93 lines
3.0 KiB
Fortran
93 lines
3.0 KiB
Fortran
recursive subroutine cualde(idim,t,n,c,nc,k1,u,d,nd,ier)
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implicit none
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c subroutine cualde evaluates at the point u all the derivatives
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c (l)
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c d(idim*l+j) = sj (u) ,l=0,1,...,k, j=1,2,...,idim
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c of a spline curve s(u) of order k1 (degree k=k1-1) and dimension idim
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c given in its b-spline representation.
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c
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c calling sequence:
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c call cualde(idim,t,n,c,nc,k1,u,d,nd,ier)
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c
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c input parameters:
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c idim : integer, giving the dimension of the spline curve.
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c t : array,length n, which contains the position of the knots.
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c n : integer, giving the total number of knots of s(u).
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c c : array,length nc, which contains the b-spline coefficients.
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c nc : integer, giving the total number of coefficients of s(u).
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c k1 : integer, giving the order of s(u) (order=degree+1).
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c u : real, which contains the point where the derivatives must
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c be evaluated.
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c nd : integer, giving the dimension of the array d. nd >= k1*idim
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c
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c output parameters:
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c d : array,length nd,giving the different curve derivatives.
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c d(idim*l+j) will contain the j-th coordinate of the l-th
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c derivative of the curve at the point u.
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c ier : error flag
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c ier = 0 : normal return
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c ier =10 : invalid input data (see restrictions)
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c
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c restrictions:
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c nd >= k1*idim
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c t(k1) <= u <= t(n-k1+1)
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c
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c further comments:
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c if u coincides with a knot, right derivatives are computed
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c ( left derivatives if u = t(n-k1+1) ).
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c
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c other subroutines required: fpader.
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c
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c references :
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c de boor c : on calculating with b-splines, j. approximation theory
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c 6 (1972) 50-62.
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c cox m.g. : the numerical evaluation of b-splines, j. inst. maths
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c applics 10 (1972) 134-149.
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c dierckx p. : curve and surface fitting with splines, monographs on
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c numerical analysis, oxford university press, 1993.
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c
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c author :
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c p.dierckx
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c dept. computer science, k.u.leuven
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c celestijnenlaan 200a, b-3001 heverlee, belgium.
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c e-mail : Paul.Dierckx@cs.kuleuven.ac.be
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c
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c latest update : march 1987
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c
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c ..scalar arguments..
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integer idim,n,nc,k1,nd,ier
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real*8 u
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c ..array arguments..
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real*8 t(n),c(nc),d(nd)
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c ..local scalars..
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integer i,j,kk,l,m,nk1
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c ..local array..
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real*8 h(6)
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c ..
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c before starting computations a data check is made. if the input data
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c are invalid control is immediately repassed to the calling program.
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ier = 10
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if(nd.lt.(k1*idim)) go to 500
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nk1 = n-k1
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if(u.lt.t(k1) .or. u.gt.t(nk1+1)) go to 500
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c search for knot interval t(l) <= u < t(l+1)
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l = k1
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100 if(u.lt.t(l+1) .or. l.eq.nk1) go to 200
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l = l+1
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go to 100
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200 if(t(l).ge.t(l+1)) go to 500
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ier = 0
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c calculate the derivatives.
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j = 1
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do 400 i=1,idim
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call fpader(t,n,c(j),k1,u,l,h)
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m = i
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do 300 kk=1,k1
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d(m) = h(kk)
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m = m+idim
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300 continue
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j = j+n
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400 continue
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500 return
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end
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