Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Text
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Ignore
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Enumeration
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Caption
Figure B.3: ROC curves for the DT+CRF on the paper collection. The color of the ROC curves show the cut-off value for classification. À
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Headline 1
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Footer
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Author
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Math. Comp.
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.390.590.790.99
Headline 2
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Header
Figure B.3: ROC curves for the DT+CRF on the paper collection. The color of the ROC curves show the cut-off value of the classifier. (cont.)
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Page Number
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Footnote
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Title
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.80.99
Headline 3
Figure B.3: ROC curves for the DT+CRF on the paper collection. The color of the ROC curves show the cut-off value for classification. (cont.)
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Text
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Ignore
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Enumeration
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.390.580.780.97
Caption
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Headline 1
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.150.30.450.60.74
Footer
Figure B.4: ROC curves for the DT+CRF trained on the paper collection but ap-plied to the product manuals. The color of the ROC curves show the cut-off value for classification.
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.380.570.770.96
Headline 2
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.180.370.550.740.92
Header
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.590.790.99
Page Number
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Footnote
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.150.310.460.610.76
Title
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.390.580.780.97
Headline 3
Figure B.4: ROC curves for the DT+CRF trained on the paper collection but ap-plied to the product manuals. The color of the ROC curves show the cut-off value for classification. (cont.)
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Text
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Ignore
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Enumeration
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.040.080.110.150.19
Caption
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.380.580.770.96
Headline 1
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Footer
Figure B.5: ROC curves for the DT+CRF for the product manuals. The color of the ROC curves show the cut-off value for classification.
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.390.590.780.98
Headline 2
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Header
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.80.99
Page Number
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.040.080.130.170.21
Footnote
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.390.580.770.96
Title
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Headline 3
Figure B.5: ROC curves for the DT+CRF for the product manuals. The color of the ROC curves show the cut-off value for classification. (cont.)
Functional Structure Analysis
C.1 Results of Classifier Selection
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
Methodology
SVM ANN k−NN
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
Introduction
SVM ANN k−NN
Figure C.1: ROC curves for the three best classifiers on the different functional structures at a text length of 300 words.À
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
Evaluation
SVM ANN k−NN
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
References
SVM ANN k−NN
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
Related Work
SVM ANN k−NN
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
Conclusion
SVM ANN k−NN
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
Use Case
SVM ANN k−NN
Specificity Sensitivity 0.00.20.40.60.81.0
1.0 0.8 0.6 0.4 0.2 0.0
Abstract
SVM ANN k−NN
Figure C.1: ROC curves for the three best classifiers on the different functional structures at a text length of 300 words. (cont.)
C.2 Evaluation Results
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Methodology
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.390.580.780.97
Introduction
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Evaluation
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Reference
Figure C.2: ROC curves of the SVM classifier and the POS tagged features on the computer science data set. The color is mapped to the cut-off values.À
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.380.570.760.95
Related Work
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.180.370.550.730.91
Conclusion
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.390.590.780.98
Use Case
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.590.790.99
Abstract
Figure C.2: ROC curves of the SVM classifier and the POS tagged features on the computer science data set. The color is mapped to the cut-off values. (cont.)
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.390.590.790.98
Evaluation
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Methodology
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.390.590.780.98
Introduction
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.10.20.30.40.5
Abstract
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.020.040.060.070.09
Conclusion
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.010.010.020.020.03
Acknowledgment
Figure C.3: ROC curves of the SVM classifier and the POS tagged features on the PubMed data set. The color is mapped to the cut-off values.
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.390.590.790.98
Evaluation
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.20.40.60.81
Methodology
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.190.380.560.750.94
Introduction
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.110.220.320.430.54
Abstract
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.020.040.060.080.1
Conclusion
Specificity
Sensitivity
1.0 0.8 0.6 0.4 0.2 0.0
0.00.20.40.60.81.0 00.010.020.030.040.05
Acknowledgment
Figure C.4: ROC curves of the SVM classifier and the Abner tagged features on the PubMed data set. The color is mapped to the cut-off values.
