<section>
<title>The Title</title>
<section>
<title>Namespaces</title>
<itemizedlist>
<listitem><para><link linkend="Paths">Paths</link></para></listitem>
</itemizedlist>
</section>
<section id="Paths">
<title>Namespace Paths</title>
<section id="Paths-Bezier">
<title>class Bezier</title>
<indexterm type="types"><primary>Bezier</primary><secondary>Paths::Bezier</secondary></indexterm>
<mediaobject>
<imageobject><imagedata fileref="images/Paths::Bezier.png" format="PNG"></imagedata></imageobject>
<imageobject><imagedata fileref="images/Paths::Bezier.svg" format="SVG"></imagedata></imageobject>
</mediaobject>
<para>
The Bezier class. It implements a Bezier curve
for the given order.</para>
<section id="Paths-Bezier-Bezier.l.r">
<title>Bezier()</title>
<indexterm type="functions"><primary>Bezier</primary><secondary>Paths::Bezier::Bezier</secondary></indexterm>
<synopsis> Bezier();
</synopsis>
<para>Create a new Bezier.</para>
</section>
<section id="Paths-Bezier-draw.l.r">
<title>draw()</title>
<indexterm type="functions"><primary>draw</primary><secondary>Paths::Bezier::draw</secondary></indexterm>
<synopsis>void draw();
</synopsis>
</section>
<section id="Paths-Bezier-controls_">
<title>controls_</title>
<synopsis>std::vector<Vertex> controls_;
</synopsis>
<para>The data...</para>
</section>
<section id=".l'Manipulators'.c.r">
<title>Manipulators</title>
<section id="Paths-Bezier-add_control_point.lconst.sVertex.A.r">
<title>add_control_point(const Vertex&)</title>
<indexterm type="functions"><primary>add_control_point</primary><secondary>Paths::Bezier::add_control_point</secondary></indexterm>
<synopsis>void add_control_point(const Vertex&);
</synopsis>
<para>
Add a new control point.
</para>
<variablelist ><title >Parameters</title>
<varlistentry ><term >p</term><listitem ><para >A point</para></listitem></varlistentry></variablelist>
</section>
<section id="Paths-Bezier-remove_control_point.lsize_t.r">
<title>remove_control_point(size_t)</title>
<indexterm type="functions"><primary>remove_control_point</primary><secondary>Paths::Bezier::remove_control_point</secondary></indexterm>
<synopsis>void remove_control_point(size_t i);
</synopsis>
<para>
Remove the control point at index i.
</para>
<variablelist ><title >Parameters</title>
<varlistentry ><term >i</term><listitem ><para >An index</para></listitem></varlistentry></variablelist>
</section>
</section>
</section>
<section id="Paths-Nurbs">
<title>class Nurbs</title>
<indexterm type="types"><primary>Nurbs</primary><secondary>Paths::Nurbs</secondary></indexterm>
<mediaobject>
<imageobject><imagedata fileref="images/Paths::Nurbs.png" format="PNG"></imagedata></imageobject>
<imageobject><imagedata fileref="images/Paths::Nurbs.svg" format="SVG"></imagedata></imageobject>
</mediaobject>
<para>The Nurbs class. It implements a nurbs curve
for the given order. It is a very powerful
and flexible curve representation. For simpler
cases you may prefer to use a <link linkend="Paths-Bezier">Bezier</link> curve.</para><para>While non-rational curves are not sufficient to represent a circle,
this is one of many sets of NURBS control points for an almost uniformly
parameterized circle:</para><informaltable frame="all">
<tgroup cols="3">
<colspec colname="col_1" />
<colspec colname="col_2" />
<colspec colname="col_3" />
<thead>
<row>
<entry><para>x</para></entry>
<entry><para>y</para></entry>
<entry><para>weight</para></entry>
</row>
</thead>
<tbody>
<row>
<entry><para>1</para></entry>
<entry><para>0</para></entry>
<entry><para>1</para></entry>
</row>
<row>
<entry><para>1</para></entry>
<entry><para>1</para></entry>
<entry><para><emphasis>sqrt(2)/2</emphasis></para></entry>
</row>
<row>
<entry><para>0</para></entry>
<entry><para>1</para></entry>
<entry><para>1</para></entry>
</row>
<row>
<entry><para>-1</para></entry>
<entry><para>1</para></entry>
<entry><para><emphasis>sqrt(2)/2</emphasis></para></entry>
</row>
<row>
<entry><para>-1</para></entry>
<entry><para>0</para></entry>
<entry><para>1</para></entry>
</row>
<row>
<entry><para>-1</para></entry>
<entry><para>-1</para></entry>
<entry><para><emphasis>sqrt(2)/2</emphasis></para></entry>
</row>
<row>
<entry><para>0</para></entry>
<entry><para>-1</para></entry>
<entry><para>1</para></entry>
</row>
<row>
<entry><para>1</para></entry>
<entry><para>-1</para></entry>
<entry><para><emphasis>sqrt(2)/2</emphasis></para></entry>
</row>
<row>
<entry><para>1</para></entry>
<entry><para>0</para></entry>
<entry><para>1</para></entry>
</row>
</tbody>
</tgroup>
</informaltable>
<para>The order is three, the knot vector is {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4}.
