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Figure 4.18. Detection of arc-arc intersection and the direction of s .
Figure 4.19. Edge-edge cases: not candidate support pairs.
4.7.3 Non-Three-Dimensional Polytopes
In order for the arc-arc intersection test in Equation (4.9) to work, direction e must
be the right-screw direction for the rotation from n 0 to n 1 (see Figure 4.20(a) ). It
is easy to establish that e = norm ||·|| ( n 0 ×
n 1 ) but that n 0 ×
n 1 = 0 in the case
where n 1 =
n 0 , i.e., in the case of a wedge collision shape. Furthermore, the
tetrahedron test also breaks down unless we replace n 0 ×
n 1 with a valid nonzero
direction.
Fortunately, this special case is easy to handle with a little bit of precompu-
tation. The main requirements for e are that it is orthogonal to the arc plane and
is the axis of right-hand-rule rotation from n 0 to n 1 (it also implies e
n 0 and
e
n 1 ),
see Figure 4.20(a) ) , and in the unfolded angle case ( Figure 4.20(b) ) , we can
n 1 ). This automatically holds in common cases ( e = norm ||·|| ( n 0 ×
 
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