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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 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 <>


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.