Game Development Reference

In-Depth Information

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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