茂之钳
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417 lines
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<a href="#pub-methods">Public 成员函数</a> |
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<a href="classvde_1_1curves_1_1NurbsCurve-members.html">所有成员列表</a> </div>
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<div class="headertitle">
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<div class="title">vde::curves::NurbsCurve类 参考<div class="ingroups"><a class="el" href="group__curves.html">曲线曲面模块 (vde::curves)</a></div></div> </div>
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</div><!--header-->
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<div class="contents">
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<p>NURBS 曲线（Non-Uniform Rational B-Spline）
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<a href="classvde_1_1curves_1_1NurbsCurve.html#details">更多...</a></p>
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<p><code>#include <<a class="el" href="nurbs__curve_8h_source.html">nurbs_curve.h</a>></code></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
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Public 成员函数</h2></td></tr>
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<tr class="memitem:a60b17bb3a21d4a9fcd0925845babc9b8"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a60b17bb3a21d4a9fcd0925845babc9b8">NurbsCurve</a> (std::vector< Point3D > <a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a0cbed910c2a02a658a4431cb8545f533">control_points</a>, std::vector< double > <a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a4c288f68dc1cacd4b8ffb3d827c2aeea">knots</a>, std::vector< double > <a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#aab263a3fd901ca9202624b7c18f5bca4">weights</a>, int <a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a9431265e260e07287800ae277eec3cad">degree</a>)</td></tr>
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<tr class="memdesc:a60b17bb3a21d4a9fcd0925845babc9b8"><td class="mdescLeft"> </td><td class="mdescRight">构造 NURBS 曲线 <a href="classvde_1_1curves_1_1NurbsCurve.html#a60b17bb3a21d4a9fcd0925845babc9b8">更多...</a><br /></td></tr>
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<tr class="separator:a60b17bb3a21d4a9fcd0925845babc9b8"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a28fe084bb7cb16f140e77e856f5574ba"><td class="memItemLeft" align="right" valign="top">Point3D </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a28fe084bb7cb16f140e77e856f5574ba">evaluate</a> (double t) const</td></tr>
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<tr class="memdesc:a28fe084bb7cb16f140e77e856f5574ba"><td class="mdescLeft"> </td><td class="mdescRight">在参数 t 处求值 <a href="classvde_1_1curves_1_1NurbsCurve.html#a28fe084bb7cb16f140e77e856f5574ba">更多...</a><br /></td></tr>
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<tr class="separator:a28fe084bb7cb16f140e77e856f5574ba"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a4bb2ebc6deb70d30647dacd100fbd418"><td class="memItemLeft" align="right" valign="top">Vector3D </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a4bb2ebc6deb70d30647dacd100fbd418">derivative</a> (double t, int order=1) const</td></tr>
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<tr class="memdesc:a4bb2ebc6deb70d30647dacd100fbd418"><td class="mdescLeft"> </td><td class="mdescRight">在参数 t 处求导数 <a href="classvde_1_1curves_1_1NurbsCurve.html#a4bb2ebc6deb70d30647dacd100fbd418">更多...</a><br /></td></tr>
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<tr class="separator:a4bb2ebc6deb70d30647dacd100fbd418"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a9431265e260e07287800ae277eec3cad"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a9431265e260e07287800ae277eec3cad">degree</a> () const</td></tr>
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<tr class="memdesc:a9431265e260e07287800ae277eec3cad"><td class="mdescLeft"> </td><td class="mdescRight">曲线阶次 <a href="classvde_1_1curves_1_1NurbsCurve.html#a9431265e260e07287800ae277eec3cad">更多...</a><br /></td></tr>
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<tr class="separator:a9431265e260e07287800ae277eec3cad"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a05403f0de5812c4a9e64130198ea1c1f"><td class="memItemLeft" align="right" valign="top">std::pair< double, double > </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a05403f0de5812c4a9e64130198ea1c1f">domain</a> () const</td></tr>
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<tr class="memdesc:a05403f0de5812c4a9e64130198ea1c1f"><td class="mdescLeft"> </td><td class="mdescRight">参数定义域 <a href="classvde_1_1curves_1_1NurbsCurve.html#a05403f0de5812c4a9e64130198ea1c1f">更多...</a><br /></td></tr>