Applications
D.1 Document Overview
Eurographics / IEEE Symposium on Visualization2011 (EuroVis 2011) H. Hauser, H. Pfister, andJ. J. van Wijk (Guest Editors)
Volume 30(2011),Number 3
Illustrative MolecularVisualization withContinuous Abstraction
Matthewvan derZwan,1 Wouter Lueks,1 Henk Bekker,1 and Tobias Isenberg1,2 1Johann Bernoulli Institute of Mathematics andComputer Science, University of Groningen, The Netherlands
2DIGITEO in collaboration with VENISE–LIMSI–CNRS and AVIZ–INRIA, Saclay, France
Abstract
Molecular systems may bevisualizedwithvarious degrees of structural abstraction,support of spatialperception, and‘illustrativeness.’Inthisworkwe propose andrealizemethods to create seamless transformations thatallow us to affectand change each of these three parameters individually.The resultingtransitions giveviewers a dedicated control ofabstractionin illustrative molecularvisualizationand,consequently,allow them to seamlessly explore the resulting abstraction space for obtaininga fundamental understanding of molecular systems.We show example visualizationscreatedwith our approach and report informal feedback on our technique from domain experts. Categories and SubjectDescriptors (according to ACM CCS): I.3.m [Computer Graphics]: Miscellaneous— Scientificvisualization; molecular visualization; illustrative visualization; dedicated seamless abstraction.
1.Introduction
Molecularvisualization is of tremendousimportance for un-derstandingprocesses that are relevant in fields such as mate-rial sciences,genetics, pharmacy, immunology, and biology andchemistry in general. Researchers in these domains are trying tocope with an ever increasing complexity of molec-ular datawhiletrying to gain insight in the structure and function oflarge molecules such asproteins. In our work we exlore theapplication of illustrative visualization techniques tothis field of molecularvisualization which isparticularly suitable forillustrative visualizationapproaches because no
‘photorealism’ exists at the sizes of atoms [Goo03].
Research into the structuralproperties of small and large molecules isincreasingly gainingimportance. The function and interaction of molecules is oftenprimarily analyzed basedonan understanding of this structural information. Re-searchershavea number of tools at their disposal to visualize the collected molecular data [OGF 10], for example PyMol, VMD and Chimera. Visualizations are created by blending (parts of) the molecule shown in different structuralrepre-sentations. However, the connection between these represen-tations is often difficult toexplore by switching/blending alone. It is this problem that we address with our work.
Basedon the structural data that is available in large molecular databases [BWF00, BBB 02] and by taking inspiration from traditional hand-made illustration styles
Figure1:Proteinwith selective structural abstraction, medium‘illustrativeness,’and support of spatial perception. [Hod03],we describe how tovisualizecontinuous transi-tionsbetween different stages of structural abstraction as well as aspects ofspatial perception and ‘illustrativeness’
(e.g., Fig. 1). All of these parameters can be controlled in-dependently and continuously in real-time to enable users to interactivelyexplore the structure of complex molecules.
©2011 The Author(s)
Journalcompilation ©2011 The Eurographics Association and Blackwell Publishing Ltd.
Publishedby Blackwell Publishing,9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.
DOI: 10.1111/j.1467-8659.2011.01917.x
M.v. d. Zwan, W. Lueks, H. Bekker, T. Isenberg / Illustrative Molecular Visualization with Continuous Abstraction In particular, we extend a previous GPU-based approach
for molecularvisualization [TCM06] such that we can transi-tion from solid geometry to aplanar one and provide means tomove toa smooth, spline-based representation. In addi-tion,we support a seamless interpolation between ‘photore-alistic,’ celshading, and stylized black-and-whitedepiction.
Finally, we integratetechniques such as object attenuation and halos forall these abstraction stages.
Insummary, our main contribution is thecontinuous ab-straction space for illustrative molecularvisualization. This abstractionspace facilitates aninteractive and seamless ex-plorationof structural informationas well as depiction styles for molecular datain which each of the aspects can be con-trolledindividually. We discuss the realization of the transi-tions and theirimplementation using GPU techniques and report on informal feedback from domain experts.
In the remainder of thispaper we first review work related toourown in Section2. Next, we discuss abstraction tech-niques for molecular visualization and identify aspects that we combine to forma continuous abstractionspace in Sec-tion3. In Section 4 we then describe how we realize our molecularvisualizationusing this abstractionspace. After-ward,we present results of our technique and report informal feedbackon our technique in Section5. Finally, Section 6 concludes thepaper and discusses aspects of future work.
