A Visualization System For
Mineral Elasticity
Richard Perkins
Introduction

Objectives:

To continue development on the interactive
elasticity visualization system


To support remote visualization


To interactively visualize elastic constants and wave
velocities-direction data of crystals with different
pressures, temperatures and compositional factors
Client-Server architecture approach
To support an online data repository
Definitions

Elasticity/Elastic


Elastic constants (Cij’s)



The relation between stress and strain as defined in Hooke’s Law
Used to define the elasticity of a crystal as a multivariate physical
quantity
Wave velocity-direction data



When a material is elastic it deforms under stress but return to its
original state when the stress is removed
Calculated from the elastic constants and wave propagation
direction using Cristoffel’s 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
Plots

Star plots and parallel plots


An-plot


Used to directly represent the elastic constants
Plots anisotropy factors for longitudinal and shear
waves
Polygon-base surface rendering

Graphically represent the three waves
(one longitudinal and two shear waves)
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
Cristoffel’s equation to figure out each velocity at each
vertex (propagation direction)
Re-position the vertices in 3D space to represent the
velocity-direction distribution.___
1st Degree
2nd Degree
80 triangles
320 triangles
3rd Degree
4th Degree
1280 triangles
5120 triangles
Velocity-direction Features

Features pertaining to wave velocity-direction
rendering

Views



Frame



Solid/wire
Shading


3d velocity
XY/YZ/ZX plane
Enables/Disabled/Scaled
Axis
Degree
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
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
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