Sagitta

Type:: float, or section
Range:: [-inf, inf]
Default:: -/-
Appearance:: optional
Excludes:: Radius

The signed sagitta $S$ is the perpendicular displacement from the midpoint of the chord to the midpoint of the arc. Its sign selects the side on which the arc bulges, as described in Arc.

For a chord of length $L$ , a valid sagitta satisfies

$\begin{eqnarray*} 0 < |S| \leq \frac{L}{2}. \end{eqnarray*}$

Equality produces a semicircle. For $s=|S|$ , the corresponding circle radius is

$\begin{eqnarray*} r = \frac{(L/2)^2+s^2}{2s}. \end{eqnarray*}$

Sagitta and Radius are mutually exclusive.