Math::Bezier (3pm)

    use Math::Bezier;

    # create curve passing list of (x, y) control points
    my $bezier = Math::Bezier->new($x1, $y1, $x2, $y2, ..., $xn, $yn);

    # or pass reference to list of control points
    my $bezier = Math::Bezier->new([ $x1, $y1, $x2, $y2, ..., $xn, $yn]);

    # determine (x, y) at point along curve, range 0 -> 1
    my ($x, $y) = $bezier->point(0.5);

    # returns list ref in scalar context
    my $xy = $bezier->point(0.5);

    # return list of 20 (x, y) points along curve
    my @curve = $bezier->curve(20);

    # returns list ref in scalar context
    my $curve = $bezier->curve(20);

This module implements the algorithm for the solution of Bezier curves as presented by Robert D. Miller in Graphics Gems V, \*(L"Quick and Simple Bezier Curve Drawing\*(R".

A new Bezier curve is created using the new() constructor, passing a list of (x, y) control points.

use Math::Bezier;

my @control = ( 0, 0, 10, 20, 30, -20, 40, 0 ); my $bezier = Math::Bezier->new(@control);

Alternately, a reference to a list of control points may be passed.

my $bezier = Math::Bezier->new(\@control);

The point($theta) method can then be called on the object, passing a value in the range 0 to 1 which represents the distance along the curve. When called in list context, the method returns the x and y coordinates of that point on the Bezier curve.

my ($x, $y) = $bezier->point(0.5); print "x: $x y: $y\n

When called in scalar context, it returns a reference to a list containing the x and y coordinates.

my $point = $bezier->point(0.5); print "x: $point->[0] y: $point->[1]\n";

The curve($n) method can be used to return a set of points sampled along the length of the curve (i.e. in the range 0 <= $theta <= 1). The parameter indicates the number of sample points required, defaulting to 20 if undefined. The method returns a list of ($x1, $y1, $x2, $y2, ..., $xn, $yn) points when called in list context, or a reference to such an array when called in scalar context.

my @points = $bezier->curve(10);

while (@points) { my ($x, $y) = splice(@points, 0, 2); print "x: $x y: $y\n"; }

my $points = $bezier->curve(10);

while (@$points) { my ($x, $y) = splice(@$points, 0, 2); print "x: $x y: $y\n"; }

Andy Wardley <[email protected]>

Graphics Gems 5, edited by Alan W. Paeth, Academic Press, 1995, \s-1ISBN\s0 0-12-543455-3. Section \s-1IV\s0.8, 'Quick and Simple Bezier Curve Drawing' by Robert D. Miller, pages 206-209.