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subroutine curev(idim,t,n,c,nc,k,u,m,x,mx,ier)
c subroutine curev evaluates in a number of points u(i),i=1,2,...,m
c a spline curve s(u) of degree k and dimension idim, given in its
c b-spline representation.
c
c calling sequence:
c call curev(idim,t,n,c,nc,k,u,m,x,mx,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 k : integer, giving the degree of s(u).
c u : array,length m, which contains the points where s(u) must
c be evaluated.
c m : integer, giving the number of points where s(u) must be
c evaluated.
c mx : integer, giving the dimension of the array x. mx >= m*idim
c
c output parameters:
c x : array,length mx,giving the value of s(u) at the different
c points. x(idim*(i-1)+j) will contain the j-th coordinate
c of the i-th point on the curve.
c ier : error flag
c ier = 0 : normal return
c ier =10 : invalid input data (see restrictions)
c
c restrictions:
c m >= 1
c mx >= m*idim
c t(k+1) <= u(i) <= u(i+1) <= t(n-k) , i=1,2,...,m-1.
c
c other subroutines required: fpbspl.
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,k,m,mx,ier
c ..array arguments..
real*8 t(n),c(nc),u(m),x(mx)
c ..local scalars..
integer i,j,jj,j1,k1,l,ll,l1,mm,nk1
real*8 arg,sp,tb,te
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 (m.lt.1) go to 100
if (m.eq.1) go to 30
go to 10
10 do 20 i=2,m
if(u(i).lt.u(i-1)) go to 100
20 continue
30 if(mx.lt.(m*idim)) go to 100
ier = 0
c fetch tb and te, the boundaries of the approximation interval.
k1 = k+1
nk1 = n-k1
tb = t(k1)
te = t(nk1+1)
l = k1
l1 = l+1
c main loop for the different points.
mm = 0
do 80 i=1,m
c fetch a new u-value arg.
arg = u(i)
if(arg.lt.tb) arg = tb
if(arg.gt.te) arg = te
c search for knot interval t(l) <= arg < t(l+1)
40 if(arg.lt.t(l1) .or. l.eq.nk1) go to 50
l = l1
l1 = l+1
go to 40
c evaluate the non-zero b-splines at arg.
50 call fpbspl(t,n,k,arg,l,h)
c find the value of s(u) at u=arg.
ll = l-k1
do 70 j1=1,idim
jj = ll
sp = 0.
do 60 j=1,k1
jj = jj+1
sp = sp+c(jj)*h(j)
60 continue
mm = mm+1
x(mm) = sp
ll = ll+n
70 continue
80 continue
100 return
end
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