Fanuc Series 15i/150i-MA (Programming) Operators Manual

4.INTERPOLATION FUNCTIONS PROGRAMMING B-63324EN/03
- 122 -
Weight is always specified as a 9-digit absolute value of the minimum
data unit of the reference axis. For example, if the unit of the reference
axis is set as millimeter input at IS-B, then weight can be specified
within the range -999999.999 to +999999.999.
- Knot
The number of specified knots must equal the number of control points
plus the rank value. In the blocks specifying the first to last control
points, each control point and a knot are specified in the same block.
After these blocks, as many blocks (including only a knot) as the rank
value are specified. P/S alarm No. 1002 is issued for blocks in which
knot is not specified.
The NURBS curve programmed for NURBS interpolation must start
from the first control point and end at the last control point. The first k
knots (where k is the rank) must have the same values as the last k knots
(multiple knots). If multiple knots are not specified, P/S alarm No.
1007 is issued.
Knots of the same value that continue in excess of the rank value
cannot be specified in other blocks. If knots of the same value are
specified, P/S alarm No. 1008 is issued.
Knots are always specified as a 9-digit absolute value of the minimum
data unit of the reference axis. For example, if the unit of the reference
axis is set as millimeter input at IS-B, then weight can be specified
within the range -999999.999 to +999999.999.
- NURBS curve
Using these variables:
k :Rank
Pi
: Control point
wi
: Weight
xi
: Knot
()xxii +1
Knot vector
[,,..., ]xx xm01
()mnk=+
t
: Spline parameter,
the spline basis function N can be expressed with the de Boor-Cox
recursive formula, as indicated below:
Nt
xtx
txx t
i
ii
ii
.
()
()
(, )
1
1
1
1
0
=
≤≤
<<
+
+
Nt
txN t
xx
xtN t
xx
ik
iik
ik i
ik i k
ik i
,
,,
()
( ) () ( ) ()
=
+
+−
++
++
1
1
11
1
The NURBS curve P(t) of interpolation can be expressed as follows:
P
P
()
()
()
,
,
t
Ntw
Ntw
ik i i
i
n
ik i
i
n
=
=
=
0
0
()xtxm0 ≤≤
- NUBRS curved line segments
From the definition of NUBRS curved lines given above, it can be seen
that the points on an NURBS curved line of rank n (degree (n-1))
consist of n successive control points. A part of an NUBRS curved line,

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