1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
|
subroutine insert(iopt,t,n,c,k,x,tt,nn,cc,nest,ier)
c subroutine insert inserts a new knot x into a spline function s(x)
c of degree k and calculates the b-spline representation of s(x) with
c respect to the new set of knots. in addition, if iopt.ne.0, s(x)
c will be considered as a periodic spline with period per=t(n-k)-t(k+1)
c satisfying the boundary constraints
c t(i+n-2*k-1) = t(i)+per ,i=1,2,...,2*k+1
c c(i+n-2*k-1) = c(i) ,i=1,2,...,k
c in that case, the knots and b-spline coefficients returned will also
c satisfy these boundary constraints, i.e.
c tt(i+nn-2*k-1) = tt(i)+per ,i=1,2,...,2*k+1
c cc(i+nn-2*k-1) = cc(i) ,i=1,2,...,k
c
c calling sequence:
c call insert(iopt,t,n,c,k,x,tt,nn,cc,nest,ier)
c
c input parameters:
c iopt : integer flag, specifying whether (iopt.ne.0) or not (iopt=0)
c the given spline must be considered as being periodic.
c t : array,length nest, which contains the position of the knots.
c n : integer, giving the total number of knots of s(x).
c c : array,length nest, which contains the b-spline coefficients.
c k : integer, giving the degree of s(x).
c x : real, which gives the location of the knot to be inserted.
c nest : integer specifying the dimension of the arrays t,c,tt and cc
c nest > n.
c
c output parameters:
c tt : array,length nest, which contains the position of the knots
c after insertion.
c nn : integer, giving the total number of knots after insertion
c cc : array,length nest, which contains the b-spline coefficients
c of s(x) with respect to the new set of knots.
c ier : error flag
c ier = 0 : normal return
c ier =10 : invalid input data (see restrictions)
c
c restrictions:
c nest > n
c t(k+1) <= x <= t(n-k)
c in case of a periodic spline (iopt.ne.0) there must be
c either at least k interior knots t(j) satisfying t(k+1)<t(j)<=x
c or at least k interior knots t(j) satisfying x<=t(j)<t(n-k)
c
c other subroutines required: fpinst.
c
c further comments:
c subroutine insert may be called as follows
c call insert(iopt,t,n,c,k,x,t,n,c,nest,ier)
c in which case the new representation will simply replace the old one
c
c references :
c boehm w : inserting new knots into b-spline curves. computer aided
c design 12 (1980) 199-201.
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 : february 2007 (second interval search added)
c
c ..scalar arguments..
integer iopt,n,k,nn,nest,ier
real*8 x
c ..array arguments..
real*8 t(nest),c(nest),tt(nest),cc(nest)
c ..local scalars..
integer kk,k1,l,nk
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(nest.le.n) go to 40
k1 = k+1
nk = n-k
if(x.lt.t(k1) .or. x.gt.t(nk)) go to 40
c search for knot interval t(l) <= x < t(l+1).
l = k1
10 if(x.lt.t(l+1)) go to 20
l = l+1
if(l.eq.nk) go to 14
go to 10
c if no interval found above, then reverse the search and
c look for knot interval t(l) < x <= t(l+1).
14 l = nk-1
16 if(x.gt.t(l)) go to 20
l = l-1
if(l.eq.k) go to 40
go to 16
20 if(t(l).ge.t(l+1)) go to 40
if(iopt.eq.0) go to 30
kk = 2*k
if(l.le.kk .and. l.ge.(n-kk)) go to 40
30 ier = 0
c insert the new knot.
call fpinst(iopt,t,n,c,k,x,l,tt,nn,cc,nest)
40 return
end
|
