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<a name="Bezier-Curves"></a>
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<p>
Next: <a href="Path-Finding.html#Path-Finding" accesskey="n" rel="next">Path Finding</a>, Previous: <a href="Easings.html#Easings" accesskey="p" rel="prev">Easings</a>, Up: <a href="Math.html#Math" accesskey="u" rel="up">Math</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html#Index" title="Index" rel="index">Index</a>]</p>
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<a name="Bezier-Curves-1"></a>
<h4 class="subsection">2.2.8 Bezier Curves</h4>
<p>The <code>(chickadee math bezier)</code> module provides an API for
describing cubic Bezier curves in 2D space. These curves are notably
used in font description, vector graphics programs, and when it comes
to games: path building. With Bezier curves, it’s somewhat easy to
create a smooth looking path for an enemy to move along, for example.
Bezier curves become particularly interesting when they are chained
together to form a Bezier “path”, where the end point of one curve
becomes the starting point of the next.
</p>
<p>Currently, the rendering of Bezier curves is rather crude and provided
mostly for visualizing and debugging curves that would be unseen in
the final game. See See <a href="Lines-and-Shapes.html#Lines-and-Shapes">Lines and Shapes</a> for more information.
</p>
<dl>
<dt><a name="index-make_002dbezier_002dcurve"></a>Procedure: <strong>make-bezier-curve</strong> <em>p0 p1 p2 p3</em></dt>
<dd><p>Return a new Bezier curve object whose starting point is <var>p0</var>,
ending point is <var>p3</var>, and control points are <var>p1</var> and
<var>p2</var>. All points are 2D vectors.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dcurve_003f"></a>Procedure: <strong>bezier-curve?</strong> <em>obj</em></dt>
<dd><p>Return <code>#t</code> if <var>obj</var> is a Bezier curve.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dcurve_002dp0"></a>Procedure: <strong>bezier-curve-p0</strong> <em>bezier</em></dt>
<dd><p>Return the starting point of <var>bezier</var>.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dcurve_002dp1"></a>Procedure: <strong>bezier-curve-p1</strong> <em>bezier</em></dt>
<dd><p>Return the first control point of <var>bezier</var>.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dcurve_002dp2"></a>Procedure: <strong>bezier-curve-p2</strong> <em>bezier</em></dt>
<dd><p>Return the second control point of <var>bezier</var>.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dcurve_002dp3"></a>Procedure: <strong>bezier-curve-p3</strong> <em>bezier</em></dt>
<dd><p>Return the end point of <var>bezier</var>.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dpath"></a>Procedure: <strong>bezier-path</strong> <em>. control-points</em></dt>
<dd><p>Return a list of connected bezier curves defined by
<var>control-points</var>. The first curve is defined by the first 4
arguments and every additional curve thereafter requires 3 additional
arguments.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dcurve_002dpoint_002dat"></a>Procedure: <strong>bezier-curve-point-at</strong> <em>bezier t</em></dt>
<dd><p>Return the coordinates for <var>bezier</var> at <var>t</var> (a value in the
range [0, 1] representing how far from the start of the curve to
check) as a 2D vector.
</p></dd></dl>
<dl>
<dt><a name="index-bezier_002dcurve_002dpoint_002dat_0021"></a>Procedure: <strong>bezier-curve-point-at!</strong> <em>dest bezier t</em></dt>
<dd><p>Modify the 2D vector <var>dest</var> in-place to contain the coordinates
for <var>bezier</var> at <var>t</var>.
</p></dd></dl>
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