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subroutine cualde(idim,t,n,c,nc,k1,u,d,nd,ier)
c subroutine cualde evaluates at the point u all the derivatives
c (l)
c d(idim*l+j) = sj (u) ,l=0,1,...,k, j=1,2,...,idim
c of a spline curve s(u) of order k1 (degree k=k1-1) and dimension idim
c given in its b-spline representation.
c
c calling sequence:
c call cualde(idim,t,n,c,nc,k1,u,d,nd,ier)
c
c input parameters:
c idim : integer, giving the dimension of the spline curve.
c t : array,length n, which contains the position of the knots.
c n : integer, giving the total number of knots of s(u).
c c : array,length nc, which contains the b-spline coefficients.
c nc : integer, giving the total number of coefficients of s(u).
c k1 : integer, giving the order of s(u) (order=degree+1).
c u : real, which contains the point where the derivatives must
c be evaluated.
c nd : integer, giving the dimension of the array d. nd >= k1*idim
c
c output parameters:
c d : array,length nd,giving the different curve derivatives.
c d(idim*l+j) will contain the j-th coordinate of the l-th
c derivative of the curve at the point u.
c ier : error flag
c ier = 0 : normal return
c ier =10 : invalid input data (see restrictions)
c
c restrictions:
c nd >= k1*idim
c t(k1) <= u <= t(n-k1+1)
c
c further comments:
c if u coincides with a knot, right derivatives are computed
c ( left derivatives if u = t(n-k1+1) ).
c
c other subroutines required: fpader.
c
c references :
c de boor c : on calculating with b-splines, j. approximation theory
c 6 (1972) 50-62.
c cox m.g. : the numerical evaluation of b-splines, j. inst. maths
c applics 10 (1972) 134-149.
c dierckx p. : curve and surface fitting with splines, monographs on
c numerical analysis, oxford university press, 1993.
c
c author :
c p.dierckx
c dept. computer science, k.u.leuven
c celestijnenlaan 200a, b-3001 heverlee, belgium.
c e-mail : Paul.Dierckx@cs.kuleuven.ac.be
c
c latest update : march 1987
c
c ..scalar arguments..
integer idim,n,nc,k1,nd,ier
real*8 u
c ..array arguments..
real*8 t(n),c(nc),d(nd)
c ..local scalars..
integer i,j,kk,l,m,nk1
c ..local array..
real*8 h(6)
c ..
c before starting computations a data check is made. if the input data
c are invalid control is immediately repassed to the calling program.
ier = 10
if(nd.lt.(k1*idim)) go to 500
nk1 = n-k1
if(u.lt.t(k1) .or. u.gt.t(nk1+1)) go to 500
c search for knot interval t(l) <= u < t(l+1)
l = k1
100 if(u.lt.t(l+1) .or. l.eq.nk1) go to 200
l = l+1
go to 100
200 if(t(l).ge.t(l+1)) go to 500
ier = 0
c calculate the derivatives.
j = 1
do 400 i=1,idim
call fpader(t,n,c(j),k1,u,l,h)
m = i
do 300 kk=1,k1
d(m) = h(kk)
m = m+idim
300 continue
j = j+n
400 continue
500 return
end
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