Incorporating interactive 3-dimensional graphics in astronomy research papers
Most research data collections created or used by astronomers are intrinsically multi-dimensional. In contrast, all visual representations of data presented within research papers are exclusively 2-dimensional. We present a resolution of this dichotomy that uses a novel technique for embedding 3-dimensional (3-d) visualisations of astronomy data sets in electronic-format research papers. Our technique uses the latest Adobe Portable Document Format extensions together with a new version of the S2PLOT programming library. The 3-d models can be easily rotated and explored by the reader and, in some cases, modified. We demonstrate example applications of this technique including: 3-d figures exhibiting subtle structure in redshift catalogues, colour-magnitude diagrams and halo merger trees; 3-d isosurface and volume renderings of cosmological simulations; and 3-d models of instructional diagrams and instrument designs.
keywords:methods: data analysis, techniques: miscellaneous, surveys, cosmology: large-scale structure of universe, galaxies: general, stars: fundamental parameters
1.1 Visualisation in astronomy
Astrophysical data collections (datasets) are predominantly large and multi-dimensional. Accordingly, the principle approach to studying and comparing datasets is to calculate statistical measures such as the moments (mean, skewness, etc.) and correlation functions. Even substantial techniques such as Fourier analysis and principal components analysis rely heavily on basic statistical measures. These methods provide valuable information on the ensemble properties of the datasets. What they are less well-suited to is identifying anomalies or special cases within the data: are there features that we cannot understand or explain based on purely statistical approaches? Usually, there is a great deal of information that can be obtained simply by looking at the data. This is called scientific visualisation, hereafter simply “visualisation”.
Broadly speaking, visualisation methods can be classified as being qualitative (direct visual inspection), quantitative (including selection of regions of interest and computation of statistical properties), or comparative (including comparisons between objects with secondary observational catalogues, side-by-side comparisons between datasets, or overlays such as isodensity surfaces).
Visualisation in various forms has played a role in astronomy since
early times. The Ancient Egyptians mapped the locations of prominent
stars in their tomb decorations, Greek constellations are seen
inscribed on the Farnese globe (c. 2nd century CE) and Chinese star
maps have been found dating back to 940 CE. The 14th and 15th
centuries saw the development of star atlases of increasing accuracy
and beauty - truly works of “cognitive art” (Tufte, 1990) in their
own right. Beniger and Robyn (1978) and the extremely comprehensive web-site
of Friendly & Denis
The advent of computer graphics revolutionised visualisation in astronomy. It enabled dynamic presentation, and more importantly, real-time exploration of astrophysical datasets. In general, an interactive digital representation allows the user to actively rotate, zoom, and pan multi-dimensional datasets in order to find a viewpoint that provides more information and understanding. This is visualisation-led knowledge discovery and is now a standard and necessary tool in all of the physical sciences.
The first computerised astrophysical visualisation systems were expensive to operate and difficult to use. For example, the 3-dimensional representations of the Centre for Astrophysics (CfA) galaxy surveys, which helped reveal the “Great Wall” and other major filamentary features (e.g. Geller and Huchra, 1989), required custom processors. Image sequences were generated by outputting individual frames that were then printed to 16 mm film for viewing! Real-time interactive motion was merely “a fond hope” (Geller et al., 1992).
Today, an entry-level laptop or workstation provides an extraordinary level of graphics performance. In fact, in many modern desktop computers, the graphics processing unit is actually more powerful than the central processing unit. Consequently, there is now a wide selection of commercial and free software applications, programming libraries and data processing environments that provide varying levels of 3-dimensional graphics capabilities to scientists. It is fair to say that astronomers now can, and increasingly do, make use of advanced 3-dimensional visualisation in their quest for knowledge discovery.
1.2 Publishing in astronomy
The growth of the World Wide Web (Berners-Lee et al., 1994) as a global information repository and communication tool has profoundly affected the way science is performed and reported. In particular, there has been a dramatic change in how research articles are published, with a steady trend away from physical, paper-based journals to fully online digital publications. The way was paved in the early 1990s, as the Astrophysical Journal (ApJ) introduced video tapes for “illustrations that are not well suited to single frames or figures” (Abt, 1992) and CD-ROMS of datasets, both of which were distributed with the paper editions. The first online edition of ApJ appeared in September 1995 (Abt, 2002). During the same period, the ADS Abstract Service began its service, providing astronomers with new capabilities to search for and obtain abstracts (Murray et al., 1992; Kurtz et al., 2000), followed soon after with the provision of scanned articles (Eichhorn et al., 1994).
