At nonzero curvature point on a regular space curve where the twist
out of its osculating plane attains a local maximum or minimum, namely
, leads to the necessary condition
[57]
(8.30)
where
(8.31)
and
,
and
are defined in
(8.10), (8.24) and (8.19), respectively.
Figure 8.8 shows the corresponding significant
points, marked by
's. Moreover, comparing
(8.19) and (8.30), both
and
of a regular curve vanish at nonzero
curvature points if and only if
.