It should be noted that the circle is composed of four quarter circles,
tied together with double knots. Although double knots in a third order NURBS
curve would normally result in loss of continuity in the first derivative,
the control points are positioned in such a way that the first derivative is continuous.
(From <ulink url="http://en.wikipedia.org/wiki/NURBS">Wikipedia</ulink> )</para><para id="wikipedia">Example:</para><programlisting>
Nurbs<3> circle;
circle.insert_control_point(0, Vertex(1., 0.), 1.);
circle.insert_control_point(0, Vertex(1., 1.), sqrt(2.)/2.);
...</programlisting>
<section id="Paths-Nurbs-Nurbs.l.r">
<title>Nurbs()</title>
<indexterm type="functions"><primary>Nurbs</primary><secondary>Paths::Nurbs::Nurbs</secondary></indexterm>
<synopsis> Nurbs();
</synopsis>
<para>Create a new Nurbs curve.</para>
</section>
<section id="Paths-Nurbs-insert_control_point.ldouble.cconst.sVertex.A.cdouble.r">
<title>insert_control_point(double,const Vertex&,double)</title>
<indexterm type="functions"><primary>insert_control_point</primary><secondary>Paths::Nurbs::insert_control_point</secondary></indexterm>
<synopsis>void insert_control_point(double knot, const Vertex& vertex, double weight);
</synopsis>
<para>Inserts a control point with the given weight.
The knot value determines the position in the sequence.</para><variablelist>
<varlistentry>
<term>
<varname>Parameters:</varname></term>
<listitem>
<variablelist>
<varlistentry>
<term>
knot</term>
<listitem>
<para>the parameter value at which to insert a new knot</para></listitem>
</varlistentry>
<varlistentry>
<term>
vertex</term>
<listitem>
<para>the control point</para></listitem>
</varlistentry>
<varlistentry>
<term>
weight</term>
<listitem>
<para>the weight of the control point</para></listitem>
</varlistentry>
</variablelist>
</listitem>
</varlistentry>
</variablelist>
</section>
<section id="Paths-Nurbs-draw.l.r">
<title>draw()</title>
<indexterm type="functions"><primary>draw</primary><secondary>Paths::Nurbs::draw</secondary></indexterm>
<synopsis>void draw();
</synopsis>
</section>
<section id="Paths-Nurbs-controls_">
<title>controls_</title>
<synopsis>std::vector<Vertex> controls_;
</synopsis>
<para>The data...</para>
</section>
<section id="Paths-Nurbs-weights_">
<title>weights_</title>
<synopsis>std::vector<double> weights_;
</synopsis>
</section>
<section id="Paths-Nurbs-knots_">
<title>knots_</title>
<synopsis>std::vector<double> knots_;
</synopsis>
</section>
</section>
<section id="Paths-Polyline">
<title>class Polyline</title>
<indexterm type="types"><primary>Polyline</primary><secondary>Paths::Polyline</secondary></indexterm>
<mediaobject>
<imageobject><imagedata fileref="images/Paths::Polyline.png" format="PNG"></imagedata></imageobject>
<imageobject><imagedata fileref="images/Paths::Polyline.svg" format="SVG"></imagedata></imageobject>
</mediaobject>
<para>The Polyline class. It is an ordered set of
connected line segments.</para>
<section id="Paths-Polyline-Polyline.l.r">
<title>Polyline()</title>
<indexterm type="functions"><primary>Polyline</primary><secondary>Paths::Polyline::Polyline</secondary></indexterm>
<synopsis> Polyline();
</synopsis>
<para>Create a new Polyline.
