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real*8 function evapol(tu,nu,tv,nv,c,rad,x,y)
c function program evacir evaluates the function f(x,y) = s(u,v),
c defined through the transformation
c x = u*rad(v)*cos(v) y = u*rad(v)*sin(v)
c and where s(u,v) is a bicubic spline ( 0<=u<=1 , -pi<=v<=pi ), given
c in its standard b-spline representation.
c
c calling sequence:
c f = evapol(tu,nu,tv,nv,c,rad,x,y)
c
c input parameters:
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), which contains the
c b-spline coefficients.
c rad : real function subprogram, defining the boundary of the
c approximation domain. must be declared external in the
c calling (sub)-program
c x,y : real values.
c before entry x and y must be set to the co-ordinates of
c the point where f(x,y) must be evaluated.
c
c output parameter:
c f : real
c on exit f contains the value of f(x,y)
c
c other subroutines required:
c bispev,fpbisp,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 1989
c
c ..scalar arguments..
integer nu,nv
real*8 x,y
c ..array arguments..
real*8 tu(nu),tv(nv),c((nu-4)*(nv-4))
c ..user specified function
real*8 rad
c ..local scalars..
integer ier
real*8 u,v,r,f,one,dist
c ..local arrays
real*8 wrk(8)
integer iwrk(2)
c ..function references
real*8 atan2,sqrt
c ..
c calculate the (u,v)-coordinates of the given point.
one = 1
u = 0.
v = 0.
dist = x**2+y**2
if(dist.le.0.) go to 10
v = atan2(y,x)
r = rad(v)
if(r.le.0.) go to 10
u = sqrt(dist)/r
if(u.gt.one) u = one
c evaluate s(u,v)
10 call bispev(tu,nu,tv,nv,c,3,3,u,1,v,1,f,wrk,8,iwrk,2,ier)
evapol = f
return
end
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