book

Data Visualization, 2nd Edition

by Alexandru C. Telea

September 2014

Beginner to intermediate

617 pages

17h 56m

English

A K Peters/CRC Press

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1.1 How Visualization WorksVisualization and insightConcrete questionsQuantitative vs. qualitative questionsExact vs. fuzzy questionsDiscover the unknownExamples.Subfields of data visualizationScientific visualizationInformation visualizationVisual anayticsInteractive exploration1.2 Positioning in the FieldInteractive Data Visualization: Foundations, Techniques, and ApplicationsThe Visualization ToolkitThe Visualization HandbookInformation Visualization Literature1.3 Book StructureChapter 2.Chapter 3.Chapter 4.Chapter 5-7.Chapter 8.Chapter 9.Chapter 10.Chapter 11.Chapter 12.Appendix1.4 Notation1.5 Online MaterialAcknowledgmentsFigure 1.1Figure 1.2Figure 1.3
2.1 A Simple Example2.2 Graphics-Rendering BasicsRendering equation2.3 Rendering the Height PlotFlat shadingSmooth shadingComputing vertex normals2.4 Texture Mapping2.5 Transparency and Blending2.6 ViewingVirtual cameraProjectionViewport2.7 Putting It All TogetherInitializationViewingDrawingImprovements2.8 ConclusionFigure 2.1Figure 2.2Figure 2.3Figure 2.4Figure 2.5Figure 2.6Figure 2.7Figure 2.8Figure 2.9Figure 2.10Figure 2.11Figure 2.12Listings 2.1Listings 2.2Listings 2.3Listings 2.4Listings 2.5Listings 2.6Listings 2.7
3.1 Continuous Data3.1.1 What Is Continuous Data?3.1.2 Mathematical Continuity3.1.3 Dimensions: Geometry, Topology, and Attributes3.2 Sampled DataInterpolationGrids and cellsPutting it all together3.3 Discrete Datasets3.4 Cell Types3.4.1 Vertex3.4.2 Line3.4.3 Triangle3.4.4 Quad3.4.5 Tetrahedron3.4.6 Hexahedron3.4.7 Other Cell Types3.5 Grid Types3.5.1 Uniform Grids3.5.2 Rectilinear Grids3.5.3 Structured Grids3.5.4 Unstructured Grids3.6 Attributes3.6.1 Scalar Attributes3.6.2 Vector Attributes3.6.3 Color AttributesRGB spaceHSV spaceConverting between RGB and HSVColor perception3.6.4 Tensor AttributesCurvature as a tensorTensors, vectors, and scalars3.6.5 Non-Numerical Attributes3.6.6 Properties of Attribute DataCompletenessMultivariate dataNode vs. cell attributesHigh-variate interpolationNormalsVectorsColorsTensors3.7 Computing Derivatives of Sampled Data3.8 Implementation3.8.1 Grid ImplementationUniform gridsRectilinear gridsStructured gridsUnstructured grids3.8.2 Attribute Data ImplementationScalar attributesVector attributesStoring several attribute instances3.9 Advanced Data Representation3.9.1 Data ResamplingCell to vertex resamplingVertex to cell resamplingSubsampling and supersampling3.9.2 Scattered Point InterpolationConstructing a grid from scattered pointsGridless interpolationPerformance issuesShepard interpolation3.10 ConclusionFigure 3.1Figure 3.2Figure 3.3Figure 3.4Figure 3.5Figure 3.6Figure 3.7Figure 3.8Figure 3.9Figure 3.10Figure 3.11Figure 3.12Figure 3.13Figure 3.14Figure 3.15Figure 3.16Figure 3.17Figure 3.18Figure 3.19Table 3.1Table 3.2Listings 3.1Listings 3.2Listings 3.3Listings 3.4Listings 3.5Listings 3.6Listings 3.7Listings 3.8Listings 3.9Listings 3.10Listings 3.11Listings 3.12
