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.\" ========================================================================
.\"
.IX Title "Bezier 3pm"
.TH Bezier 3pm "2022-10-13" "perl v5.34.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::Bezier \- solution of Bezier Curves
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&    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);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This module implements the algorithm for the solution of Bezier curves
as presented by Robert D. Miller in Graphics Gems V, \*(L"Quick and Simple
Bezier Curve Drawing\*(R".
.PP
A new Bezier curve is created using the \fBnew()\fR constructor, passing a list
of (x, y) control points.
.PP
.Vb 1
\&    use Math::Bezier;
\&
\&    my @control = ( 0, 0, 10, 20, 30, \-20, 40, 0 );
\&    my $bezier  = Math::Bezier\->new(@control);
.Ve
.PP
Alternately, a reference to a list of control points may be passed.
.PP
.Vb 1
\&    my $bezier  = Math::Bezier\->new(\e@control);
.Ve
.PP
The point($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.
.PP
.Vb 2
\&    my ($x, $y) = $bezier\->point(0.5);
\&    print "x: $x  y: $y\en
.Ve
.PP
When called in scalar context, it returns a reference to a list containing
the x and y coordinates.
.PP
.Vb 2
\&    my $point = $bezier\->point(0.5);
\&    print "x: $point\->[0]  y: $point\->[1]\en";
.Ve
.PP
The curve($n) method can be used to return a set of points sampled
along the length of the curve (i.e. in the range 0 <= \f(CW$theta\fR <= 1).
The parameter indicates the number of sample points required,
defaulting to 20 if undefined.  The method returns a list of ($x1,
\&\f(CW$y1\fR, \f(CW$x2\fR, \f(CW$y2\fR, ..., \f(CW$xn\fR, \f(CW$yn\fR) points when called in list context, or 
a reference to such an array when called in scalar context.
.PP
.Vb 1
\&    my @points = $bezier\->curve(10);
\&
\&    while (@points) {
\&        my ($x, $y) = splice(@points, 0, 2);
\&        print "x: $x  y: $y\en";
\&    }
\&
\&    my $points = $bezier\->curve(10);
\&
\&    while (@$points) {
\&        my ($x, $y) = splice(@$points, 0, 2);
\&        print "x: $x  y: $y\en";
\&    }
.Ve
.SH "AUTHOR"
.IX Header "AUTHOR"
Andy Wardley <abw@kfs.org>
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Graphics Gems 5, edited by Alan W. Paeth, Academic Press, 1995,
\&\s-1ISBN 0\-12\-543455\-3.\s0  Section \s-1IV.8,\s0 'Quick and Simple Bezier Curve
Drawing' by Robert D. Miller, pages 206\-209.