</para>
</section>
<section id="Paths-Polyline-draw.l.r">
<title>draw()</title>
<indexterm type="functions"><primary>draw</primary><secondary>Paths::Polyline::draw</secondary></indexterm>
<synopsis>void draw();
</synopsis>
</section>
<section id="Paths-Polyline-vertices_">
<title>vertices_</title>
<synopsis>std::vector<Vertex> vertices_;
</synopsis>
<para>The data...</para>
</section>
<section id=".l'Manipulators'.c.r">
<title>Manipulators</title>
<section id="Paths-Polyline-add_vertex.lconst.sVertex.A.r">
<title>add_vertex(const Vertex&)</title>
<indexterm type="functions"><primary>add_vertex</primary><secondary>Paths::Polyline::add_vertex</secondary></indexterm>
<synopsis>void add_vertex(const Vertex&);
</synopsis>
<para>Add a new vertex.</para>
</section>
<section id="Paths-Polyline-remove_vertex.lsize_t.r">
<title>remove_vertex(size_t)</title>
<indexterm type="functions"><primary>remove_vertex</primary><secondary>Paths::Polyline::remove_vertex</secondary></indexterm>
<synopsis>void remove_vertex(size_t i);
</synopsis>
<para>Remove the vertex at index i.</para>
</section>
</section>
</section>
</section>
<section id="Bezier_h_">
<title>Bezier_h_</title>
<synopsis>Bezier_h_
</synopsis>
</section>
<section id="Nurbs_h_">
<title>Nurbs_h_</title>
<synopsis>Nurbs_h_
</synopsis>
</section>
<section id="Path">
<title>class Path</title>
<indexterm type="types"><primary>Path</primary><secondary>Path</secondary></indexterm>
<para>Path is the basic abstraction
used for drawing (curved) paths.</para>
<section id="Path-~Path.l.r">
<title>~Path()</title>
<indexterm type="functions"><primary>~Path</primary><secondary>Path::~Path</secondary></indexterm>
<synopsis> ~Path();
</synopsis>
</section>
<section id="Path-draw.l.r">
<title>draw()</title>
<indexterm type="functions"><primary>draw</primary><secondary>Path::draw</secondary></indexterm>
<synopsis>void draw();
</synopsis>
<para>Draw this path.</para>
</section>
</section>
<section id="Path_h_">
<title>Path_h_</title>
<synopsis>Path_h_
</synopsis>
</section>
<section id="Polyline_h_">
<title>Polyline_h_</title>
<synopsis>Polyline_h_
</synopsis>
</section>
<section id="Vertex">
<title>struct Vertex</title>
<indexterm type="types"><primary>Vertex</primary><secondary>Vertex</secondary></indexterm>
<para>A Vertex is a 2D point.</para>
<section id="Vertex-Vertex.ldouble.cdouble.r">
<title>Vertex(double,double)</title>
<indexterm type="functions"><primary>Vertex</primary><secondary>Vertex::Vertex</secondary></indexterm>
<synopsis> Vertex(double xx, double yy);
</synopsis>
</section>
<section id="Vertex-x">
<title>x</title>
<synopsis>double x;
</synopsis>
</section>
<section id="Vertex-y">
<title>y</title>
<synopsis>double y;
</synopsis>
<para> the y coordinate</para>
</section>
</section>
</section>