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<tr class="separator:a05403f0de5812c4a9e64130198ea1c1f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a0cbed910c2a02a658a4431cb8545f533"><td class="memItemLeft" align="right" valign="top">const std::vector< Point3D > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a0cbed910c2a02a658a4431cb8545f533">control_points</a> () const</td></tr>
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<tr class="memdesc:a0cbed910c2a02a658a4431cb8545f533"><td class="mdescLeft"> </td><td class="mdescRight">控制点访问 <a href="classvde_1_1curves_1_1NurbsCurve.html#a0cbed910c2a02a658a4431cb8545f533">更多...</a><br /></td></tr>
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<tr class="separator:a0cbed910c2a02a658a4431cb8545f533"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aab263a3fd901ca9202624b7c18f5bca4"><td class="memItemLeft" align="right" valign="top">const std::vector< double > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#aab263a3fd901ca9202624b7c18f5bca4">weights</a> () const</td></tr>
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<tr class="memdesc:aab263a3fd901ca9202624b7c18f5bca4"><td class="mdescLeft"> </td><td class="mdescRight">权重访问 <a href="classvde_1_1curves_1_1NurbsCurve.html#aab263a3fd901ca9202624b7c18f5bca4">更多...</a><br /></td></tr>
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<tr class="separator:aab263a3fd901ca9202624b7c18f5bca4"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a4c288f68dc1cacd4b8ffb3d827c2aeea"><td class="memItemLeft" align="right" valign="top">const std::vector< double > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1NurbsCurve.html#a4c288f68dc1cacd4b8ffb3d827c2aeea">knots</a> () const</td></tr>
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<tr class="memdesc:a4c288f68dc1cacd4b8ffb3d827c2aeea"><td class="mdescLeft"> </td><td class="mdescRight">节点向量访问 <a href="classvde_1_1curves_1_1NurbsCurve.html#a4c288f68dc1cacd4b8ffb3d827c2aeea">更多...</a><br /></td></tr>
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<tr class="separator:a4c288f68dc1cacd4b8ffb3d827c2aeea"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">详细描述</h2>
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<div class="textblock"><p>NURBS 曲线（Non-Uniform Rational B-Spline） </p>
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<p>B 样条的有理推广，引入权重 w_i 使每个控制点的影响可调。 通过投影变换将齐次坐标中的 B 样条映射到 3D 空间。</p>
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<p>求值公式：C(t) = Σ N_{i,p}(t) · w_i · P_i / Σ N_{i,p}(t) · w_i</p>
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<p>关键性质：</p><ul>
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<li>可精确表示圆锥曲线（圆、椭圆）——Bézier/B 样条无法做到</li>
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<li>权重 w_i 越大，曲线越靠近控制点 P_i</li>
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<li>所有权重 = 1 时退化为 B 样条</li>
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<li>所有权重 > 0 时在凸包内 </li>
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</ul>
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<p class="definition">在文件 <a class="el" href="nurbs__curve_8h_source.html">nurbs_curve.h</a> 第 <a class="el" href="nurbs__curve_8h_source.html#l00026">26</a> 行定义.</p>
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</div><h2 class="groupheader">构造及析构函数说明</h2>
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<a id="a60b17bb3a21d4a9fcd0925845babc9b8"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a60b17bb3a21d4a9fcd0925845babc9b8">◆ </a></span>NurbsCurve()</h2>
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<td class="memname">vde::curves::NurbsCurve::NurbsCurve </td>
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<td>(</td>
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<td class="paramtype">std::vector< Point3D > </td>
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<td class="paramname"><em>control_points</em>, </td>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">std::vector< double > </td>
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<td class="paramname"><em>knots</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">std::vector< double > </td>
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<td class="paramname"><em>weights</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>degree</em> </td>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>构造 NURBS 曲线 </p>
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<dl class="params"><dt>参数</dt><dd>
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<table class="params">
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<tr><td class="paramname">control_points</td><td>控制点序列 </td></tr>
