Math::Bezier - solution of Bezier Curves

        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,
    "Quick and Simple Bezier Curve Drawing".

    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

        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 <>

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