 Math::Bezier(3) 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->  y: \$point->\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[email protected]>