Add contours of estimated point density to a ternary plot

Use two-dimensional kernel density estimation to plot contours of point density.

TernaryDensityContour(
  coordinates,
  bandwidth,
  resolution = 25L,
  tolerance = -0.2/resolution,
  edgeCorrection = TRUE,
  direction = getOption("ternDirection", 1L),
  filled = FALSE,
  nlevels = 10,
  levels = pretty(zlim, nlevels),
  zlim,
  color.palette = function(n) hcl.colors(n, palette = "viridis", alpha = 0.6),
  fill.col = color.palette(length(levels) - 1),
  ...
)

Arguments

coordinates: A list, matrix, data.frame or vector in which each element (or row) specifies the three coordinates of a point in ternary space.
bandwidth: Vector of bandwidths for x and y directions. Defaults to normal reference bandwidth (see MASS::bandwidth.nrd). A scalar value will be taken to apply to both directions.
resolution: The number of triangles whose base should lie on the longest axis of the triangle. Higher numbers will result in smaller subdivisions and smoother colour gradients, but at a computational cost.
tolerance: Numeric specifying how close to the margins the contours should be plotted, as a fraction of the size of the triangle. Negative values will cause contour lines to extend beyond the margins of the plot.
edgeCorrection: Logical specifying whether to correct for edge effects (see details).
direction: (optional) Integer specifying the direction that the current ternary plot should point: 1, up; 2, right; 3, down; 4, left.
filled: Logical; if TRUE, contours will be filled (using .filled.contour().).
nlevels, levels, zlim, ...: parameters to pass to contour().
color.palette: parameters to pass to .filled.contour().
fill.col: Sent as col parameter to .filled.contour(). Computed from color.palette if not specified.

Value

TernaryDensityContour() invisibly returns a list containing:

x,y: the Cartesian coordinates of each grid coordinate;
z: The density at each grid coordinate.

Details

This function is modelled on MASS::kde2d(), which uses "an axis-aligned bivariate normal kernel, evaluated on a square grid".

This is to say, values are calculated on a square grid, and contours fitted between these points. This produces a couple of artefacts. Firstly, contours may not extend beyond the outermost point within the diagram, which may fall some distance from the margin of the plot if a low resolution is used. Setting a negative tolerance parameter allows these contours to extend closer to (or beyond) the margin of the plot.

Individual points cannot fall outside the margins of the ternary diagram, but their associated kernels can. In order to sample regions of the kernels that have "bled" outside the ternary diagram, each point's value is calculated by summing the point density at that point and at equivalent points outside the ternary diagram, "reflected" across the margin of the plot (see function ReflectedEquivalents). This correction can be disabled by setting the edgeCorrection parameter to FALSE.

A model based on a triangular grid may be more appropriate in certain situations, but is non-trivial to implement; if this distinction is important to you, please let the maintainers known by opening a Github issue.

Author

Adapted from MASS::kde2d() by Martin R. Smith

Examples

# Generate some example data
nPoints <- 400L
coordinates <- cbind(abs(rnorm(nPoints, 2, 3)),
                     abs(rnorm(nPoints, 1, 1.5)),
                     abs(rnorm(nPoints, 1, 0.5)))
# Set up plot
oPar <- par(mar = rep(0, 4))
TernaryPlot(axis.labels = seq(0, 10, by = 1))

# Colour background by density
ColourTernary(TernaryDensity(coordinates, resolution = 10L),
              legend = TRUE, bty = "n", title = "Density")

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

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


# The following demonstrates the behaviour of the density estimates when 
# points fall on boundaries of the triangular grid cells; text denotes the
# number of points within the cell, with cells straddling _n_ cells
# contributing 1/_n_ of a point to each cell straddled.

coordinates <- list(middle = c(1, 1, 1),
                    top = c(3, 0, 0),
                    belowTop = c(2, 1, 1),
                    leftSideSolid = c(9, 2, 9),
                    leftSideSolid2 = c(9.5, 2, 8.5),
                    right3way = c(1, 2, 0),
                    rightEdge = c(2.5, 0.5, 0),
                    leftBorder = c(1, 1, 4),
                    topBorder = c(2, 1, 3),
                    rightBorder = c(1, 2, 3)
)
par(mfrow = c(2, 2), mar = rep(0.2, 4))
TernaryPlot(grid.lines = 3, axis.labels = 1:3, point = "up")
values <- TernaryDensity(coordinates, resolution = 3L)
ColourTernary(values)
TernaryPoints(coordinates, col = "red")
text(values[1, ], values[2, ], paste(values[3, ], "/ 6"), cex = 0.8)

TernaryPlot(grid.lines = 3, axis.labels = 1:3, point = "right")
values <- TernaryDensity(coordinates, resolution = 3L)
ColourTernary(values)
TernaryPoints(coordinates, col = "red")
text(values[1, ], values[2, ], paste(values[3, ], "/ 6"), cex = 0.8)

TernaryPlot(grid.lines = 3, axis.labels = 1:3, point = "down")
values <- TernaryDensity(coordinates, resolution = 3L)
ColourTernary(values)
TernaryPoints(coordinates, col = "red")
text(values[1, ], values[2, ], paste(values[3, ], "/ 6"), cex = 0.8)

TernaryPlot(grid.lines = 3, axis.labels = 1:3, point = "left")
values <- TernaryDensity(coordinates, resolution = 3L)
ColourTernary(values)
TernaryPoints(coordinates, col = "red")
text(values[1, ], values[2, ], paste(values[3, ], "/ 6"), cex = 0.8)

TernaryDensityContour(t(vapply(coordinates, I, double(3L))),
                      resolution = 24L, tolerance = -0.02, col = "orange")



# Reset plotting parameters
par(oPar)