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Figure 1: Definitions |
SpheroellipsoidsTruncated ellipsoid capped by sphere segments; where the caps are fused to the body they have the same tangent as the ellipsoid.Advantages:
Equations: Given long and short semiaxes $c$ and $a$ and a truncation half length $z_{0}$ we have $z_{c}=z_{0}(1-a^{2}/c^{2})$ ... center of cap $r_{c}^{2}=a^{2}[1-(z_{0}^{2}/c^{2})(1-a^{2}/c^{2})]$ ... radius of cap $D=2 \, a$ ... particle width $L=2 \, (z_{c}+r_{c})$ ... particle length |
Figure 2: Hard spheroellipsoid with $c/a=6.0$, $z_{0}/a=3.06$ |
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Here is an Applet to try out various shapes: |
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Obviously, the shape may be continuously tuned between an ellipse (simply set
$z_{0}=c$) and a spherocylinder: with a large $c$ we achieve a very small
curvature of the ellipsoid near the equator, and a small truncation height
$z_{0} \ll c $ produces a near-spherocylinder. Try it out with the applet!
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Contact Distance between Convex BodiesThis is a fascinating topic, and I will prepare a thorough treatment in a further communication. Here, for the time being, is an Applet for determining the contact distance between two SpheroEllipses: |
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F. Vesely Nov-2012 | |||