4.1 Conceptual Perspective4.1.1 Importing Data4.1.2 Data Filtering and EnrichmentSee what is relevantHandle large dataEase of use4.1.3 Mapping DataMapping vs. renderingDesirable mapping propertiesInverting the mappingDistance preservationOrganization levelsFurther reading4.1.4 Rendering Data4.2 Implementation PerspectiveDataflow designDataflow implementationVisual dataflow programmingSimplified visual programming4.3 Algorithm Classification4.4 ConclusionFigure 4.1Figure 4.2Figure 4.3Figure 4.4Figure 4.5Figure 4.6Figure 4.7Figure 4.8Figure 4.9Table 4.1Listings 4.1
5.1 Color Mapping5.2 Designing Effective ColormapsColor legendsRainbow colormapOther colormap designsGrayscaleTwo-hueHeat mapDivergingZebra colormapInterpolation issuesColor bandingAdditional issues5.3 ContouringContour propertiesComputing contours5.3.1 Marching Squares5.3.2 Marching CubesMarching algorithm variationsDividing cubes algorithm5.4 Height Plots5.4.1 Enridged Plots5.5 ConclusionFigure 5.1Figure 5.2Figure 5.3Figure 5.4Figure 5.5Figure 5.6Figure 5.7Figure 5.8Figure 5.9Figure 5.10Figure 5.11Figure 5.12Figure 5.13Figure 5.14Figure 5.15Figure 5.16Figure 5.17Figure 5.18Figure 5.19Figure 5.20Figure 5.21Listings 5.1Listings 5.2
6.1 Divergence and VorticityDivergenceVorticityStreamwise vorticityHelicity6.2 Vector GlyphsLine glyphsCone and arrow glyphs6.2.1 Vector Glyph DiscussionVector glyphs in 2DVector glyphs in 3DVector glyphs on 3D surfaces6.3 Vector Color CodingColor coding on 2D surfacesColor coding on 3D surfaces6.4 Displacement PlotsParameter settings6.5 Stream Objects6.5.1 Streamlines and Their VariationsStreamlines.PathlinesStreaklinesComputing streamlinesParameter settingAccuracyStop criterionGeometryStreamline seeding6.5.2 Stream Tubes6.5.3 Streamlines and Tubes in 3D Datasets6.5.4 Stream Ribbons6.5.5 Stream Surfaces6.5.6 Streak Surfaces6.6 Texture-Based Vector VisualizationLine integral convolution6.6.1 IBFV Method6.6.2 IBFV ImplementationParametersPutting it all together6.6.3 IBFV ExamplesIBFV on curved surfacesIBFV on 3D volumes6.7 Simplified Representation of Vector Fields6.7.1 Vector Field TopologyTopology analysisInterpolation issuesExcluding critical pointsBoundaries6.7.2 Feature Detection Methods6.7.3 Field Decomposition MethodsTop-down decompositionBottom-up decompositionMultiscale decompositionMultiscale IBFV6.8 Illustrative Vector Field RenderingDepth-dependent halos6.9 ConclusionFigure 6.1Figure 6.2Figure 6.3Figure 6.4Figure 6.5Figure 6.6Figure 6.7Figure 6.8Figure 6.9Figure 6.10Figure 6.11Figure 6.12Figure 6.13Figure 6.14Figure 6.15Figure 6.16Figure 6.17Figure 6.18Figure 6.19Figure 6.20Figure 6.21Figure 6.22Figure 6.23Figure 6.24Figure 6.25Figure 6.26Figure 6.27Figure 6.28Figure 6.29Figure 6.30Figure 6.31Figure 6.32Figure 6.33Figure 6.34Figure 6.35Figure 6.36Figure 6.37Listings 6.1Listings 6.2Listings 6.3
7.1 Principal Component Analysis7.2 Visualizing Components7.3 Visualizing Scalar PCA InformationDiffusivityAnisotropy7.4 Visualizing Vector PCA Information7.5 Tensor Glyphs7.6 Fiber TrackingFocus and contextFiber clusteringTracking challenges7.7 Illustrative Fiber RenderingFiber generationAlpha blendingAnisotropy simplificationIllustrative renderingFiber bundlingFibers in context7.8 Hyperstreamlines7.9 ConclusionFigure 7.1Figure 7.2Figure 7.3Figure 7.4Figure 7.5Figure 7.6Figure 7.7Figure 7.8Figure 7.9Figure 7.10Figure 7.11Figure 7.12Figure 7.13Figure 7.14Figure 7.15Figure 7.16

