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Scientific Visualization and Animation of Trajectories


Prof. David Bernstein
James Madison University

Computer Science Department
bernstdh@jmu.edu

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Overview
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  • Important Cases:
    • A vector in \(\mathbb{R}^{2}\) over time
    • A vector in \(\mathbb{R}^{3}\) over time
  • Notation:
    • Time is denoted by \(t\)
    • Values are denoted by \(x(t)\), \(y(t)\), and \(z(t)\)
Representing Time
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  • Use One of the Axes:
    • Only applicable to vectors in \(\mathbb{R}^{2}\)
  • Use "Clock" Time:
    • Animate \(x(t)\), \(y(t)\), and \(z(t)\)
    • The animation can be first-person or third-person
    • The "tail" can persist (for a particular length or time interval) or not
  • Use Color:
    • Shades of one color
    • Shades of "related" colors (e.g., red, orange and yellow)
    • Shades of "meaningful" colors (e.g., red and gred)
  • Use Symbology:
    • Numbers
Adding Dimensions
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  • Use Color:
    • Only appropriate when time is not represented using color
  • Use Audio:
    • Pitch
    • Volume
  • Use Line Thickness:
    • Only useful when the trajectory is not dense in the viewing plane
Static Visualizations
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\(x,y\) versus \(t\)
svaexamples/trajectory/staticXY.c
 
Static Visualizations (cont.)
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\(t\) Not on an Axis
svaexamples/trajectory/staticXYZ.c
 
Third-Person Animations
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\(x,y\) versus \(t\)
svaexamples/trajectory/animationXY.c
 
Third-Person Animations
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\(t\) Not on an Axis
svaexamples/trajectory/animationXYZ.c
 
There's Always More to Learn
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