Semidiameter
From HandWiki
Short description: Term in geometry; half of a shape's diameter
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
- [math]\displaystyle{ \left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1.\,\! }[/math]
Likewise, the semi-diameters of an ellipsoid are the parameters a, b, and c of its implicit equation
- [math]\displaystyle{ \left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}+\left(\frac{z}{c}\right)^{2}=1.\,\! }[/math]
The semi-diameters of a superellipse, superellipsoid, or superquadric can be identified in the same way.
See also
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