2.Related Work O’Donoghue et al. [OGF10] give a quite comprehensive overview of the differenttechniques that are being practi-callyapplied to the domain of molecular visualization (for an overview of visualizationtechniques also see [LLC 11, Sec-tion4.3]), as well as of the visualization tools available for re-searchers. They highlight non-photorealistic (or illustrative) visualizationtechniques as very effective methods to depict theoverallshape and form of molecules, in particular forpre-sentation to others and forpublication. While O’Donoghue etal. mention andshowan image of using “flat colors and outlines” as an example for such non-photorealistic depic-tion, othershave introduced more advanced methods of il-lustrative visualizationin this field whichwe describe next.
In an early example, Goodsell and Olson [GO92] describe a number of simple techniques to visualize the molecular sur-faceusing theparallel hatching and silhouettes techniques thatwere the state of the art in the early1990s and also discuss firstapproaches to some structural abstraction us-ing cylinders and cut-aways. A similar tool for grayscale shaded illustrations of detailed and abstractedproteins was describedby Kraulis [Kra91]. In more recent approaches, Lampe et al. [LVRH07] use a two-level approach on the GPU to illustrate slow dynamics of molecules, while We-ber [Web09] explores the use of texture-based approaches using shader programming to generatepen-and-ink render-ings of molecules in real-time. Weber focuses, in particular,
on producing cartoon-style illustrations for publication and on permitting users to apply different types of abstraction to different parts of the molecule. While we also rely on shader programming for fast rendering, we concentrate, inpartic-ular,on enabling the seamless transition between different rendering and abstraction styles, in addition to being able to apply different styles to different parts of the model.
One particularly relevant illustrative visualization of large moleculeswas presented by Tarini et al. [TCM06]. They use ambient occlusionasan approximation of global illumina-tionas well as additional techniques such as halos to im-prove the perception of the spatial structure of large balls-and-sticks andspace-fill models. We also employ Tarini et al.’s imposter-based rendering with ambient occlusion and halos but focuson how to transition along the axes of struc-tural abstraction andvisualstyles in an integrated fashion.
An approach that is different from using space-fill, balls-and-sticks, and relatedtechniques that show theinner struc-tureofa molecule is to visualize itsouter surface[CG07, CPG09,KBE09,CWG 10] which is important to understand the interactionsbetween different molecules. For example, Cipriano et al. [CG07] not only examine the illustrative de-piction of the molecular surface but also explore abstraction as well as the placement of decals to represent features that have been removedthrough thesimplification. While we do notemploy surface-based visualizationtechniques it would bepossible and interesting to combine them with the visual-izations of internal structurethatwe explore.
Inspiration for our illustrative visualizations also comes from traditional illustrationtechniques [Hod03]. For exam-ple, Goodsell [Goo03] summarizes the state of the art of molecular illustration. He emphasizes the existence of tra-ditional schemesincluding the space-filling diagram and the balls-and-sticks modelas well as of structural abstractions suchas the ribbon diagram [Ric85], all of which we also support with ourtechnique. Interesting for our work are, inparticular, Goodsell’s black-and-white examples. Here he uses traditional black-and-white shading techniques such as hatching and stippling to portray the atom types forprint re-production which are otherwise often rendered in specific color schemes. We use a similar approach but show how to seamlessly transition between the two extremes.
3.A Continuous Abstraction Space In theirsurvey of molecular visualization [OGF 10], O’Do-noghue et al. note theimportance of being able to get an overview of a molecule’s structure and point out that bothnon-photorealistic/illustrative visualization techniques as well as structural abstraction such as the ribbon diagram very well support this goal. They also remark, however, that being able to “see wheresequence features are located in the three-dimensional structurecan be of substantial practi-calvalue.” This means that being able to mentally integrate
©2011 The Author(s) Journalcompilation ©2011 The Eurographics Association and Blackwell Publishing Ltd.
