Previous Work

• EulerAPE (Micallef and Rodgers 2014)
  • 3 Area proportional Ellipses
  • 71 cites mostly bioinf.
• Wilkinson (Wilkinson 2012)
  • Statistical model to draw Euler diagrams with circles.
  • Defines a "stress" model and tries to minimise it.
  • 63 cites mostly bioinf.
• Example from yesterday's Wall Street Journal

Our Contribution

• "Standard" algorithms -- force directed graph layout (Eades 1984).
• Use a force model to attract/repel circle centres.
  • Hooke's law & Coulomb's law.
  • well understood optimisations, advantages and disadvantages.
• Usable & maintainable implementation.

Vennom

• Implements the force directed layout algorithm.
• Key-weakness #1 - calculates area by drawing a bitmap.
• Key-weakness #2 - calculates forces in a pairwise manner.

Bitmaps

Advantages

• Computationally fast \(O(n^2)\), if the bitmap is small.
• Straightforward to implement.

Disadvantages

• Not perfectly accurate.
• \(O(n^2)\) grows poorly.
• Optimisations cause some corner cases with "holes".

Pairwise

TODO

• We need to add good area reporting to Vennom.
• In about 5 slides time...
• Need to compute forces is a concurrent manner.

Prevalence

• Use in Bioinformatics (Croucher et al. 2014, A. J. Page et al. (2016)).
• Little Book of Bioinformatics
• Done well it will significantly improve impact.

Example t-test

Paired t-test:

before = c(12.9, 13.5, 12.8, 15.6, 17.2, 19.2, 12.6, 15.3, 14.4, 11.3)
after  = c(12.7, 13.6, 12.0, 15.2, 16.8, 20.0, 12.0, 15.9, 16.0, 11.1)

t.test(before, after, paired=TRUE)

Example histogram

before = c(12.9, 13.5, 12.8, 15.6, 17.2, 19.2, 12.6, 15.3, 14.4, 11.3)

pdf("myhistogram.pdf")
hist(before)
svg("myhistogram.svg")
hist(before)

More Examples

• See http://www.statmethods.net/ for some good examples.
• ggplot2 is an extremely powerful graphics library for R.
  • The ideas behind ggplot2 are similar to the motivation for the VMG; developing semantics for visualisations (or vice-versa).

Exensible

• There exists an "app-store" for R.
• CRAN: Comprehensive R Archive Network.
• Modelled on CPAN (from 1993!).
• ggplot2 and venneuler are distributed via CRAN.

Using VennEuler

library("venneuler")

vd <- venneuler(c(A=0.3, B=0.3, C=1.1, "A&B"=0.1, "A&C"=0.2, "B&C"=0.1 ,"A&B&C"=0.1))
plot(vd)

EuleR wish?

library("euleR")

ed <- euleR(c(A=0.3, B=0.3, C=1.1, "A&B"=0.1, "A&C"=0.2, "B&C"=0.1 ,"A&B&C"=0.1))
plot(ed)

Be source compatible!

1. Source compatibility with venneuler.
2. Distributable via CRAN.
3. Calculate area more accurately than vennom.
4. Be maintainable.

Monolith

• Use RJava -- vennom is written in Java.
• Bundle vennom, area calculation and R-bridge as CRAN package.
• Manually manage transitive dependencies

Monolith

Web Service

• Require Internet connection.
• Move R-bridge, vennom, area calculation an dependencies to cloud.
• Allows tracking or user requests.

Web Service

Problem

• As discussed, the bitmap approach is inaccurate and doesn't scale (\(O(n^2)\)).
• How to practically calculate the area of a concrete zone.

Inkscape inspired

• Represent all primitives as paths.
• A path is a "sequence of symmetric power basis polynomials".
• Calculating the intersection of two paths is straightforward.
  • Paths can be arbitrarily shaped -- fun for the future.
• Somewhat inaccurate when representing circles (I'd like to quantify this).
• Inkscape's area calculation is broken for some complex paths.

s-basis area

JavaGeom

• A geometry package for Java
• Provides a CircleArc2D
  • we added getChordArea() and a few other things.
• Implemented an area calculation for BoundaryPolyCurve2D<CircleArc2D>.

Our Solution

• Take an input concrete diagram.
• Calculate the concrete Euler graph.
• Split each circle into 'arcs' at the intersection points indicated by the Euler graph.
• Represent each concrete zone as a BoundaryPolyCurve2D<CircleArc2D>.
• Calculate the concrete inclusion hierarchy for concrete zones.

Examples

But we're significantly faster.

Development

• The supposed hard bits were easy.
• The easy bit -- area calculation -- is surprisingly involved.
• The core vennom algorithm needs improvement.
• Development -- i.e. impact -- is a full-time commitment.