Visualization Data Representation

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Visualization Data Representation

• Ray Gasser
• rayg_at_bu.edu

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Characteristics of Data

• Data is discrete
• Interpolation functions generate data values in
  between known points
• Structure may be regular or irregular
• Regular (structured)
• need to store only beginning position, spacing,
  number of points
• smaller memory footprint per cell (topology can
  be generated on the fly)
• examples image data, rectilinear grid,
  structured grid
• Irregular (unstructured)
• information can be represented more densely where
  it changes quickly
• higher memory footprint (topology must be
  explicitly written) but more freedom
• examples polygonal data, unstructured grid

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Characteristics of Data

• Data has a topological dimension
• determines methods for visualization
• determines data representation
• examples
• 0D - points
• 1D - lines/Curves
• 2D - surfaces
• 3D - volumes
• Data is organized into datasets for visualization
• Datasets consist of two pieces
• organizing structure
• cells (topology)
• points (geometry)
• data attributes associated with the structure
• File format derived from organizing structure

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Organizing Structure (Topology)

• Topology
• the way in which constituent parts are
  interrelated or arranged
• specified by one or more cells (types vary with
  visualization packages)
• vertex - (0D) point
• polyvertex - (0D) arbitrarily ordered list of
  points
• line - (1D) defined by two points
• polyline - (1D) ordered list of one or more
  connected lines
• triangle - (2D) ordered list of three points
• triangle strip - (2D) ordered list of n 2
  points (n is the number of triangles)
• polygon - (2D) ordered list of three or more
  points lying in a plane
• pixel - (2D) ordered list of four points with
  geometric constraints
• quadrilateral - (2D) - ordered list of four
  points lying in a plane
• tetrahedron - (3D) ordered list of four nonplanar
  points
• voxel - (3D) ordered list of eight nonplanar
  points with geometric constraints
• hexahedron - (3D) ordered list of eight nonplanar
  points

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Examples of Cell Types

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Organizing Structure (Geometry)

• Geometry
• point coordinates assigned to a topology in 3D
  space
• represented by points
• example (0 0 0), (0 1 0), (1 0 0) would be the
  geometry for a triangle

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Examples of Dataset Types

• Image Data (Structured Points)
• regular in both topology and geometry
• examples lines, pixels, voxels
• applications imaging CT, MRI
• Rectilinear Grid
• regular topology but geometry only partially
  regular
• examples pixels, voxels
• Structured Grid
• regular topology and irregular geometry
• examples quadrilaterals, hexahedron
• applications fluid flow, heat transfer

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Examples of Dataset Types

• Unstructured Points
• no topology and irregular geometry
• examples vertex, polyvertex
• applications data with no inherent structure
• Polygonal Data
• irregular in both topology and geometry
• examples vertices, polyvertices, lines,
  polylines, polygons, triangle strips
• Unstructured Grid
• irregular in both topology and geometry
• examples any combination of cells
• applications finite element analysis, structural
  design, vibration

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Examples of Dataset Types

• XML
• much more complicated than the dataset types
  described above, but supports many more features
• provides the user with the ability to extend a
  file format with application specific tags
• in VTK the XML dataset has support for
  compression, portable binary encoding, random
  access, byte ordering, and multiple file
  representation of piece data

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Data Attributes

• Data attributes associated with the organizing
  structure
• Scalars
• single valued
• examples temperature, pressure, density,
  elevation
• Vectors
• magnitude and direction
• examples velocity, momentum
• Normals
• direction vectors (magnitude of 1) used for
  shading
• Texture Coordinates
• used to map a point in Cartesian space into 1, 2,
  or 3D texture space
• used for texture mapping
• Tensors (generalizations of scalars, vectors and
  matrices)
• rank 0 ( scalar), rank 1 (vector), rank 2
  (matrix), rank3 (3D rectangular array)
• examples stress, strain

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Visualization of Attributes

• Scalar Algorithms
• Color Mapping
• maps scalar data to colors
• implemented by using scalar values as an index
  into a color lookup table
• Contouring
• construct a boundary between distinct regions
• two steps
• explore space to find points near contour
• connect points into contour (2D) or surface (3D)
• 2D contour map (isoline)
• applications elevation contours from topography,
  pressure contours (weather maps) from meteorology

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Visualization of Attributes

• Contouring (cont)
• 3D isosurface
• applications tissue surfaces from tomography,
  constant pressure or temperature in fluid flow,
  implicit surfaces from math and CAD
• Scalar Generation
• extract scalars from part of data
• example extracting z coordinate (elevation) from
  terrain data to create scalar values

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Visualization of Attributes

• Vector Algorithms
• Hedgehogs
• oriented scaled line for each vector
• Oriented Glyphs
• orientation indicates direction
• scale indicates magnitude
• color indicates magnitude, pressure, temperature,
  or any variable
• Warping
• advect a simple object to indicate flow
• vertices individually translated by flow

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Visualization of Attributes

• Vector Algorithms (cont)
• Field Lines
• Fluid flow is described by a vector field in
  three dimensions for steady (fixed time) flows or
  four dimensions for unsteady (time varying) flows
• Three techniques for determining flow
• Pathline (Trace)
• tracks particle through unsteady (time-varying)
  flow
• shows particle trajectories over time
• rake releases particles from multiple positions
  at the same time instant
• reveals compression, vorticity
• Streamline
• tracks particle through steady (fixed-time) flow
• holds flow steady at a fixed time
• snapshot of flow at a given time instant
• Streakline
• particles released from the same position over a
  time interval (time-varying)
• snapshot of the variation of flow over time
• example dye steadily injected into fluid at a
  fixed point

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Visualization of Attributes

• Field Lines (cont)
• Four ways to show flow
• Streamlines
• lines show particle flow
• Streamlets
• half way between streamlines and glyphs
• example stream arrows
• Streamribbon
• rake of two particles to create a ribbon
• maintain constant tangent distance between
  particles
• reveals vorticity
• Streamtube
• circular rake of particles to create a tube
• relative radius of tube indicates
  compression/divergence
• color can indicate pressure, temperature

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Visualization of Attributes

• Modeling Algorithms
• Clipping
• can reveal internal details of a surface
• Cutting/Slicing
• cutting through a dataset with a surface
• Subsampling
• reduces data size by selecting a subset of the
  original data
• modifies topology

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Visualization of Attributes

• Volume Rendering
• used for data that is inherently volumetric
• examples biomedical imaging, MR scans, CT scans,
  ultrasounds
• Time Animation

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Sources

• The Visualization Toolkit, 3rd Edition, Will
  Schroeder, Pearson Education, Inc, 2002.
• The VTK Users Guide, 4.2 Edition, Kitware, 2003.
• Kitware www.vtk.org