Volume of the minimum circumscribed box of an elipsoid
An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to the semi-major axis and semi-minor axis of the appropriate ellipses.
There are four distinct cases of which one is degenerate:
a>b>c — tri-axial or (rarely) scalene ellipsoid;
a=b>c — oblate ellipsoid of revolution (oblate spheroid); a=b<c — prolate ellipsoid of revolution (prolate spheroid);
a=b=c — the degenerate case of a sphere;
The volume of the minimum circumscribed boxes of an elipsoid can be calculated by the semi-principal axes a,b,c of the elipsoid.
|Vmin||The volume of the minimum circumscribed box (m3)|
|a||semi-principal axis (m)|
|b||semi-principal axis (m)|
|c||semi-principal axis (m)|