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P
P
P
P
1
2
2
1
P
P
P
P
0
3
0
3
P
P
1
2
P
0
P
3
P
P
P
0
3
2
P
1
Figure 11.5. A variety of Bézier curves having control points P ,
P ,
P , and P .
This reveals that the tangent directions at the endpoints are multiples of the dif-
ferences between the endpoints and the adjacent interior control points. This pro-
vides us with a mechanism for easily translating between the Bézier form and
Hermite form of a cubic curve. To translate from Bézier to Hermite (where we
are now calling the endpoints of the Hermite curve P and P ), we simply use the
values given by Equation (11.26) as the tangents T and T corresponding to the
endpoints P and P , respectively. To translate from Hermite to Bézier, we solve
Equation (11.26) for the interior control points as follows.
T
1
PP
=+
1
0
3
T
2
PP
=−
(11.27)
2
3
3
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