Math::Splines
Raku package for splines (piecewise polynomials), like, Bezier splines or B-splines.
Installation
From Zef ecosystem:
zef install Math::Splines
From GitHub:
zef install https://github.com/antononcube/Raku-Math-Splines.git
Usage examples
The subsections below show example usage for the currently implemented functions.
B-spline basis
use Math::Splines;
use Text::Plot;
# (Any)
Using positional arguments:
b-spline-basis(3, 0, 0.5)
# 0.666667
Using named arguments:
my $degree = 3;
my @knots = b-spline-knots(:$degree, n => 6);
b-spline-basis(:$degree, :@knots, :1index, argument => 0.5)
# 0.03125
Plot the basis of degree 3:
my $m = @knots.elems - $degree - 2;
my @points = (0..$m).map( -> $k { (0, 0.01 ... 1).map({ [$_, b-spline-basis(:$degree, :@knots, index => $k, argument => $_)] }) })».Array;
text-list-plot(@points, width => 80, height => 20, title => 'B-spline basis')
# B-spline basis
# +---+-------------+-------------+-------------+-------------+-------------+----+
# | |
# + * ▷ + 1.00
# | * ▷ |
# | * ▷ |
# + + 0.80
# | * ▷ |
# | * ▷ |
# + * □□□□□□ ▽▽▽▽▽▽▽▽ ❍❍❍❍❍❍❍❍ ◇◇◇◇◇◇ ▷ + 0.60
# | * □□ □□□□ ▽▽▽ ▽▽▽ ❍❍❍ ❍❍❍ ◇◇◇ ◇◇ ▷ |
# | □□ □▽▽ ▽❍❍❍ ❍❍◇◇ ▷ |
# + □ * ▽▽ □□ ❍❍❍ ▽▽▽ ◇◇ ❍❍ ▷ ◇ + 0.40
# | □ * ▽▽ □ ❍❍ ▽▽ ◇◇ ❍❍ ▷ ◇ |
# | □ ** ▽▽ □□□ ❍❍❍ ▽▽▽ ◇◇◇ ❍❍ ▷▷ ◇ |
# + □ ▽▽ □❍❍ ▽◇◇◇ ❍▷ ◇ + 0.20
# | □ ▽▽▽** ❍❍❍❍ □□□□ ◇◇◇ ▽▽▽ ▷▷▷❍❍❍ ◇ |
# | □ ▽▽▽ ***❍❍❍❍❍❍ □□□□ ◇◇◇◇ ▽▽▽▽▽▽▷▷▷ ❍❍❍ ◇ |
# + ▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▷▽▽▽▽▽▽▽▽▽▽❍❍❍❍◇ + 0.00
# | |
# +---+-------------+-------------+-------------+-------------+-------------+----+
# 0.00 0.20 0.40 0.60 0.80 1.00
Functions instead of values
If the argument :arg(:argument(:$x)) of b-spline-basis is Whatever, then a function is returned:
my &bf = b-spline-basis(:3degree, :0index, arg => Whatever);
&bf(0.25)
# 0.125
Alternatively, the subs b-spline-basis-value and b-spline-basis-function can be used to get values and functions respectively.
Bernstein basis
my @points = (^4).map( -> $k { (0, 0.01 ... 1).map({ [$_, bernstein-basis(3, $k, $_)] }) })».Array;
text-list-plot(@points, width => 80, height => 20, title => 'Bernstein basis')
# Bernstein basis
# +---+-------------+-------------+-------------+-------------+-------------+----+
# | |
# + ** ❍ + 1.00
# | ** ❍❍ |
# | *** ❍❍❍ |
# + ** ❍ + 0.80
# | ** ❍❍ |
# | ** ❍❍ |
# + ** ❍❍❍ + 0.60
# | ** ❍❍❍ |
# | *** □□□□□□□ ▽▽▽▽▽▽▽ ❍❍❍ |
# + □□□□□□□ □□□□□□□▽▽▽▽▽▽▽▽▽ ❍❍❍▽▽▽▽ + 0.40
# | □□□□ *** ▽▽▽▽▽▽□□□□□□ ❍❍❍ ▽▽▽▽ |
# | □□□□ **▽▽▽▽ □□❍❍❍❍ ▽▽▽ |
# + □□□ ▽▽▽▽▽ ***** ❍❍❍❍❍ □□□□□ ▽▽ + 0.20
# | □□ ▽▽▽▽▽ ****❍❍❍❍❍❍ □□□□□ ▽▽ |
# | □□ ▽▽▽▽▽▽ ❍❍❍❍❍❍❍❍❍ ******** □□□□□□ ▽▽ |
# + ❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍❍ ****************□□□□□□□□□▽ + 0.00
# | |
# +---+-------------+-------------+-------------+-------------+-------------+----+
# 0.00 0.20 0.40 0.60 0.80 1.00
TODO
- TODO Implementation
- TODO Documentation
- DONE Notebooks
- TODO Demo of 2D B-spline curve with control points
References
[AAp1] Anton Antonov,
Math::Fitting Raku package,
(2024),
GitHub/antononcube.
[AAp2] Anton Antonov,
Math::Polynomial::Chebyshev Raku package,
(2024),
GitHub/antononcube.