The following routines are available (in alphabetical order):
File:
BSDemo.m
This demonstration script shows how to use some of the routines from the Matlab B-spline Repository
File:
cbanal.m
Given values (y) of a function in points 1,2,...n,
find coefficients c, such as for all k=1..n
y(k)=sum c(i) cbanal(k-i), for i=1..n
i.e., find exact cubic B-spline interpolation
Forms and solves a linear equation set, which is exact but slow for large n
See also: fspline.m
Usage: c=cbanal(y)
File:
cbderiv.m
Calculate the first derivative of a cubic B-spline at point x Usage: y=cbderiv(x)
File:
cbinterp.m
Given coefficients c of cubic B-splines at points 1,2,... (obtained, for example, from cbanal.m) calculate a value at point x See also: cbanal.m Uses: cbspln.m Usage: y=cbinterp(c,x) ;
File:
cbspln.m
Calculate the value of a cubic B-spline at point x Usage: y=cbspln(x) ;
File:
fspline.m
FSPLINE(X,N) returns the B-spline coefficients of order N of the signal x.
Given values (x) of a function in points 1,2,...n,
finds coefficients c, such as for all k=1..n
x(k)=sum c(i) spline_of_order_N(k-i), for i=1..n
i.e., finds B-spline interpolation
This function uses a FIR filter thus it is faster than qbanal and cbanal,
with usually negligible loss in accuracy. The FIR kernel is so far
implemented only in C as a MEX file.
References :
M. Unser, A. Aldroubi and M. Eden, "Fast B-spline transforms for
continuous image representation and interpolation", IEEE Trans. Pattern Anal.
Machine Intell., vol. 13, pp. 277-285, March 1991.
M. Unser, A. Aldroubi and M. Eden, "B-spline signal processing. Part II :
efficient design and applications", IEEE Trans. Signal Processing, vol. 41,
pp. 834-848, February 1993.
See also: qbanal.m cbanal.m
Uses: filiirs.c
Usage: y=fspline(x,N)
File:
lbinterp.m
Given coefficients c of linear B-splines at points 1,2,... (equal to functional values) calculate a value at point x See also: cbinterp.m qbinterp.m Uses: lbspln.m Usage: y=lbinterp(c,x) ;
File:
lbspln.m
Calculate function values of a linear B-spline at point x Usage: y=lbspln(x)
File:
lininterp.m
Given function samples g regularly placed between a and b, calculate
value at x
i.e. g=[f(a) f(a+h) f(a+2*h) ... f(b-h) f(h)]
a<=x<=b
y=f(x)
Uses: lbinterp.m
Usage: y=lininterp(g,a,b,x)
File:
qbanal.m
Given values (y) of a function in points 1,2,...n,
find coefficients c, such as for all k=1..n
y(k)=sum c(i) qbspln(k-i), for i=1..n
i.e., find exact quadratic B-spline interpolation
Forms and solves a linear equation set, which is exact but slow for large n
See also: fspline.m
Usage: c=qbanal(y)
File:
qbderiv.m
Calculate first derivative of a quadratic B-spline at point x Usage: y=qbderiv(x)
File:
qbinterp.m
Given coefficients c of quadratic B-splines at points 1,2,... (obtained, for example, from qbanal.m) calculate a value at point x See also: qbanal.m cbinterp.m lbinterp.m Usage: y=qbinterp(c,x) ;
File:
qbspln.m
Calculate function values of a quadratic B-spline at point x See also: cbspln.m lbspln.m Usage: y=qbspln(x)
File:
scbinterp.m
Given coefficients g for cubic B-splines regularly placed between a and b,
calculate value at x
i.e. g=[f(a) f(a+h) f(a+2*h) ... f(b-h) f(h)]
a<=x<=b
y=f(x)
It is a scaled version of cubic B spline interpolation
Uses: cbinterp.m
Usage: y=scbinterp(g,a,b,x)