8.1 Cutting8.1.1 Extracting a Brick8.1.2 Slicing in Structured Datasets8.1.3 Implicit Function Cutting8.1.4 Generalized Cutting8.2 SelectionSelecting cellsThresholding, segmentation, and contouring8.3 Grid Construction from Scattered Points8.3.1 Triangulation MethodsDelaunay triangulationsVoronoi diagramsVariation of the basic techniquesImplementation8.3.2 Surface Reconstruction and RenderingUsing radial basis functionsUsing signed distance functionsLocal triangulationsMultiple local triangulationsAlpha shapesBall pivotingPoisson reconstructionSurface splattingSphere splatting8.4 Grid-Processing Techniques8.4.1 Geometric Transformations8.4.2 Grid SimplificationTriangle mesh decimationVertex clusteringSimplification envelopesProgressive meshes8.4.3 Grid RefinementLoop subdivisionAdvanced subdivision tools8.4.4 Grid Smoothing8.5 ConclusionFigure 8.1Figure 8.2Figure 8.3Figure 8.4Figure 8.5Figure 8.6Figure 8.7Figure 8.8Figure 8.9Figure 8.10Figure 8.11Figure 8.12Figure 8.13Figure 8.14Figure 8.15Figure 8.16Figure 8.17Figure 8.18Figure 8.19Figure 8.20Figure 8.21
9.1 Image Data Representation2D ImagesHigher-dimension images9.2 Image Processing and Visualization9.3 Basic Imaging Algorithms9.3.1 Basic Image ProcessingTransfer functions9.3.2 Histogram Equalization9.3.3 Gaussian SmoothingFourier transformConvolution for filtering9.3.4 Edge DetectionGradient-based edge detectionRoberts operatorSobel operatorPrewitt operatorLaplacian-based edge detection9.4 Shape Representation and Analysis9.4.1 Basic Segmentation9.4.2 Advanced SegmentationSnakesNormalized cutsMean shiftImage foresting transformLevel setsThreshold sets9.4.3 Connected Components9.4.4 Morphological OperationsDilation and erosion9.4.5 Distance TransformsDistance transform properties.Brute-force implementation.Distance transforms using OpenGLFast Marching Method.Other distance transform algorithms9.4.6 SkeletonizationCenteredness.Structural and topological encoding.Geometrical encoding.Multiscale shape encoding.Applications.9.4.7 Skeleton Computation in 2DUsing distance field singularities.Using boundary collapse metric.Applications9.4.8 Skeleton Computation in 3DSurface skeletons.Curve skeletons.Thinning methods.Distance field methods.Geodesic methods.Mesh contraction methods.Curve skeleton comparison.9.5 ConclusionFigure 9.1Figure 9.2Figure 9.3Figure 9.4Figure 9.5Figure 9.6Figure 9.7Figure 9.8Figure 9.9Figure 9.10Figure 9.11Figure 9.12Figure 9.13Figure 9.14Figure 9.15Figure 9.16Figure 9.17Figure 9.18Figure 9.19Figure 9.20Figure 9.21Figure 9.22Figure 9.23Figure 9.24Figure 9.25Figure 9.26Figure 9.27Listings 9.1Listings 9.2Listings 9.3Listings 9.4Listings 9.5Listings 9.6
10.1 Motivation10.2 Volume Visualization Basics10.2.1 Classification10.2.2 Maximum Intensity Projection Function10.2.3 Average Intensity Function10.2.4 Distance to Value Function10.2.5 Isosurface Function10.2.6 Compositing FunctionTransfer functions.Integration issuesExamples10.2.7 Volumetric Shading10.3 Image Order Techniques10.3.1 Sampling and Interpolation Issues10.3.2 Classification and Interpolation Order10.4 Object Order Techniques2D texture methods.3D texture methods.10.5 Volume Rendering vs. Geometric RenderingAims.Complexity.Mixed methods.10.6 ConclusionFigure 10.1Figure 10.2Figure 10.3Figure 10.4Figure 10.5Figure 10.6Figure 10.7Figure 10.8Figure 10.9Figure 10.10Figure 10.11Figure 10.12Figure 10.13Figure 10.14Figure 10.15Figure 10.16
