sborník

DERIVATIVE OF B-SPLINE FUNCTION
which we substitute to equation 7
N n+1
i (t) ′ =
+
−
+
(
t − t i n
N n−1
i (t) −
t i+n+1 − t i t i+n − t i
t i+n+2 − t n
N n−1
i+1
t i+n+2 − t i+1 t i+n+1 − t (t)
i+1
t i+n+2 − t n
N n−1
i+2
t i+n+2 − t i+1 t i+n+2 − t (t))
i+2
1
Ni n (t) −
t i+n+1 − t i
)
n
N n−1
i+1
t i+n+1 − t (t) i+1
1
t i+n+2 − t i+1
N n i+1(t) (8)
This equation must be modified to desirable form:
N n+1
i (t) ′ =
n + 1
t i+n+1 − t i
N n i (t) −
n + 1
t i+n+2 − t i+1
N n i+1(t) (9)
N n+1
i (t) ′ =
−
n
N n 1
i (t) +
N
t i+n+1 − t i t i+n+1 − t
i+1(t)
n
i
n
N n 1
t i+n+2 − t
i+1(t) −
N
i+1 t i+n+2 − t
i+1(t)
n
i+1
by decomposition of the first and the third member of previous
formula
N n+1
i (t) ′ =
+
+
−
−
1
N n 1
i (t) −
N
t i+n+1 − t i t i+n+2 − t
i+1(t) n (10)
i+1
(
)
n t − ti
N n−1
i (t)
(11)
t i+n+1 − t i t i+n − t i
(
)
n ti+n+1 − t
N n−1
i+1
t i+n+1 − t i t i+n+1 − t (t) (12)
i+1
(
)
n t − ti+1
N n−1
i+1
t i+n+2 − t i+1 t i+n+1 − t (t) (13)
i+1
(
)
n ti+n+2 − t
N n−1
i+2
t i+n+2 − t i+1 t i+n+2 − t (t) (14)
i+2
201