The constraint on proportions means that the mixture data can be described in one dimension lower than the total number of components. For example when there are three mixture components a two dimension plot can be used to represent the mixture within an equilateral triangle.

To create a surface within the mixture triangle we can create a grid of points and then convert these pairs of points into mixture triples.

mygrid = rbind(
	expand.grid(
		x = seq(0, 1.0, length.out = 500),
		y = seq(0, sqrt(3)/2, length.out = 500)
	)
)

The conversion formulae are shown below:

mygrid$a = (sqrt(3) * (mygrid$x - 0.5) + (mygrid$y - 0.5 * sqrt(3))) /
  (- sqrt(3) - 0.5 * sqrt(3))
mygrid$b = (- sqrt(3) * (mygrid$x - 0.5) + (mygrid$y - 0.5 * sqrt(3))) /
  (- sqrt(3) - 0.5 * sqrt(3))
mygrid$c = 1 - mygrid$a - mygrid$b

The next step is to calculate our surface values, a trivial example of which is:

mygrid$z = 10 + 4 * mygrid$a + 3 * mygrid$b

We then need to trick the plotting function by setting all invalid mixture combinations to be missing values.

mygrid$z[mygrid$a < 0 | mygrid$b < 0 | mygrid$c < 0] = NA
mygrid$z[mygrid$a > 1 | mygrid$b > 1 | mygrid$c > 1] = NA

Lastly we use the levelplot function in the lattice package.

trellis.par.set("axis.line",list(col=NA,lty=1,lwd=1))
levelplot(z ~ x*y, data = mygrid,
	col.regions = gray(101:0/101), scales = list(draw=FALSE),
	xlab = "", ylab = "",
	panel = function(x, y, z, ...)
	{
		panel.levelplot(x, y, z, ...)
		panel.lines(c(0,1), c(0,0), col = "black")
		panel.lines(c(0,0.5), c(0,sqrt(3)/2), col = "black")
		panel.lines(c(0.5,1), c(sqrt(3)/2,0), col = "black")
		panel.text(0.5, sqrt(3)/2, "C", pos=3)
		panel.text(0, 0, "A", pos=2)
		panel.text(1, 0, "B", pos=4)
	},
	xlim = c(-0.2,1.2),
	ylim = c(-0.2, 0.2+sqrt(3)/2)
)

This forms the basis of a ternary surface plot and various adjustments can be easily made to customise the plot.

Example of a surface plot in a ternary diagram

Other useful resources are provided on the Supplementary Material page.

To change the paper to A3 in our document and in landscape orientation we would use the following:

\documentclass[12pt,landscape]{article}
\usepackage[a3paper]{geometry}
\begin{document}
...
\end{document}

The use of nodes and the current.page label in conjunction with some other parameters attached to the tikz drawing will allow us to achieve the absolute positioning on the page.

As an example consider a one page drawing where we want to put a text box in the centre of the page.

\begin{tikzpicture}[remember picture,overlay]
\draw (current page.center) node {Add Text};
\end{tikzpicture}

If we wanted to add elements to the edge of a page we could use the current page.north west anchor to locate in the top left of the page.

Other useful resources are provided on the Supplementary Material page.

Fast Tube by Casper

When creating a tikz picture the origin is assumed to be at (0,0) and objects are placed with positioning relative to the origin on the picture. If we wanted to add a grid with lines from -3 to +3 in both the horizontal and vertical axes then we would use the \draw command combined with grid.

\draw (-3,-3) grid (3,3);

We can use the draw options to change how the grid is displayed. To make the grid lines thin we could add very thin and change the colour to a light gray (black!20):

\draw[very thin,black!20] (-3,-3) grid (3,3);

To add a node with text we use a combination of \draw and node, For example to put the node with a single letter A at (1,1):

\draw (1,1) node {A};

We can put an outline around the text in a node by specifying a shape and the draw option (which refers to the colour of the outline of the shape).

\node[shape=rectangle,draw=black] at (0,2) {B};

The fill option is for the inside of the shape. A circle with outline and filled background could be drawn with the following code:

\node[shape=circle,draw=blue,fill=blue!50] at (2,2) {D};

Other useful resources are provided on the Supplementary Material page.

Fast Tube by Casper

As with all LaTeX documents we need to select a document class and include some preamble material prior to the body of our document. A blank template for a document with a single tikz picture is shown here:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}
...
\end{tikzpicture}
\end{document}

The tikz picture has a coordinate system similar to that which you would expect where moving from left to right on the page corresponds to increasing the x value and bottom to top increases the y value. A line can be drawn between two points wit the \draw command:

\draw (0,0) -- (1,0);

To draw a line between multiple points these can be chained together in a single draw command:

\draw (0,0) -- (1,0) -- (1, 4);

The line style can be altered by adding various options in square brackets directly after the draw command. So to change to a dashed red line we would write the following code:

\draw[red,dashed] (0,0) -- (2,0);

A circle of a given radius can be draw using the \draw command and we specify the radius of the circle in round brackets:

\draw (0,0) circle (2.5cm);

This will draw a circle with radius of 2.5 cm. The circle could be changed into an ellipse and we would then need to specify the radius in two directions, an example of this:

\draw (0,0) ellipse (2cm and 3.5cm);

Other useful resources are provided on the Supplementary Material page.

It is difficult to specify a set of criteria to determine whether a player can be described as an all-rounder. To compare the performances of various all-rounders we can look at the subset of crickters who have scored at least 1,000 runs and taken at least 100 wickets at Test Match level. This is not a perfect criteria as there will be players who have taken part in sufficient test matches that they will be included even though they are clearly much stronger in one of the two disciplines but very handy in the other.

A total of 54 test match cricketers were identified based on this criteria (up to and including test match 2004) and a scatter plot of the performances can be seen here. The graph shows that the majority of players in the bottom left region of the graph with a handful of batsmen and bowlers at the extremes in terms of runs or wickets.

To get a better idea of the balance between wickets and runs we can zoom in on the bottom left hand region of the graph to get this display. This new graph suggests that although there have been a number of English cricketers that has scored 1,000 runs and taken 100 wickets they do not have the longevity of players from other countries.

There are naturally other measures of performance that could be used to compare this set of allround cricketers which might provided a more illuminating insight into all round performances.

One idea for enhancing scatter plots covered in Tufte’s book Beautiful Evidence is the use of images in place of traditional symbols to provide additional information about that point. To illustrate this idea I have taken the batting data from the recent test series between England and India played in England 2011. The graph is a display of the number of runs scored and number of balls faced with an English or Indian flag indicating the team of the player involved. The graph can be seen here and this has an advantage over the usual scatter plot as there is no need for a legend to accompany the graph.

Other useful resources are provided on the Supplementary Material page.

Fast Tube by Casper

Other useful resources are provided on the Supplementary Material page.

The stringr package has a handy function str_trim (edited) that comes to the rescue and is straightforward to use. First up make sure that the package is available in the R session:

require(stringr)

Here is a basic example with a simple string:

> "  This is an example of whitespace.  "
[1] "  This is an example of whitespace.  "
> str_trim("  This is an example of whitespace.  ")
[1] "This is an example of whitespace."

As we can see this is very simple and is set up to work on a vector of character strings as well.

Other useful resources are provided on the Supplementary Material page. Visit here for more examples of string manipulation.