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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 => $_)] }) })Ā».Array;
text-list-plot(@points, width => 80, height => 20, title => 'B-spline basis')
# B-spline basis                                 
# +---+-------------+-------------+-------------+-------------+-------------+----+      
# |                                                                              |      
# +   *                                                                     ā–·    +  1.00
# |    *                                                                    ā–·    |      
# |     *                                                                  ā–·     |      
# +                                                                              +  0.80
# |      *                                                                ā–·      |      
# |      *                                                                ā–·      |      
# +       *    ā–”ā–”ā–”ā–”ā–”ā–”        ā–½ā–½ā–½ā–½ā–½ā–½ā–½ā–½          āāāāāāāā        ā—‡ā—‡ā—‡ā—‡ā—‡ā—‡    ā–·       +  0.60
# |        * ā–”ā–”     ā–”ā–”ā–”ā–”  ā–½ā–½ā–½        ā–½ā–½ā–½    āāā        āāā  ā—‡ā—‡ā—‡      ā—‡ā—‡ ā–·        |      
# |        ā–”ā–”          ā–”ā–½ā–½              ā–½āāā             āāā—‡ā—‡          ā–·         |      
# +        ā–” *        ā–½ā–½ ā–”ā–”           āāā  ā–½ā–½ā–½           ā—‡ā—‡ āā        ā–· ā—‡        +  0.40
# |       ā–”  *      ā–½ā–½     ā–”        āā        ā–½ā–½       ā—‡ā—‡     āā     ā–·   ā—‡       |      
# |      ā–”    **  ā–½ā–½        ā–”ā–”ā–”  āāā            ā–½ā–½ā–½  ā—‡ā—‡ā—‡        āā  ā–·ā–·    ā—‡      |      
# +      ā–”      ā–½ā–½            ā–”āā                 ā–½ā—‡ā—‡ā—‡            āā–·      ā—‡      +  0.20
# |     ā–”     ā–½ā–½ā–½**        āāāā ā–”ā–”ā–”ā–”            ā—‡ā—‡ā—‡  ā–½ā–½ā–½        ā–·ā–·ā–·āāā     ā—‡     |      
# |    ā–”   ā–½ā–½ā–½     ***āāāāāā        ā–”ā–”ā–”ā–”    ā—‡ā—‡ā—‡ā—‡        ā–½ā–½ā–½ā–½ā–½ā–½ā–·ā–·ā–·    āāā    ā—‡    |      
# +   ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–·ā–½ā–½ā–½ā–½ā–½ā–½ā–½ā–½ā–½ā–½āāāāā—‡    +  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, $_)] }) })Ā».Array;
text-list-plot(@points, width => 80, height => 20, title => 'Bernstein basis')
# Bernstein basis                                 
# +---+-------------+-------------+-------------+-------------+-------------+----+      
# |                                                                              |      
# +   **                                                                    ā    +  1.00
# |     **                                                                āā     |      
# |      ***                                                            āāā      |      
# +        **                                                          ā         +  0.80
# |          **                                                      āā          |      
# |            **                                                  āā            |      
# +              **                                             āāā              +  0.60
# |                **                                         āāā                |      
# |                  ***   ā–”ā–”ā–”ā–”ā–”ā–”ā–”                ā–½ā–½ā–½ā–½ā–½ā–½ā–½   āāā                  |      
# +                 ā–”ā–”ā–”ā–”ā–”ā–”ā–”       ā–”ā–”ā–”ā–”ā–”ā–”ā–”ā–½ā–½ā–½ā–½ā–½ā–½ā–½ā–½ā–½       āāāā–½ā–½ā–½ā–½                 +  0.40
# |             ā–”ā–”ā–”ā–”       ***      ā–½ā–½ā–½ā–½ā–½ā–½ā–”ā–”ā–”ā–”ā–”ā–”      āāā       ā–½ā–½ā–½ā–½             |      
# |          ā–”ā–”ā–”ā–”             **ā–½ā–½ā–½ā–½            ā–”ā–”āāāā             ā–½ā–½ā–½           |      
# +        ā–”ā–”ā–”             ā–½ā–½ā–½ā–½ā–½ *****        āāāāā ā–”ā–”ā–”ā–”ā–”             ā–½ā–½         +  0.20
# |       ā–”ā–”          ā–½ā–½ā–½ā–½ā–½          ****āāāāāā          ā–”ā–”ā–”ā–”ā–”          ā–½ā–½       |      
# |     ā–”ā–”      ā–½ā–½ā–½ā–½ā–½ā–½          āāāāāāāāā  ********           ā–”ā–”ā–”ā–”ā–”ā–”      ā–½ā–½     |      
# +   āāāāāāāāāāāāāāāāāāāāāāāāāāā                  ****************ā–”ā–”ā–”ā–”ā–”ā–”ā–”ā–”ā–”ā–½    +  0.00
# |                                                                              |      
# +---+-------------+-------------+-------------+-------------+-------------+----+      
#     0.00          0.20          0.40          0.60          0.80          1.00

TODO

  • TODO Implementation

    • TODO Bezier curve

  • TODO Documentation

References

[AAp1] Anton Antonov, Math::Fitting Raku package, (2024), GitHub/antononcube.

[AAp2] Anton Antonov, Math::Polynomial::Chebyshev Raku package, (2024), GitHub/antononcube.

Math::Splines v0.0.1

Raku package for splines (piecewise polynomials), like, Bezier splines or B-splines.

Authors

  • Anton Antonov

License

Artistic-2.0

Dependencies

Test Dependencies

Provides

  • Math::Splines

Documentation

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