PROGRAMMING
B–63534EN/02
4. INTERPOLATION FUNCTIONS
81
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 an identical block. After
these blocks, as many blocks (including only a knot) as the rank value are
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 the absolute coordinates of the start point of
NURBS interpolation do not match the position of the first control point,
P/S alarm No. 5117 is issued. (To specify incremental values, G06.2 X0
Y0 Z0 K_ must be programmed.)
Using these variables:
k : Rank
P
i
: Control point
W
i
: Weight
X
i
: Knot (X
i
v X
i
+ 1)
Knot vector [X
0
, X
1
, ..., X
m
] (m = n + k)
t : Spline parameter,
the spline basis function N can be expressed with the de Boor–Cox
recursive formula, as indicated below:
N
i,1
(t) +
NJ
1(x
i
v t v x
i)1
)
0(t t x
i
, x
i)1
t t)
N
i,k
(t) +
(t–x
i
) N
i,k–1
(t)
x
i
)
k–1
–x
i
)
(x
i)k
–t) N
i)1,k–1
(t)
x
i
)
k
–x
i)1
The NURBS curve P(t) of interpolation can be expressed as follows:
P(t) +
S
n
i+0
N
i,k
(t)w
i
P
i
S
n
i+0
N
i,k
(t)w
i
(x
0
v tv x
m)
A reset during NURBS interpolation results in the clear state. The modal
code of group 1 enters the state specified in the G01 bit (bit 0 of parameter
3402).
NURBS interpolation can be performed on up to three axes. The axes of
NURBS interpolation must be specified in the first block. A new axis
cannot be specified before the beginning of the next NURBS curve or
before NURBS interpolation mode ends.
In NURBS interpolation mode, any command other than the NURBS
interpolation command (miscellaneous function and others) cannot be
specified.
If manual intervention is attempted while manual absolute mode is set,
P/S alarm No. 5118 is issued.
Cutter compensation cannot be simultaneously executed. NURBS
interpolation can only be specified after cutter compensation has been
canceled.
D Knot
D NURBS curve
D Reset
Limitations
D Controlled axes
D Command in NURBS
interpolation mode
D Manual intervention
D Cutter compensation