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subroutine insert(iopt,t,n,c,k,x,tt,nn,cc,nest,ier)
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c subroutine insert inserts a new knot x into a spline function s(x)
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c of degree k and calculates the b-spline representation of s(x) with
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c respect to the new set of knots. in addition, if iopt.ne.0, s(x)
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c will be considered as a periodic spline with period per=t(n-k)-t(k+1)
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c satisfying the boundary constraints
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c t(i+n-2*k-1) = t(i)+per ,i=1,2,...,2*k+1
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c c(i+n-2*k-1) = c(i) ,i=1,2,...,k
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c in that case, the knots and b-spline coefficients returned will also
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c satisfy these boundary constraints, i.e.
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c tt(i+nn-2*k-1) = tt(i)+per ,i=1,2,...,2*k+1
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c cc(i+nn-2*k-1) = cc(i) ,i=1,2,...,k
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c call insert(iopt,t,n,c,k,x,tt,nn,cc,nest,ier)
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c iopt : integer flag, specifying whether (iopt.ne.0) or not (iopt=0)
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c the given spline must be considered as being periodic.
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c t : array,length nest, which contains the position of the knots.
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c n : integer, giving the total number of knots of s(x).
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c c : array,length nest, which contains the b-spline coefficients.
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c k : integer, giving the degree of s(x).
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c x : real, which gives the location of the knot to be inserted.
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c nest : integer specifying the dimension of the arrays t,c,tt and cc
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c tt : array,length nest, which contains the position of the knots
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c nn : integer, giving the total number of knots after insertion
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c cc : array,length nest, which contains the b-spline coefficients
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c of s(x) with respect to the new set of knots.
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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 t(k+1) <= x <= t(n-k)
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c in case of a periodic spline (iopt.ne.0) there must be
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c either at least k interior knots t(j) satisfying t(k+1)<t(j)<=x
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c or at least k interior knots t(j) satisfying x<=t(j)<t(n-k)
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c other subroutines required: fpinst.
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c subroutine insert may be called as follows
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c call insert(iopt,t,n,c,k,x,t,n,c,nest,ier)
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c in which case the new representation will simply replace the old one
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c boehm w : inserting new knots into b-spline curves. computer aided
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c design 12 (1980) 199-201.
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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 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 latest update : march 1987
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c ..scalar arguments..
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integer iopt,n,k,nn,nest,ier
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real*8 t(nest),c(nest),tt(nest),cc(nest)
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integer kk,k1,l,nk,nk1
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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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if(nest.le.n) go to 40
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if(x.lt.t(k1) .or. x.gt.t(nk)) go to 40
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c search for knot interval t(l) <= x < t(l+1).
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10 if(x.lt.t(l+1) .or. l.eq.nk1) go to 20
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20 if(t(l).ge.t(l+1)) go to 40
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if(iopt.eq.0) go to 30
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if(l.le.kk .and. l.ge.(n-kk)) go to 40
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c insert the new knot.
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call fpinst(iopt,t,n,c,k,x,l,tt,nn,cc,nest)
added
removed
Lib/interpolate/fitpack/insert.f
