A spheroid is a quadricsurface in three dimensions obtained by rotating an ellipse about one of its principal axes. If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a rugby ball). If the minor axis is chosen, the surface is called an oblate spheroid (similar to the shape of the planet Earth).
Prolate spheroid.
Oblate spheroid.
The sphere is a special case of the spheroid in which the generating ellipse is a circle.
A spheroid is a special case of an ellipsoid where two of the three major axes are equal.
By this is meant ellipsoids with axes in the ratio of 1:1:5, and 5:5:1.
Figure 10 shows the volume and surface area for a 5:1 prolateellipsoid as a function of the number of spherical harmonic coefficients used (in terms of N), for an ellipsoid that now has axis dimensions, in terms of voxels, of 11:11:55.
For an aspect ratio of 20, the oblate ratio is 1.085, and the prolate ratio is 1.371.
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