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<tr><td class="paramname">knots</td><td>节点向量 </td></tr>
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<tr><td class="paramname">weights</td><td>权重序列，必须与 control_points 等长，各分量 > 0 </td></tr>
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<tr><td class="paramname">degree</td><td>阶次 p </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section note"><dt>注解</dt><dd>所有权重必须 > 0 以保证分母不为零（非退化） <div class="fragment"><div class="line"><span class="comment">// 用 NURBS 表示四分之一圆（7 个控制点，三次）</span></div>
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<div class="line"><a class="code" href="classvde_1_1curves_1_1NurbsCurve.html#a60b17bb3a21d4a9fcd0925845babc9b8">NurbsCurve</a> arc(cps, {0,0,0,0, 0.5, 1,1,1,1},</div>
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<div class="line"> {1, sqrt2/2, 1, sqrt2/2, 1, sqrt2/2, 1}, 3);</div>
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<div class="ttc" id="aclassvde_1_1curves_1_1NurbsCurve_html_a60b17bb3a21d4a9fcd0925845babc9b8"><div class="ttname"><a href="classvde_1_1curves_1_1NurbsCurve.html#a60b17bb3a21d4a9fcd0925845babc9b8">vde::curves::NurbsCurve::NurbsCurve</a></div><div class="ttdeci">NurbsCurve(std::vector< Point3D > control_points, std::vector< double > knots, std::vector< double > weights, int degree)</div><div class="ttdoc">构造 NURBS 曲线</div></div>
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</div><!-- fragment --> </dd></dl>
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</div>
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</div>
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<h2 class="groupheader">成员函数说明</h2>
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<a id="a0cbed910c2a02a658a4431cb8545f533"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a0cbed910c2a02a658a4431cb8545f533">◆ </a></span>control_points()</h2>
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<td class="memname">const std::vector<Point3D>& vde::curves::NurbsCurve::control_points </td>
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<td>(</td>
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<td class="paramname"></td><td>)</td>
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<td> const</td>
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<td class="mlabels-right">
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<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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<p>控制点访问 </p>
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<dl class="section return"><dt>返回</dt><dd>只读引用 </dd></dl>
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<p class="definition">在文件 <a class="el" href="nurbs__curve_8h_source.html">nurbs_curve.h</a> 第 <a class="el" href="nurbs__curve_8h_source.html#l00079">79</a> 行定义.</p>
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<a id="a9431265e260e07287800ae277eec3cad"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a9431265e260e07287800ae277eec3cad">◆ </a></span>degree()</h2>
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<td class="memname">int vde::curves::NurbsCurve::degree </td>
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<td>(</td>
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<td class="paramname"></td><td>)</td>
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<td> const</td>
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<td class="mlabels-right">
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<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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</div><div class="memdoc">
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<p>曲线阶次 </p>
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<dl class="section return"><dt>返回</dt><dd>p </dd></dl>
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<p class="definition">在文件 <a class="el" href="nurbs__curve_8h_source.html">nurbs_curve.h</a> 第 <a class="el" href="nurbs__curve_8h_source.html#l00067">67</a> 行定义.</p>
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<a id="a4bb2ebc6deb70d30647dacd100fbd418"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a4bb2ebc6deb70d30647dacd100fbd418">◆ </a></span>derivative()</h2>
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">Vector3D vde::curves::NurbsCurve::derivative </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>t</em>, </td>
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</tr>
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<tr>
|
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>order</em> = <code>1</code> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td> const</td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>在参数 t 处求导数 </p>
