def insert(x, tck, m=1, per=0):
"""Insert knots into a B-spline.
Description:
Given the knots and coefficients of a B-spline representation, create a
new B-spline with a knot inserted m times at point x.
This is a wrapper around the FORTRAN routine insert of FITPACK.
Inputs:
x (u) -- A 1-D point at which to insert a new knot(s). If tck was returned
from splprep, then the parameter values, u should be given.
tck -- A sequence of length 3 returned by splrep or splprep containg the
knots, coefficients, and degree of the spline.
m -- The number of times to insert the given knot (its multiplicity).
per -- If non-zero, input spline is considered periodic.
Outputs: tck
tck -- (t,c,k) a tuple containing the vector of knots, the B-spline
coefficients, and the degree of the new spline.
Requirements:
t(k+1) <= x <= t(n-k), where k is the degree of the spline.
In case of a periodic spline (per != 0) there must be
either at least k interior knots t(j) satisfying t(k+1)<t(j)<=x
or at least k interior knots t(j) satisfying x<=t(j)<t(n-k).
Notes:
Based on algorithms from:
Boehm W : Inserting new knots into b-spline curves. Computer Aided
Design 12 (1980) 199-201.
Dierckx P. : Curve and surface fitting with splines, Monographs on
Numerical Analysis, Oxford University Press, 1993.
"""
t, c, k = tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
cc = []
for c_vals in c:
tt, cc_val, kk = insert(x, [t, c_vals, k], m)
cc.append(cc_val)
return (tt, cc, kk)
else:
tt, cc, ier = _fitpack._insert(per, t, c, k, x, m)
if ier == 10: raise ValueError, "Invalid input data"
if ier: raise TypeError, "An error occurred"
return (tt, cc, k)
def insert(x,tck,m=1,per=0):
"""Insert knots into a B-spline.
Description:
Given the knots and coefficients of a B-spline representation, create a
new B-spline with a knot inserted m times at point x.
This is a wrapper around the FORTRAN routine insert of FITPACK.
Inputs:
x (u) -- A 1-D point at which to insert a new knot(s). If tck was returned
from splprep, then the parameter values, u should be given.
tck -- A sequence of length 3 returned by splrep or splprep containg the
knots, coefficients, and degree of the spline.
m -- The number of times to insert the given knot (its multiplicity).
per -- If non-zero, input spline is considered periodic.
Outputs: tck
tck -- (t,c,k) a tuple containing the vector of knots, the B-spline
coefficients, and the degree of the new spline.
Requirements:
t(k+1) <= x <= t(n-k), where k is the degree of the spline.
In case of a periodic spline (per != 0) there must be
either at least k interior knots t(j) satisfying t(k+1)<t(j)<=x
or at least k interior knots t(j) satisfying x<=t(j)<t(n-k).
Notes:
Based on algorithms from:
Boehm W : Inserting new knots into b-spline curves. Computer Aided
Design 12 (1980) 199-201.
Dierckx P. : Curve and surface fitting with splines, Monographs on
Numerical Analysis, Oxford University Press, 1993.
"""
t,c,k=tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
cc = []
for c_vals in c:
tt, cc_val, kk = insert(x, [t, c_vals, k], m)
cc.append(cc_val)
return (tt, cc, kk)
else:
tt, cc, ier = _fitpack._insert(per, t, c, k, x, m)
if ier==10: raise ValueError,"Invalid input data"
if ier: raise TypeError,"An error occurred"
return (tt, cc, k)
def insert(x,tck,m=1,per=0):
"""
Insert knots into a B-spline.
Given the knots and coefficients of a B-spline representation, create a
new B-spline with a knot inserted m times at point x.
This is a wrapper around the FORTRAN routine insert of FITPACK.
Parameters
----------
x (u) : array_like
A 1-D point at which to insert a new knot(s). If `tck` was returned
from `splprep`, then the parameter values, u should be given.
tck : tuple
A tuple (t,c,k) returned by `splrep` or `splprep` containing
the vector of knots, the B-spline coefficients,
and the degree of the spline.
m : int, optional
The number of times to insert the given knot (its multiplicity).
Default is 1.
per : int, optional
If non-zero, input spline is considered periodic.
Returns
-------
tck : tuple
A tuple (t,c,k) containing the vector of knots, the B-spline
coefficients, and the degree of the new spline.
``t(k+1) <= x <= t(n-k)``, where k is the degree of the spline.
In case of a periodic spline (`per` != 0) there must be
either at least k interior knots t(j) satisfying ``t(k+1)<t(j)<=x``
or at least k interior knots t(j) satisfying ``x<=t(j)<t(n-k)``.
Notes
-----
Based on algorithms from [1]_ and [2]_.
References
----------
.. [1] W. Boehm, "Inserting new knots into b-spline curves.",
Computer Aided Design, 12, p.199-201, 1980.
.. [2] P. Dierckx, "Curve and surface fitting with splines, Monographs on
Numerical Analysis", Oxford University Press, 1993.
"""
t,c,k=tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
cc = []
for c_vals in c:
tt, cc_val, kk = insert(x, [t, c_vals, k], m)
cc.append(cc_val)
return (tt, cc, kk)
else:
tt, cc, ier = _fitpack._insert(per, t, c, k, x, m)
if ier==10: raise ValueError,"Invalid input data"
if ier: raise TypeError,"An error occurred"
return (tt, cc, k)
def insert(x, tck, m=1, per=0):
"""
Insert knots into a B-spline.
Given the knots and coefficients of a B-spline representation, create a
new B-spline with a knot inserted m times at point x.
This is a wrapper around the FORTRAN routine insert of FITPACK.
Parameters
----------
x (u) : array_like
A 1-D point at which to insert a new knot(s). If `tck` was returned
from `splprep`, then the parameter values, u should be given.
tck : tuple
A tuple (t,c,k) returned by `splrep` or `splprep` containing
the vector of knots, the B-spline coefficients,
and the degree of the spline.
m : int, optional
The number of times to insert the given knot (its multiplicity).
Default is 1.
per : int, optional
If non-zero, input spline is considered periodic.
Returns
-------
tck : tuple
A tuple (t,c,k) containing the vector of knots, the B-spline
coefficients, and the degree of the new spline.
``t(k+1) <= x <= t(n-k)``, where k is the degree of the spline.
In case of a periodic spline (`per` != 0) there must be
either at least k interior knots t(j) satisfying ``t(k+1)<t(j)<=x``
or at least k interior knots t(j) satisfying ``x<=t(j)<t(n-k)``.
Notes
-----
Based on algorithms from [1]_ and [2]_.
References
----------
.. [1] W. Boehm, "Inserting new knots into b-spline curves.",
Computer Aided Design, 12, p.199-201, 1980.
.. [2] P. Dierckx, "Curve and surface fitting with splines, Monographs on
Numerical Analysis", Oxford University Press, 1993.
"""
t, c, k = tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
cc = []
for c_vals in c:
tt, cc_val, kk = insert(x, [t, c_vals, k], m)
cc.append(cc_val)
return (tt, cc, kk)
else:
tt, cc, ier = _fitpack._insert(per, t, c, k, x, m)
if ier == 10:
raise ValueError("Invalid input data")
if ier:
raise TypeError("An error occurred")
return (tt, cc, k)
