++ed by:
1 non-PAUSE user

# 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->  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@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.