---
name: "Math::Bezier"
section: "3pm"
platform: "linux"
package: "libmath-bezier-perl"
version: "0.01-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/Math::Bezier"
---

# Math::Bezier(3pm)

solution of Bezier Curves

## NAME

Math::Bezier - solution of Bezier Curves

## SYNOPSIS

```
    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);
```

## DESCRIPTION

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";
    }
```

## AUTHOR

Andy Wardley \<abw@kfs.org\>

## SEE ALSO

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.