Today, the standard graphics cards that ship with new computers are
immensely powerful. They are perfectly suited to running the
advanced, 3-d visualisation programs that are becoming necessary for
the rapid comprehension of large and complex data collections. Yet
despite the nearly complete migration to an electronic workflow in
research publishing, published visualisations remain almost
1.3 This paper
The latest extensions to the Adobe Portable Document Format (PDF) create an exciting opportunity to bring together the interactivity of a real-time, 3-dimensional visualisation system with the requirements for standardised academic publication (within an electronic document context). In this paper, we describe a relatively straightforward technique for developing and embedding interactive, 3-dimensional science visualisations as figures in PDF files that can be viewed with the freely downloadable Adobe Reader application. We use the S2PLOT library (Barnes et al., 2006) and Adobe Acrobat 3D Version 8.1 software, although other approaches are possible (Goodman et al., priv. comm.).
2 3-dimensional PDF
2.1 Portable Document Format
Portable Document Format (PDF) is an open document standard developed
by Adobe Systems Incorporated.
Uptake of PDF by journal publishers is virtually complete in the sense that nearly all publishers have adopted PDF as a standard target file type, for both pre-press operations and electronic distribution. Astronomy has been no exception, with the major journals using PDF for most parts of the paper publication and distribution workflow since the late 1990s. The ability of LaTeX to produce PDF files, initially via conversion from PostScript and then directly, was pivotal in the embracing of PDF by the physical sciences research community.
2.2 Acrobat 3D and Adobe Reader
In May 2007, Adobe announced the availability of “Adobe Acrobat 3D
Version 8” software.
Acrobat 3D Version 8 (hereafter “Acrobat 3D”) is directed at Computer Aided Design (CAD) and Computer Aided Modelling (CAM) professionals. It can import 3-d models from more than 50 third-party file formats. Roughly two-thirds of the supported formats are polygonal meshes from CAD/CAM applications, while the remaining formats cover animation packages, game models, and more generic 3-d formats. In some circumstances, Acrobat 3D can also capture 3-d geometry from the hardware graphics pipeline as it is displayed.
Once a 3-d model has been imported to Acrobat 3D, the publisher can set the preferred lighting, shading and viewing for the model. A number of different configurations can be saved as views. The model tree can be exposed, and its various branches (corresponding to particular geometric elements of the scene) can be switched in or out of the visualisation. Options on import allow colouring of different parts of the model, and optimisation of properties such as surface smoothness and detail. It is evident from the example PDF files supplied with Acrobat 3D that Adobe’s focus is firmly on the ability to embed and share 3-d engineering models in PDF files.
2.3 3-dimensional PDF for astronomy
3-dimensional PDF holds great promise for improving science reporting, We propose the judicious use of 3-d PDF to add 3-dimensional, interactive figures to astronomy journal papers. We contend that there are many circumstances where the use of 3-d figures can be substantially more illustrative of concepts, relationships and properties, than can their 2-d counterparts. While 3-d figures (and more commonly, dynamic content such as movies) have been attached to astronomy papers (for some recent examples see Diemand et al., 2007; Okamota et al., 2007; Price and Bate, 2007) this has until now been achieved using ephemeral web addresses to direct readers to supplementary material. Directly embedding 3-d figures in a standard document format — for which viewers exist on all major desktop platforms — affords a major improvement for both present useability and future compatibility.
Despite Acrobat 3D being openly targeted at the CAD/CAM user community, we show in this paper that 3-d PDF is also suitable for scientific data. Together with software that produces 3-d models, Acrobat 3D can be used to produce publication-quality, scientifically instructive 3-dimensional figures. The basic geometric elements required to produce scientific plots — lines and points — are readily available, together with an extensive set of higher-level objects such as surfaces and textures.
3 S2PLOT and 3-d PDF
We now describe one approach to producing 3-d figures in PDF files,
using the S2PLOT programming library and Adobe Acrobat 3D Version 8.1.
S2PLOT (Barnes et al., 2006) is an advanced graphics library with a
programming interface familiar to users of PGPLOT.
S2PLOT is ideally-structured to produce 3-d model output that can be imported into Acrobat 3D. Internally, the S2PLOT library maintains a list of all geometry that is used to make up a scene. On each screen redraw, the active geometry is sent to the graphics pipeline with standard OpenGL calls. In S2PLOT version 2.0 the geometry list can be exported to a file in Virtual Reality Modeling Language (VRML) format. As well as being a supported input format for Acrobat 3D, this language has the distinct advantages that it is (i) text-based, enabling easy editing prior to Acrobat 3D import; and (ii) web-based, yielding further possibilities for model and figure sharing and publication. VRML has received occasional attention from the astronomy community (see e.g. Plante et al., 1999; Crutcher et al., 1998), and one of us (Barnes) has previously developed a VRML viewer for Virtual Observatory data (Beeson et al., 2004).