684 M.v. d. Zwan, W. Lueks, H. Bekker, T. Isenberg / Illustrative Molecular Visualization with Continuous Abstraction
(a) (b) ( (c) d) (e)
Figure2:Structural abstraction stages: (a) space fill,(b)balls-and-sticks,(c) licorice,(d) backbone,and (e) ribbon. both detailedviews with abstracted andpotentially stylistic
depictions is essential, which to date is usually only possible by switching or -blending between different visualizations.
Abstractionin the context of molecular visualization typ-ically refers tostructural abstraction. Here, various forms ofdepicting the structure of a molecule are commonly used (e.g., see [Goo05]): the space fill diagram (Fig. 2(a)) which depicts each atom using its van der Waals radius, the balls-and-sticks model (Fig. 2(b)) which uses smaller radii and adds bondsas cylinders, and the ribbons model [Ric85]
(Fig. 2(e)) which further abstracts parts of the molecule to ribbon helices and sheetsso that secondary, tertiary, and quaternary structures becomeapparent. A stage between the balls-and-sticks and ribbon models is the licoricevisualiza-tion (Fig. 2(c)) that only shows the bonds, colored accord-ing to the typical colors associated to atom types. The re-moval of lessimportant parts of this structure leads to ab-stractionsthatemphasize the molecule’s backbone [NCS88]
(Fig. 2(d)). These structural abstraction stages form a natu-ralprogression (as in Fig. 2) which we can place along an axis of structural abstraction,and forwhichwe later define transitionsin order to support the mental integration.
Besides the mentioned stages there exists avariety of ad-ditional structural abstractions. In addition to the previously mentioned surfacevisualizations [CG07,CPG09,KBE09], the inner structure of moleculescan be abstracted with car-toonviews where -sheets aredepicted as arrows [DB04] or simplified 2D schematics (see, e. g., [OGF10, Fig. 4(g, h)]).
Other abstraction types arecoarse-grained abstractions (e.g., [MRY07]) that combine several atoms into larger pseudo-atoms tofacilitate the simulation ofvery large systems. We currently do not support these abstractions because mostrep-resenta fundamental paradigm shift, while our work focuses on the aspect of dedicated control of abstraction. However, one can envision potential extensions such as transitions from thespace fill diagram to the surface visualization or from the ribbonvisualization tocoarse-grained models,po-tentially leading to more than onepossible abstraction path.
Aside from structural abstraction,stylistic rendering is alsofrequentlyapplied in molecular illustration and visual-ization (e.g., [Ric85,Goo03,Goo05,Web09,OGF 10]). This type ofdepiction can also be considered to be a type of ab-straction. By reducing the detailed shading, for example,
il-lustrativedepictions of molecules can abstract from other-wiseoverwhelming detail and instead highlight the overall shape [Goo05, OGF 10]. Illustrative depiction can also sup-port the use of structural abstraction by emphasizing through stylization the fact that abstraction has beenapplied [CG07].
Finally, we consider the use of visualizationtechniques that more or less support the perception of the spatial shape (am-bient occlusion and halos [TCM06] or halos and line attenu-ation [EBRI09]) to be a third axis of abstraction that can be applied in molecular visualization. These techniques selec-tively reduce detail andemphasis in certain places such as the inside ofa molecule or visually distant parts and, there-fore, introduce localized abstraction [LKZD08].
Researcherswork with visualizationsin diverse combina-tion of the mencombina-tioned abstraccombina-tions, bothstructurally and vi-sually [OGF10]. Higher levels of abstraction, e. g., are well suited toprovide an overview, but at the same time these lack detail [CG07] whichmay be required for other tasks. More-over, it is not only desirable to be able to combine views of differentlevels of scale or abstraction [Goo05], but in fact tobe able toseamlesslytransition between abstraction lev-els. This seamless transition is what we are addressing in thiswork. For this purpose we define anabstraction space whose main axis is that ofstructural abstraction;this axis is augmented by changes to the visual style of the visualization:
‘illustrativeness’andsupport ofperception of spatiality. We need each of theseindependent axes to be continuous (i. e., not tocontainvisible ‘jumps’) to support the desired seam-lessnavigation andexploration. This continuity implies that we need to definean order between the previously discrete stages within each axis andmeaningful transitions between adjacent ones. This order isgiven for structural abstraction as depicted in Fig. 2, and understandable stages in-between these discrete stages caneasily be envisioned.
