recursive subroutine surev(idim,tu,nu,tv,nv,c,u,mu,v,mv,f,mf,
* wrk,lwrk,iwrk,kwrk,ier)
implicit none
c subroutine surev evaluates on a grid (u(i),v(j)),i=1,...,mu; j=1,...
c ,mv a bicubic spline surface of dimension idim, given in the
c b-spline representation.
c
c calling sequence:
c call surev(idim,tu,nu,tv,nv,c,u,mu,v,mv,f,mf,wrk,lwrk,
c * iwrk,kwrk,ier)
c
c input parameters:
c idim : integer, specifying the dimension of the spline surface.
c tu : real array, length nu, which contains the position of the
c knots in the u-direction.
c nu : integer, giving the total number of knots in the u-direction
c tv : real array, length nv, which contains the position of the
c knots in the v-direction.
c nv : integer, giving the total number of knots in the v-direction
c c : real array, length (nu-4)*(nv-4)*idim, which contains the
c b-spline coefficients.
c u : real array of dimension (mu).
c before entry u(i) must be set to the u co-ordinate of the
c i-th grid point along the u-axis.
c tu(4)<=u(i-1)<=u(i)<=tu(nu-3), i=2,...,mu.
c mu : on entry mu must specify the number of grid points along
c the u-axis. mu >=1.
c v : real array of dimension (mv).
c before entry v(j) must be set to the v co-ordinate of the
c j-th grid point along the v-axis.
c tv(4)<=v(j-1)<=v(j)<=tv(nv-3), j=2,...,mv.
c mv : on entry mv must specify the number of grid points along
c the v-axis. mv >=1.
c mf : on entry, mf must specify the dimension of the array f.
c mf >= mu*mv*idim
c wrk : real array of dimension lwrk. used as workspace.
c lwrk : integer, specifying the dimension of wrk.
c lwrk >= 4*(mu+mv)
c iwrk : integer array of dimension kwrk. used as workspace.
c kwrk : integer, specifying the dimension of iwrk. kwrk >= mu+mv.
c
c output parameters:
c f : real array of dimension (mf).
c on successful exit f(mu*mv*(l-1)+mv*(i-1)+j) contains the
c l-th co-ordinate of the bicubic spline surface at the
c point (u(i),v(j)),l=1,...,idim,i=1,...,mu;j=1,...,mv.
c ier : integer error flag
c ier=0 : normal return
c ier=10: invalid input data (see restrictions)
c
c restrictions:
c mu >=1, mv >=1, lwrk>=4*(mu+mv), kwrk>=mu+mv , mf>=mu*mv*idim
c tu(4) <= u(i-1) <= u(i) <= tu(nu-3), i=2,...,mu
c tv(4) <= v(j-1) <= v(j) <= tv(nv-3), j=2,...,mv
c
c other subroutines required:
c fpsuev,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,nu,nv,mu,mv,mf,lwrk,kwrk,ier
c ..array arguments..
integer iwrk(kwrk)
real*8 tu(nu),tv(nv),c((nu-4)*(nv-4)*idim),u(mu),v(mv),f(mf),
* wrk(lwrk)
c ..local scalars..
integer i,muv
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(mf.lt.mu*mv*idim) go to 100
muv = mu+mv
if(lwrk.lt.4*muv) go to 100
if(kwrk.lt.muv) go to 100
if (mu.lt.1) go to 100
if (mu.eq.1) go to 30
go to 10
10 do 20 i=2,mu
if(u(i).lt.u(i-1)) go to 100
20 continue
30 if (mv.lt.1) go to 100
if (mv.eq.1) go to 60
go to 40
40 do 50 i=2,mv
if(v(i).lt.v(i-1)) go to 100
50 continue
60 ier = 0
call fpsuev(idim,tu,nu,tv,nv,c,u,mu,v,mv,f,wrk(1),wrk(4*mu+1),
* iwrk(1),iwrk(mu+1))
100 return
end