11.1 What Is Infovis?11.2 Infovis vs. Scivis: A Technical Comparison11.2.1 Dataset11.2.2 Data Domain11.2.3 Data Attributes11.2.4 Interpolation11.3 Table VisualizationPrinting the contentsMapping valuesSampling issues11.4 Visualization of Relations11.4.1 Tree VisualizationNode-link visualizationRooted tree layoutRadial tree layoutBubble tree layoutCone tree layoutTreemapsSquarified treemapsCushion treemaps11.4.2 Graph VisualizationHierarchical graph visualizationOrthogonal layoutsHierarchical edge bundlingImage-based edge bundlingForce-directed layoutsMultiple viewsGraph splattingGeneral graph-edge bundlingFDEBGBEBWRSBEBKDEEBComparing bundling algorithmsVisualizing dynamic graphsTypes of dynamic graphsOnline vs. offline drawingVisualizing small numbers of keyframesUsing animation11.4.3 Diagram Visualization11.5 Multivariate Data Visualization11.5.1 Parallel Coordinate Plots11.5.2 Dimensionality Reduction11.5.3 Multidimensional Scaling11.5.4 Projection-Based Dimensionality Reduction11.5.5 Advanced Dimensionality Reduction Techniques1. Least Square Projection (LSP)2. Part-Linear Multidimensional Projection (PLMP)3. Local Affine Multidimensional Projection (LAMP)Implementations11.5.6 Explaining ProjectionsAttribute axesAxis legends11.5.7 Assessing Projection QualityAggregate point-wise errorFalse neighborsMissing neighborsGroup membersComparing projections11.6 Text Visualization11.6.1 Content-Based Visualization11.6.2 Visualizing Program Code11.6.3 Visualizing Evolving DocumentsAnalyzing the project structureAnalyzing activityAnalyzing growthVisualizing quality metrics11.7 ConclusionFigure 11.1Figure 11.2Figure 11.3Figure 11.4Figure 11.5Figure 11.6Figure 11.7Figure 11.8Figure 11.9Figure 11.10Figure 11.11Figure 11.12Figure 11.13Figure 11.14Figure 11.15Figure 11.16Figure 11.17Figure 11.18Figure 11.19Figure 11.20Figure 11.21Figure 11.22Figure 11.23Figure 11.24Figure 11.25Figure 11.26Figure 11.27Figure 11.28Figure 11.29Figure 11.30Figure 11.31Figure 11.32Figure 11.33Figure 11.34Figure 11.35Figure 11.36Figure 11.37Figure 11.38Figure 11.39Figure 11.40Figure 11.41Figure 11.42Figure 11.43Table 11.1Table 11.2Listings 11.1
Scientific visualizationInformation visualizationSynergies and challengesThe way forwardEfficiency and effectivenessMeasuring valueIntegrationExplorers vs. practitionersSpecialists vs. generalists
A.1 Taxonomies of Visualization SystemsA.2 Scientific Visualization SoftwareThe Visualization Toolkit (VTK)MeVisLabAVS/ExpressIRIS ExplorerSCIRunParaViewMayaViA.3 Imaging SoftwareThe Insight Toolkit (ITK)3D SlicerTeemImageJBinvoxOpenVDBA.4 Grid Processing SoftwareMeshLabPCLCGALA.5 Information Visualization SoftwareThe Infovis Toolkit (IVTK)PrefuseGraphVizTulipGephiManyEyesTreemapXmdvTool

Content preview from Data Visualization, 2nd Edition

Chapter 5

Scalar Visualization

VISUALIZING scalar data is frequently encountered in science, engineering, and medicine, but also in daily life. Recalling from Section 3.6, scalar datasets, or scalar fields, represent functions f : D → ℝ, where D is usually a subset of ℝ2 or ℝ3. There exist many scalar visualization techniques, both for two-dimensional (2D) and three-dimensional (3D) datasets. In this chapter, we present a number of the most popular scalar visualization techniques: color mapping, contouring, and height plots. We start in Section 5.1 with color mapping and then discuss the design of effective colormaps in Section 5.2. In Section 5.3, we discuss contouring in two and three dimensions. In Section 5.4, we present the height plots. ...