The tangent vector of the transversal
intersection curve
lies on the tangent planes of both
surfaces. Therefore it can be obtained as the cross product of the unit
surface normal vectors of the two surfaces at
as illustrated in
Fig. 6.1:
(6.23)
where
and
are the unit surface normal vectors
of the two surfaces which are given either by (3.3) or
by (3.9) according to the type of two
intersecting surfaces. When the two normals are parallel to each
other, the tangent direction cannot be determined by
(6.23). This happens when the two surfaces intersect
tangentially and the tangent direction must be treated in a different
way. We will investigate the tangential intersection case in Sect.
6.4.
Figure 6.1:
Transversal intersection of two surfaces
(adapted from [458])
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December 2009