Fractals//Mathematics/Vector field

Types

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  • time independent (= stationary = Steady ) or time dependent
  • dimension: 2D, 3D, ...


Algorithm

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  • start with scalar field
  • create vector field from scalar field using vector function
  • compute:
    • filed lines

Visualisation of vector field

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Plot types (Visualization Techniques for Flow Data) : [1]

  • arrow plot = quiver plot
  • Glyphs = Icons or signs for visualizing vector fields
    • simplest glyph = Line segment (hedgehog plots)
  • Characteristic Lines [2]
    • streamlines = curve everywhere tangential to the instantaneous vector (velocity) field (time independent vector field)
    • Path lines = Extensions of stream lines for time-varying data. Trace of a single particle in continuous time
    • streak lines [3]
  • texture (line integral convolution = LIC)[4]
  • Topological skeleton [5]
    • fixed point extraction ( Jacobian)


References

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  1. Flow Visualisation from TUV
  2. Data visualisation by Tomáš Fabián
  3. A Streakline Representation of Flow in Crowded Scenes from UCF
  4. lic by Zhanping Liu
  5. Vector Field Topology in Flow Analysis and Visualization by Guoning Chen