A Visualization System For Mineral Elasticity

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A Visualization System For Mineral Elasticity

• Richard Perkins

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Introduction

• Objectives
• To continue development on the interactive
  elasticity visualization system
• To interactively visualize elastic constants and
  wave velocities-direction data of crystals with
  different pressures, temperatures and
  compositional factors
• To support remote visualization
• Client-Server architecture approach
• To support an online data repository

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Visualization Algorithm

• Use elastic constants as input
• Solve Cristoffels equation to obtain wave
  velocities-direction data
• Display computed velocities as continuous
  surfaces
• Provide interactive graphic user interface

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Definitions

• Elasticity/Elastic
• When a material is elastic it deforms under
  stress but return to its original state when the
  stress is removed
• Elastic constants (Cijs)
• The relation between stress and strain as defined
  in Hookes Law
• Used to define the elasticity of a crystal as a
  multivariate physical quantity
• Wave velocity-direction data
• Calculated from the elastic constants and wave
  propagation direction using Cristoffels equation
• Produces three sets of wave velocities-direction
  data a longitudinal wave parallel to the
  propagation direction and two shear waves
  perpendicular to the propagation direction
• Anisotropic factors
• Are used to compare the velocities of the
  different waves

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Plots

• Star plots and parallel plots
• Used to directly represent the elastic constants
• An-plot
• Plots anisotropy factors for longitudinal and
  shear waves
• Polygon-base surface rendering
• Graphically represent the three waves (one
  longitudinal and two shear waves)

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Polygon-based surface Rendering

• How waves are rendered
• Use an icosahedron in which each vertex on the
  surface represents a propagation direction
• Recursively subdivide triangles into 4 triangle
  thereby increasing the number of vertexes
• Use the wave velocity-direction data calculated
  from Cristoffels equation to figure out each
  velocity at each vertex (propagation direction)
• Re-position the vertices in 3D space to represent
  the velocity-direction distribution.___

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1st Degree 80 triangles
2nd Degree 320 triangles
3rd Degree 1280 triangles
4th Degree 5120 triangles
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Velocity-direction Features

• Features pertaining to wave velocity-direction
  rendering
• Views
• 3d velocity
• XY/YZ/ZX plane
• Frame
• Solid/wire
• Shading
• Enables/Disabled/Scaled
• Axis
• Degree

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Other Features

• Personalized line color and thickness
• Single and Multiple mode
• Temperature and pressure
• Zooming
• Clear screen
• Removal of data from screen
• Data being visualized is selected in tree
• Manipulation of star plot which include
• Changing axes
• Removing axes
• Rotating axes
• And many more

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Conclusion

• Our system allows us to visualize elastic
  constants and wave velocities as a function of
  pressure, temperature and composition
• Our system visualizes the data through the use of
  star plots, parallel plots, an-plots, and
  polygon-based surface rendering

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Future Prospects

• Make remote application access more user friendly
• Expand the database
• Extend the visualization system to
  polycrystalline and multiphase composites
• Make the visualization system more user
  interactive