|
alls |
bsplvb
|
|
|
onverts the b-representation | | |
t, bcoef, n, k of some spline into its
|
|
|
pp-representation | | |
break, coef, l, k .
|
|
|
|
****** |
i n p u t ******
|
|
|
t.....knot sequence, of length | | |
n+k
|
bcoef.....b-spline coefficient sequence, of length
n.....length of | | |
bcoef and dimension of spline space spline(k,t)
k.....order of the spline
|
|
w a r n i n g | | |
[char46] . . the restriction k .le. kmax (= 20) is impo-
|
|
|
sed by the arbitrary dimension statement for | | |
biatx below, but
|
|
is |
n o w h e r e c h e c k e d for.
|
|
|
|
|
|
****** |
w o r k a r e a ******
|
|
|
scrtch......of size | | |
(k,k) , needed to contain bcoeffs of a piece of
|
|
|
the spline and its | | |
k-1 derivatives
|
|
|
|
|
|
****** |
o u t p u t ******
|
|
|
break.....breakpoint sequence, of length | | |
l+1, contains (in increas-
|
|
|
ing order) the distinct points in the sequence | | |
t(k),...,t(n+1)
|
|
|
|
coef.....array of size (k,l), with | | |
coef(i,j) = (i-1)st derivative of
spline at break(j) from the right
l.....number of polynomial pieces which make up the spline in the in-
|
|
|
|
****** |
m e t h o d ******
|
|
|
for each breakpoint interval, the | | |
k relevant b-coeffs of the
spline are found and then differenced repeatedly to get the b-coeffs
of all the derivatives of the spline on that interval. the spline and
|
|
|
|
its first | | |
k-1 derivatives are then evaluated at the left end point
|
|
|
of that interval, using | | |
bsplvb repeatedly to obtain the values of
all b-splines of the appropriate order at that point.
|
|
|
|
|
