctip = expression(paste(Al[2], O[3]))
    )

    # Plot the points
    TernaryPoints(dat[, c("sio2", "fe2o3", "al2o3")],
                  cex = pointSize, # Point size
                  col = pointCol,  # Point colour
                  pch = 16         # Plotting symbol (16 = filled circle)
                  )

    # Legend for colour scale
    PlotTools::SpectrumLegend(
      "topleft",
      cex = 0.8, # Font size
      palette = mySpectrum,
      legend = paste(
        seq(from = max(dat$reflectance), to = min(dat$reflectance),
            length.out = 5),
        "%"
      ),
      bty = "n", # No framing box
      xpd = NA, # Don't clip at margins
      # title.font = 2, # Bold.  Argument only available in R>3.6
      title = "Reflectance"
    )

    # Legend for point size
    PlotTools::SizeLegend(
      "topright",
      width = c(0, maxSize),
      lend = "round", # Round end of scale bar
      legend = paste(
        signif(seq(max(sizes), 0, length.out = 5), digits = 3),
        "\u03bcm" # µm
      ),
      title = "Grain size",
      # title.font = 2, # Bold. Argument only available in R>3.6
      bty = "n", # Do not frame with box
      cex = 0.8
    )

See the “Points” tab of the shiny app for a point-and-click implementation.

### Cartesian coordinates

It is also possible to use Cartesian coordinates to plot onto the graph.

By default, the plotting area is a 1×1 square.

    par(mar = rep(0, 4)) # Reduce margins
    TernaryPlot(point = "right", clockwise = FALSE)
    cat("X range in this orientation:", TernaryXRange())

    ## X range in this orientation: -0.0669873 0.9330127

    cat("Y range in this orientation:", TernaryYRange())

    ## Y range in this orientation: -0.5 0.5

    arrows(x0 = 0.5, y0 = 0.4, x1 = sqrt(3) / 2, y1 = 0.4, length = 0.1,
           col = cbPalette8[2])
    text(x = mean(c(0.5, sqrt(3) / 2)), y = 0.4, "Increasing X", pos = 3,
         col = cbPalette8[2])
    text(x = 0.5, y = 0, "(0.5, 0)", col = cbPalette8[3])
    text(x = 0.8, y = -0.5, "(0.8, -0.5)", col = cbPalette8[3])

Note the anticlockwise axis labelling on this plot, obtained using `clockwise = FALSE`.

## Contours

A plot can be coloured and contoured according to the output of a mathematical expression:

    par(mar = rep(0.2, 4))
    TernaryPlot(alab = "a", blab = "b", clab = "c")

    FunctionToContour <- function(a, b, c) {
      a - c + (4 * a * b) + (27 * a * b * c)
    }

    # Add contour lines
    values <- TernaryContour(FunctionToContour, resolution = 36L, filled = TRUE)
    zRange <- range(values$z, na.rm = TRUE)

    # Continuous legend for colour scale
    PlotTools::SpectrumLegend(
      "topleft",
      legend = round(seq(zRange[1], zRange[2], length.out = 4), 3),
      palette = hcl.colors(265, palette = "viridis", alpha = 0.6),
      bty = "n",    # No framing box
      inset = 0.02,
      xpd = NA      # Do not clip at edge of figure
    )

or according to the density of points across the plot:

    par(mar = rep(0.2, 4))
    TernaryPlot(axis.labels = seq(0, 10, by = 1))

    nPoints <- 4000L
    coordinates <- cbind(abs(rnorm(nPoints, 2, 3)),
                         abs(rnorm(nPoints, 1, 1.5)),
                         abs(rnorm(nPoints, 1, 0.5)))

    # Colour plot background
    ColourTernary(TernaryDensity(coordinates, resolution = 10L))

    # Add points
    TernaryPoints(coordinates, col = "red", pch = ".")

    # Contour by point density
    TernaryDensityContour(coordinates, resolution = 30L)

## Magnification

Perhaps the action on a plot is constrained to a small region of ternary space. It’s possible to “zoom in” – i.e. magnify and crop the ternary plot to the region of interest.

To do this you can specify the x and y limits of the region of interest.

`TernaryCoords` might be useful in establishing the Cartesian coordinates of a particular point in ternary space.
Ensure that dx = dy if you want an isometric plot.

    # Define points corresponding to corners of a region to plot
    my_corners <- list(c(22, 66, 12), c(22, 72, 6), c(15, 80, 5), c(12, 76, 12))

    # Print Cartesian coordinates of points
    vapply(my_corners, TernaryCoords, direction = 1, FUN.VALUE = c(x = 0, y = 0))

    ##        [,1]      [,2]      [,3]     [,4]
    ## x 0.2700000 0.3300000 0.3750000 0.320000
    ## y 0.1905256 0.1905256 0.1299038 0.103923

The `padding` parameter is added as a margin to each side of the region specified using `xlim` and `ylim`:

    # Remove plot margins
    par(mar = rep(0, 4))

    # Create clipped plotting area
    TernaryPlot(xlim = c(0.28, 0.38), ylim = c(0.1, 0.2), padding = 0.04)

    # Annotate grid lines at user-specified points:
    TernaryText(list(c(8, 72, 20), c(8, 82, 10)), c(20, 10), srt = -60, cex = 0.9,
                col = "darkgrey")
    TernaryText(list(c(10, 69, 21), c(20, 64, 16)), c(10, 20), srt = 0, cex = 0.9,
                col = "darkgrey")

    # Plot desired polygon
    TernaryPolygon(my_corners, col = "#2cbe4e88")

    # Show xlim, ylim and padding, using Cartesian coordinates
    lines(c(0.28, 0.28, 0.38, 0.38, 0.28), c(0.1, 0.2, 0.2, 0.1, 0.1))
    text(0.28, 0.15, "xlim[1]", pos = 2, srt = 90)
    text(0.38, 0.15, "xlim[2]", pos = 4, srt = 90)
    text(0.33, 0.1, "ylim[1]", pos = 1)
    text(0.33, 0.2, "ylim[2]", pos = 3)
    text(0.38, 0.1, "<padding>", pos = 4, cex = 0.75)
    text(0.38, 0.1, "<padding> ", pos = 2, cex = 0.75, srt = 90)

An alternative approach is to plot a triangular sub-region of the larger ternary space, allowing axis annotations to be read more easily.

    par(mar = rep(0.2, 4))
    TernaryPlot(region = my_corners) # Fit plotted region to data
    TernaryPolygon(my_corners, col = "#2cbe4e88")

A region can be defined manually; the smallest triangle that covers the region will be employed.

    par(mar = rep(0.2, 4))
    region <- list(
       c(amin = 10, bmin = 70, cmin = 0),
       c(amax = 30, bmax = 70, cmax = 10)
    )
    TernaryPlot(region = region)

    # Data will be plotted even if it falls outside the plotted axes
    TernaryPolygon(my_corners, col = "#2cbe4e88")

## Further tutorials

For further examples of usage, see the accompanying vignettes:

- Introduction for new R users

- Interpolating and contouring

- Annotation of points

- Plotting Holdridge climate zones

## Bugs and feature requests

I hope the package proves useful. If there’s anything it can’t do that you wish it could, please let me know by opening a Github issue.