For basic 3-dimensional figures and diagrams, embedding an S2PLOT-based 3-d figure in a PDF paper is accomplished via a standard key press to export S2PLOT geometry into a VRML file, then importing the VRML file into Acrobat 3D. Within Acrobat 3D, the author can place the 3-d figure anywhere within the PDF file, add annotations, and set default rendering, lighting and viewing properties. Where necessary, special views that exhibit particular features of the figure discussed in the text of the paper can be saved and named for the reader to select.
We now give three examples of relatively simple, 3-dimensional figures that are illustrative of common plotting requirements in astronomy: a dark matter merger tree, a survey catalogue redshift distribution and a colour-magnitude diagram.
3.1 Example 1: Halo merger trees
Semi-analytic modelling has been developed as an efficient way to study the hierarchical formation of galaxies (see e.g. White and Frenk, 1991; Cole et al., 2000). The first stage in the process is to generate a merger tree of dark matter halos from direct -body simulations or Monte Carlo methods. Analytic solutions are applied on top of the dark matter framework to treat the baryonic component, and to model the physical processes required to build a galaxy (initial mass function, star formation history, feedback, etc.). While merger trees are predominantly studied statistically, individual trees feature intricate and exquisite structure that can only be fully appreciated via interactive 3-d visualisations. Conventional, static 2-d projections simply fail to represent this structure.
Figure 1 is a 3-d representation of a merger tree, using
data from the Virgo-Millennium
3.2 Example 2: Redshift catalogues
The redshift wedge or cone diagram is somewhat peculiar to astronomy. It is typically used to exhibit large-scale structure (LSS) as (right ascension, declination, redshift)-tuples, and can comprises several individual plots to show different slices from a larger volume of the Universe. This is a classic case of the traditional publishing medium (i.e. paper) limiting the communication of genuine 3-dimensional information, and the opportunity for advancement by provision of interactive 3-d figures is clear.
In Figure 2 we present an interactive, 3-dimensional plot of the redshift distribution of the combined HICAT (Meyer et al., 2004) and HICAT+N (Wong et al., 2006) galaxies. Meyer et al. (2004) presented two sky projections of HICAT in its entirety, coloured by redshift, as well as two full-page figures for a multi-layer wedge diagram. Here, for the first time we combine HICAT and HICAT+N into one figure, using the same colour coding as Meyer et al. (2004). The reader is invited to explore the plot by moving the camera around, into and out of the galaxy distribution. The filamentary LSS is much more obvious than in a static figure, and the local void is particularly noticeable from certain orientations. The coordinate grid and labels may be toggled (off) on by expanding the model tree and (de)selecting the GRID and LABELS nodes.
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3.3 Example 3: Colour-magnitude diagrams
Widely-used 2-dimensional plots such as colour-magnitude diagrams (CMDs) can benefit from a 3-dimensional treatment. CMDs are most frequently presented as scatter plots, where each measurement is added to the plot as a dot. The quantitative interpretation of these plots is becoming more difficult as star counts increase with instrument capability. One obvious improvement is to dispense with the scatter plot approach entirely.
In Figure 3 we demonstrate that a simple 2-d histogram is an effective replacement for a conventional CMD. The source data for the figure are 28 568 stellar photometry measurements for the Large Magellanic Cloud globular cluster NGC 1898 made with Hubble WFPC2 (Olsen, 1999). The figure shows the result of binning the pairs onto a grid, and plotting the result as a logarithmic 2-d histogram. In certain orientations, the surface colour alone aids the eye in interpreting relative star counts; viewed “side-on” the height of the surface above the base gives a direct and quantitative comparison between different parts of the colour-magnitude plane: something that colour alone cannot accomplish. Some choices of colour scales, such as the standard “rainbow” map, should be avoided for presenting relative data values - grey-scales offer a more intuitive choice (Tufte, 1990).
4.1 Example 4: Large scale structure isosurfaces
In this era of galaxy surveys (Adelman-McCarthy et al., 2007) and particle simulations (Springel etl al., 2005), scatter plot wedge diagrams quickly become overcrowded, and the large scale structures we aim to understand are lost in a sea of points. An alternative approach is to draw isodensity contours (usually calculated on a regular mesh) over the point distributions. These help to highlight connected structures, and isolate the regions of highest (or lowest) density.
