### Static and moving circles

After the previous post on the packcircles package for R someone suggested it would be useful to be able to fix the position of selected circles. As a first attempt, I've added an optional `weights` argument to the `circleLayout` function. Weights can be in the range 0-1 inclusive, where a weight of 0 prevents a circle from moving, while a weight of 1 allows full movement. The updated code is at GitHub.

Here's an example where the largest of a set of initially overlapping circles is fixed in place:

And here is the code for the example:
``````
library(packcircles)
library(ggplot2)
library(gridExtra)

# Generate some random overlapping circles
ncircles <- 200
limits <- c(-50, 50)
inset <- diff(limits) / 3
rmax <- 20

xyr <- data.frame(
x = runif(ncircles, min(limits) + inset, max(limits) - inset),
y = runif(ncircles, min(limits) + inset, max(limits) - inset),
r = rbeta(ncircles, 1, 10) * rmax)

# Index of the largest circle
largest.id <- which(xyr\$r == max(xyr\$r))

## Generate plot data for the `before` layout
dat.before <- circlePlotData(xyr)

# Add a column to the plot data for the 'before' circles
# to indicate whether a circle is static of free to move
dat.before\$state <- ifelse(dat.before\$id == largest.id, "static", "free")

# Run the layout algorithm with a weights vector to fix the position
# of the largest circle
wts <- rep(1.0, nrow(xyr))
wts[ largest.id ] <- 0.0

res <- circleLayout(xyr, limits, limits, maxiter = 1000, weights=wts)

# A plot function to colour circles based on the state column
doPlot <- function(dat, title)
ggplot(dat) +
geom_polygon(aes(x, y, group=id, fill=state), colour="brown1") +
scale_fill_manual(values=c("NA", "brown4")) +
coord_equal(xlim=limits, ylim=limits) +
theme_bw() +
theme(axis.text=element_blank(),
axis.ticks=element_blank(),
axis.title=element_blank(),
legend.position="none") +
labs(title=title)

g.before <- doPlot(dat.before, "before")

# Generate a plot for the 'after' circles
dat.after <- circlePlotData(res\$layout)
dat.after\$state <- ifelse(dat.after\$id == largest.id, "static", "free")

g.after <- doPlot(dat.after, "after")

grid.arrange(g.before, g.after, nrow=1)
``````

### Fitting an ellipse to point data

Some time ago I wrote an R function to fit an ellipse to point data, using an algorithm developed by Radim Halíř and Jan Flusser 1 in Matlab, and posted it to the r-help list . The implementation was a bit hacky, returning odd results for some data. A couple of days ago, an email arrived from John Minter asking for a pointer to the original code. I replied with a link and mentioned that I'd be interested to know if John made any improvements to the code. About ten minutes later, John emailed again with a much improved version ! Not only is it more reliable, but also more efficient. So with many thanks to John, here is the improved code: fit.ellipse <- function (x, y = NULL) { # from: # http://r.789695.n4.nabble.com/Fitting-a-half-ellipse-curve-tp2719037p2720560.html # # Least squares fitting of an ellipse to point data # using the algorithm described in: # Radim Halir & Jan Flusser. 1998. # Numerically stable direct least squares fitting of ellipses

### Graph-based circle packing

The previous two posts showed examples of a simple circle packing algorithm using the packcircles package (available from CRAN and GitHub ). The algorithm involved iterative pair-repulsion to jiggle the circles until (hopefully) a non-overlapping arrangement emerged. In this post we'll look an alternative approach. An algorithm to find an arrangement of circles satisfying a prior specification of circle sizes and tangencies was described by Collins and Stephenson in their 2003 paper in Computation Geometry Theory and Applications. A version of their algorithm was implemented in Python by David Eppstein as part of his PADS library (see CirclePack.py ). I've now ported David's version to R/Rcpp and included it in the packcircles package. In the figure below, the graph on the left represents the desired pattern of circle tangencies: e.g. circle 7 should touch all of, and only, circles 1, 2, 6 and 8. Circles 5, 7, 8 and 9 are internal , while the remaining circles are exter

### packcircles version 0.2.0 released

Version 0.2.0 of the packcircles package has just been published on CRAN. This package provides functions to find non-overlapping arrangements of circles in bounded and unbounded areas. The package how has a new circleProgressiveLayout function. It uses an efficient deterministic algorithm to arrange circles by consecutively placing each one externally tangent to two previously placed circles while avoiding overlaps. It was adapted from a version written in C by Peter Menzel who lent his support to creating this R/Rcpp version. The underlying algorithm is described in the paper: Visualization of large hierarchical data by circle packing by Weixin Wang, Hui Wang, Guozhong Dai, and Hongan Wang. Published in Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, 2006, pp. 517-520 (Available from ACM ). Here is a small example of the new function, taken from the package vignette: library(packcircles) library(ggplot2) t <- theme_bw() + theme(panel.grid =