# 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.