Game Development Reference

In-Depth Information

The blending functions are shown in Figure 11.1. As expected, only the weight

corresponding to
P
is nonzero at

=

, and only the weight corresponding to
P
is

t

0

nonzero at

=

1

.

t

()

()

2
H
that share a common

endpoint. If the geometry matrix corresponding to the curve

Figure 11.2 shows two Hermite curves

H

1
t

and

()

H

1
t

is given by

]

G
continuity is achieved if the geometry matrix for the

PP TT
, then

[

1

2

1

2

()

]

C
continuity is

curve

H

2
t

is equal to

PP TT
with

u

>

0

, and

[

u

2

3

2

3

achieved if

=

1

.

u

2

3

13

−+

t

2

t

1

2

(

)

t

32

−

t

(

)

2

t t

1

−

t

0

1

2

(

)

t

1

−

t

Figure 11.1.
Blending functions for the Hermite class of cubic curves.

−
T

2

P

()

2

H

t

1

()

H

t

2

P

P

1

3

T

T

2

3

−
T

Figure 11.2.
Two Hermite curves sharing the endpoint
P
.

1

Search Nedrilad ::

Custom Search