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||
<dl class="params"><dt>参数</dt><dd>
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||
<table class="params">
|
||
<tr><td class="paramname">t</td><td>参数值 </td></tr>
|
||
<tr><td class="paramname">order</td><td>导数阶数 </td></tr>
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||
</table>
|
||
</dd>
|
||
</dl>
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||
<dl class="section return"><dt>返回</dt><dd>导数向量 </dd></dl>
|
||
<dl class="section note"><dt>注解</dt><dd>有理导数公式： C^{(k)} = (A^{(k)} - Σ_{j=1}^{k} C(k,j) · w^{(j)} · C^{(k-j)}) / w 其中 A(t) = Σ N_i(t)·w_i·P_i，w(t) = Σ N_i(t)·w_i </dd></dl>
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||
</div>
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||
</div>
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||
<a id="a05403f0de5812c4a9e64130198ea1c1f"></a>
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||
<h2 class="memtitle"><span class="permalink"><a href="#a05403f0de5812c4a9e64130198ea1c1f">◆ </a></span>domain()</h2>
|
||
|
||
<div class="memitem">
|
||
<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">std::pair<double, double> vde::curves::NurbsCurve::domain </td>
|
||
<td>(</td>
|
||
<td class="paramname"></td><td>)</td>
|
||
<td> const</td>
|
||
</tr>
|
||
</table>
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||
</div><div class="memdoc">
|
||
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<p>参数定义域 </p>
|
||
<dl class="section return"><dt>返回</dt><dd>[knots[degree], knots[n+1]] </dd></dl>
|
||
|
||
</div>
|
||
</div>
|
||
<a id="a28fe084bb7cb16f140e77e856f5574ba"></a>
|
||
<h2 class="memtitle"><span class="permalink"><a href="#a28fe084bb7cb16f140e77e856f5574ba">◆ </a></span>evaluate()</h2>
|
||
|
||
<div class="memitem">
|
||
<div class="memproto">
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||
<table class="memname">
|
||
<tr>
|
||
<td class="memname">Point3D vde::curves::NurbsCurve::evaluate </td>
|
||
<td>(</td>
|
||
<td class="paramtype">double </td>
|
||
<td class="paramname"><em>t</em></td><td>)</td>
|
||
<td> const</td>
|
||
</tr>
|
||
</table>
|
||
</div><div class="memdoc">
|
||
|
||
<p>在参数 t 处求值 </p>
|
||
<dl class="params"><dt>参数</dt><dd>
|
||
<table class="params">
|
||
<tr><td class="paramname">t</td><td>参数值 </td></tr>
|
||
</table>
|
||
</dd>
|
||
</dl>
|
||
<dl class="section return"><dt>返回</dt><dd>曲线上对应 t 的点坐标 </dd></dl>
|
||
<dl class="section note"><dt>注解</dt><dd>内部将 (w·P, w) 提升为齐次坐标的 B 样条，求值后投影回 3D </dd></dl>
|
||
|
||
</div>
|
||
</div>
|
||
<a id="a4c288f68dc1cacd4b8ffb3d827c2aeea"></a>
|
||
<h2 class="memtitle"><span class="permalink"><a href="#a4c288f68dc1cacd4b8ffb3d827c2aeea">◆ </a></span>knots()</h2>
|
||
|
||
<div class="memitem">
|
||
<div class="memproto">
|
||
<table class="mlabels">
|
||
<tr>
|
||
<td class="mlabels-left">
|
||
<table class="memname">
|
||
<tr>
|
||
<td class="memname">const std::vector<double>& vde::curves::NurbsCurve::knots </td>
|
||
<td>(</td>
|
||
<td class="paramname"></td><td>)</td>
|
||
<td> const</td>
|
||
</tr>
|
||
</table>
|
||
</td>
|
||
<td class="mlabels-right">
|
||
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
|
||
</tr>
|
||
</table>
|
||
</div><div class="memdoc">
|
||
|
||
<p>节点向量访问 </p>
|
||
<dl class="section return"><dt>返回</dt><dd>只读引用 </dd></dl>
|
||
|
||
<p class="definition">在文件 <a class="el" href="nurbs__curve_8h_source.html">nurbs_curve.h</a> 第 <a class="el" href="nurbs__curve_8h_source.html#l00091">91</a> 行定义.</p>
|
||
|
||
</div>
|
||
</div>
|
||
<a id="aab263a3fd901ca9202624b7c18f5bca4"></a>
|
||
<h2 class="memtitle"><span class="permalink"><a href="#aab263a3fd901ca9202624b7c18f5bca4">◆ </a></span>weights()</h2>
|
||
|
||
<div class="memitem">
|
||
<div class="memproto">
|
||
<table class="mlabels">
|
||
<tr>
|
||
<td class="mlabels-left">
|
||
<table class="memname">
|
||
<tr>
|
||
<td class="memname">const std::vector<double>& vde::curves::NurbsCurve::weights </td>
|
||
<td>(</td>
|
||
<td class="paramname"></td><td>)</td>
|
||
<td> const</td>
|
||
</tr>
|
||
</table>
|
||
</td>
|
||
<td class="mlabels-right">
|
||
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
|
||
</tr>
|
||
</table>
|
||
</div><div class="memdoc">
|
||
|
||
<p>权重访问 </p>
|
||
<dl class="section return"><dt>返回</dt><dd>只读引用 </dd></dl>
|
||
|
||
<p class="definition">在文件 <a class="el" href="nurbs__curve_8h_source.html">nurbs_curve.h</a> 第 <a class="el" href="nurbs__curve_8h_source.html#l00085">85</a> 行定义.</p>
|
||
|
||
</div>
|
||
</div>
|
||
<hr/>该类的文档由以下文件生成:<ul>
|
||
<li>include/vde/curves/<a class="el" href="nurbs__curve_8h_source.html">nurbs_curve.h</a></li>
|
||
</ul>
|
||
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