Please obtain paper with figures from:
4.2 Example 5: Substructure in a dark matter halo
The Cold Dark Matter (CDM) model, and its variants, has been very successful at explaining a number of observational properties of galaxies and galaxy clustering, particularly on large scales. However, on small scales and/or in high density regions, contradictions between CDM model predictions and observations exist. One such example is the “missing satellite” problem (Bardeen et al., 1996; Kauffmann et al., 1993; Klypin et al., 1999; Moore et al., 1999; Kamionkowski and Liddle, 2000): high resolution CDM simulations of Milky Way-type dark matter haloes produce many more bound sub-structures than there are observed satellites. Visualisation techniques are extremely valuable for studying individual haloes, in order to better understand the role and spatial distribution of sub-structures.
5 Other approaches
While the preceding examples have highlighted the data visualisation advantages of 3-d PDF, there are other aspects of academic publication where the CAD/CAM functionality can be used. Two such cases are in instrument design and the presentation of instructional models (3-d cartoons), which we now demonstrate.
5.1 Example 6: Instrument design
Advances in astronomy are intimately linked to technological developments, particularly through new instrument designs which enhance the capability of existing facilities. CAD/CAM packages are a natural source of engineering models for astronomy instrumentation, but a range of polygon modelling packages exist, many developed and used within the computer animation industry.
As a means of promoting design concepts for the Square Kilometer Array
(SKA) and Australian SKA Pathfinder (ASKAP), one of us (Fluke) worked
with engineers from the CSIRO Australian National Telescope Facility
to create a series of 3-d radiotelescope models.
5.2 Example 7: Instructional diagrams
An important component of many research articles and textbooks is the instructional diagram, often presented in a simplified cartoon format. These diagrams usually show spatial and/or other relationships between the elements of a model. In many cases only a single orientation of a model is presented yet, as with astronomical datasets, these models are often inherently three-dimensional. 3-d PDF makes possible the inclusion of simple but interactive, 3-d diagrams in electronic articles, with applications in teaching, pedagogy and outreach.
One particular instructional diagram common in astronomy is the unified model for Active Galactic Nuclei (AGN) and quasars (e.g. Antonucci, 1993). Classification of an AGN as either Type 1, Type 2 or Blazar depends on the orientation of the dusty molecular torus to the observer’s line-of-sight. The viewing angle determines the presence or absence of broad and narrow line emission, and beamed radiation from jets. In Figure 7 we present an interactive 3-d AGN (components of the model are not to scale). By rotating the model, the reader is able to “observe” the AGN from arbitrary viewpoints, and see for example the obscuration of the broad line region and central engine by the torus.
6 Closing Remarks
We have demonstrated that the new 3-d extensions to the PDF standard
can be used to publish instructive and interactive 3-d figures in
astronomy research papers. Our approach uses the S2PLOT programming
library and VRML as an intermediary 3-d model description format. It
is sufficiently easy to create and embed 3-d figures in PDF articles
that we believe it can become a standard technique in the publication
of scientific research results, particularly in the fields of
astronomy and astrophysics. 3-d PDF files are portable, relatively
compact and viewable on many desktop platforms today.
There is one major caution to be made on the use of 3-d PDF in science. Scientists traditionally use large collections of points to representing instances in parameter spaces, while the CAD/CAM community works primarily with surfaces. Like their CAD/CAM and animation software counterparts, Acrobat 3D and Reader show a clear preference for mesh (surface) data over point data. We found that the 3-d PDF reader client (Acrobat Reader) — and to a lesser extent the content creation tool (Acrobat 3D) — did not perform well when more than –20 000 points were used in a single 3-d figure. Gridding point data and then rendering isosurfaces and/or volumes is one effective work-around. Some improvement in the underlying software is required before 3-d figures of eg. redshift catalogues containing to galaxies can be published, although doing so would have an obvious impact on the file size of the article.
Finally, the opportunity to improve the science community’s capacity to convey advances in our disciplines to the wider public should not be ignored. PDF is the most widely-used, self-contained electronic document format. Our funding agencies, governments and public can now easily interact with instructive, 3-dimensional graphical representations of our work — all we have to do is create and publish them.
We thank Alyssa Goodman and colleagues at the Initiative in Innovative Computing at Harvard for discussions on their approach to 3-d PDF. We are grateful to Chris Power for providing cosmological simulation data. The telescope model shown was originally developed with Peter Hall and colleagues at the CSIRO Australia Telescope National Facility. Barnes acknowledges the support of iVEC visitor fund which enabled parts of this work.
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