More formally, the abstractionspace is a spaceFof func-tions. Every functionf(ts,tp,ti)Fwithts,tp,ti[0,1] consists ofa function triple(fs(ts),f p(tp),fi(ti)),wherefs determines thedegree of structural abstraction,f pthesup-port ofspatial perception, andfithe ‘illustrativeness.’ Each of these functionsfkhasseveral discrete levelstk,n,evenly spaced in[0,1],associated toit that mark knownstyles. Each fkneeds tospecify how to seamlessly transition between fk(tk,n)andfk(tk,n+1). A mappingAassigns to each
amino-©2011 The Author(s)
Journalcompilation ©2011 The Eurographics Association and Blackwell Publishing Ltd.
685
M.v. d. Zwan, W. Lueks, H. Bekker, T. Isenberg / Illustrative Molecular Visualization with Continuous Abstraction acidain theprotein a tuple(ts(a),ti(a)),thusdetermining
itsstyle. The parametertpcan only be controlled globally.
4.InteractiveVisualization withSeamless Abstraction To achieve our goal of seamless structural and visual abstrac-tionwe first describe how to achieve the continuous transi-tion offsbetween the structural abstractransi-tion stagests,nbefore outlining the realization of the visual abstractionsf pandfi.
4.1.From Space FillingtoRibbonVisualization The seamless structural transition fromspace-fill (ts,0) to-wards balls-and-sticks (ts,1) is straightforward, both concep-tually and in itsimplementation. Spheres represent atoms with theirvan der Waals radii in thespace fill model, while smallerspheres (whose sizes do not have a physical mean-ing) with additional cylinders to represent the bonds are used for balls-and-sticks. Thus, we can gradually abstract from thespace fill to the balls-and-sticks representation by reduc-ing thespheres’ sizes, hence revealreduc-ing the bond-representreduc-ing cylinders that were previously hidden by the largerspheres.
A further shrinking of the spheres until they vanish results in the licoricerepresentation (ts,2). We confirmed for the re-sulting animation with our collaborating domain experts that they create nothing but theexpected visualizations.
The next discrete stage in the common structural abstrac-tionsequence shows only the protein skeleton (ts,3). The core ofan amino acid consists of asequence of a nitrogen atom followedby two carbon atoms. Theprotein skeleton is the sequence of these core atoms. Therefore, to transition from the licoricerepresentation to the protein skeleton we need toremove those bonds that are not part of the core atoms ina structured and continuous fashion. For this purpose we define therankofan atom as the minimum distance to the protein skeleton along the bonds. All atoms in the protein’s skeletonare assigned rank0, those immediately adjacent rank1, etc.,up to a maximum rank for the molecule. Since a bond connects two atoms, each endpoint has a naturally definedrank as well. Hence, we can also compute a rank for every point on the cylinder by linear interpolation. This rank allows us tospecify the continuous transition from the entire molecule toonly the backbone using a rank thresholdt: only the part of every cylinder withrank tisshown. Again, we sought feedback from our collaborating chemists about this transitionthatcontinuously removes the bonds, with bonds distant from the skeletonbeing removed first. Also in this case the chemists confirmed that this animation does not in-troduceunwanted artifacts of structural or other nature.
Thefinal discrete structural abstraction levelsupported by our approach is the ribbon diagram (ts,4) in which helices represent abstractspiral structures ( -helices) in the protein backbone. Thus, in order to achieve a continuous abstraction from the backbonewe need to smoothly transition between a cylinder representation with sharp bends and smooth lines
and ribbons. This transition comprises two aspects: to shift from the solid geometry of thecylinders in the backbone to theplanar geometry of the lines and ribbons and to linearly interpolate between polylines along the cylinders in the back-bone and the smoothed ribbonrepresentation. An additional challenge that relates to both aspects is that theplanar
and ribbons. This transition comprises two aspects: to shift from the solid geometry of thecylinders in the backbone to theplanar geometry of the lines and ribbons and to linearly interpolate between polylines along the cylinders in the back-bone and the smoothed ribbonrepresentation. An additional challenge that relates to both aspects is that theplanar