Semidiameter

In geometry, the semidiameter or semi-diameter of a set of points may be one half of its diameter; or, sometimes, one half of its extent along a particular direction.

Special cases

The semi-diameter of a sphere, circle, or interval is the same thing as its radius — namely, any line segment from the center to its boundary.

The semi-diameters of a non-circular ellipse are the halves of its extents along the two axes of symmetry. They are the parameters a, b of the implicit equation

${\displaystyle \left({\frac {x}{a}}\right)^{2}+\left({\frac {y}{b}}\right)^{2}=1.\,\!}$

Likewise, the semi-diameters of an ellipsoid are the parameters a, b, and c of its implicit equation

${\displaystyle \left({\frac {x}{a}}\right)^{2}+\left({\frac {y}{b}}\right)^{2}+\left({\frac {z}{c}}\right)^{2}=1.\,\!}$

The semi-diameters of a superellipse, superellipsoid, or superquadric can be identified in the same way.

See also

• Semi-major and semi-minor axes