茂之钳
494 lines
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494 lines
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<div id="projectname">ViewDesignEngine
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 <span id="projectnumber">3.1.0</span>
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<div id="projectbrief">高性能 CAD 计算几何引擎</div>
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<div class="header">
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<div class="summary">
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<a href="#pub-methods">Public 成员函数</a> |
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<a href="classvde_1_1sketch_1_1ConstraintSolver-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::sketch::ConstraintSolver类 参考<div class="ingroups"><a class="el" href="group__sketch.html">草图模块 (vde::sketch)</a></div></div> </div>
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</div><!--header-->
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<div class="contents">
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<p>二维几何约束求解器
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<a href="classvde_1_1sketch_1_1ConstraintSolver.html#details">更多...</a></p>
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<p><code>#include <<a class="el" href="constraint__solver_8h_source.html">constraint_solver.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:a2e7b997e006b4daa6c2243bf2131fc85"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#a2e7b997e006b4daa6c2243bf2131fc85">add_point</a> (double x, double y, bool fixed=false)</td></tr>
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<tr class="memdesc:a2e7b997e006b4daa6c2243bf2131fc85"><td class="mdescLeft"> </td><td class="mdescRight">添加自由点 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#a2e7b997e006b4daa6c2243bf2131fc85">更多...</a><br /></td></tr>
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<tr class="separator:a2e7b997e006b4daa6c2243bf2131fc85"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ac19676b3a70a8fa2a5e0379f0c5f721c"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#ac19676b3a70a8fa2a5e0379f0c5f721c">add_line</a> (int p0, int p1)</td></tr>
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<tr class="memdesc:ac19676b3a70a8fa2a5e0379f0c5f721c"><td class="mdescLeft"> </td><td class="mdescRight">添加线段 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#ac19676b3a70a8fa2a5e0379f0c5f721c">更多...</a><br /></td></tr>
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<tr class="separator:ac19676b3a70a8fa2a5e0379f0c5f721c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ad4e765480991df078531640548ea665b"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#ad4e765480991df078531640548ea665b">add_circle</a> (int center, double radius)</td></tr>
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<tr class="memdesc:ad4e765480991df078531640548ea665b"><td class="mdescLeft"> </td><td class="mdescRight">添加圆 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#ad4e765480991df078531640548ea665b">更多...</a><br /></td></tr>
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<tr class="separator:ad4e765480991df078531640548ea665b"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa6842123b8a570cf802a26276a540d85"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#aa6842123b8a570cf802a26276a540d85">add_constraint</a> (<a class="el" href="group__sketch.html#gaad27ecad61ea382a4ea2f61366fdd1b3">ConstraintType</a> type, const std::vector< int > &elements, double val=0.0)</td></tr>
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<tr class="memdesc:aa6842123b8a570cf802a26276a540d85"><td class="mdescLeft"> </td><td class="mdescRight">添加约束 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#aa6842123b8a570cf802a26276a540d85">更多...</a><br /></td></tr>
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<tr class="separator:aa6842123b8a570cf802a26276a540d85"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a4053dee188a1d77c9633d7606e304dba"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#a4053dee188a1d77c9633d7606e304dba">fix_point</a> (int pid)</td></tr>
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<tr class="memdesc:a4053dee188a1d77c9633d7606e304dba"><td class="mdescLeft"> </td><td class="mdescRight">标记点为固定（硬约束） <a href="classvde_1_1sketch_1_1ConstraintSolver.html#a4053dee188a1d77c9633d7606e304dba">更多...</a><br /></td></tr>
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<tr class="separator:a4053dee188a1d77c9633d7606e304dba"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a4ee3bc183f2d651f89c584675b8c10d9"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structvde_1_1sketch_1_1SolverResult.html">SolverResult</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#a4ee3bc183f2d651f89c584675b8c10d9">solve</a> (int max_iter=100, double tol=1e-8)</td></tr>
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<tr class="memdesc:a4ee3bc183f2d651f89c584675b8c10d9"><td class="mdescLeft"> </td><td class="mdescRight">执行约束求解 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#a4ee3bc183f2d651f89c584675b8c10d9">更多...</a><br /></td></tr>
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<tr class="separator:a4ee3bc183f2d651f89c584675b8c10d9"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a91d17aa7e2f52755b4af5dd424b34120"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#a91d17aa7e2f52755b4af5dd424b34120">degrees_of_freedom</a> () const</td></tr>
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<tr class="memdesc:a91d17aa7e2f52755b4af5dd424b34120"><td class="mdescLeft"> </td><td class="mdescRight">计算自由度 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#a91d17aa7e2f52755b4af5dd424b34120">更多...</a><br /></td></tr>
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<tr class="separator:a91d17aa7e2f52755b4af5dd424b34120"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a9d03d290c64a652a98245552583919f9"><td class="memItemLeft" align="right" valign="top">const std::vector< <a class="el" href="structvde_1_1sketch_1_1SketchPoint.html">SketchPoint</a> > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#a9d03d290c64a652a98245552583919f9">points</a> () const</td></tr>
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<tr class="memdesc:a9d03d290c64a652a98245552583919f9"><td class="mdescLeft"> </td><td class="mdescRight">当前点集访问 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#a9d03d290c64a652a98245552583919f9">更多...</a><br /></td></tr>
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<tr class="separator:a9d03d290c64a652a98245552583919f9"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a11d82c59907150da286cafe0f52cc62a"><td class="memItemLeft" align="right" valign="top">Point2D </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1sketch_1_1ConstraintSolver.html#a11d82c59907150da286cafe0f52cc62a">get_point</a> (int id) const</td></tr>
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<tr class="memdesc:a11d82c59907150da286cafe0f52cc62a"><td class="mdescLeft"> </td><td class="mdescRight">查询点坐标 <a href="classvde_1_1sketch_1_1ConstraintSolver.html#a11d82c59907150da286cafe0f52cc62a">更多...</a><br /></td></tr>
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<tr class="separator:a11d82c59907150da286cafe0f52cc62a"><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>二维几何约束求解器 </p>
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<p>基于 Gauss-Newton 非线性最小二乘的 2D 草图约束求解器。 支持点、线段、圆元素的水平/垂直/平行/垂直/相切/距离/角度等约束。</p>
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<p>求解流程：</p><ol type="1">
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<li>构建变量向量（非固定点的 x,y 坐标）</li>
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<li>对每个约束方程计算残差向量 r(x)</li>
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<li>数值 Jacobian J = ∂r/∂x（中心差分）</li>
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<li>Gauss-Newton 步：Δx = -(J^T J)^{-1} J^T r</li>
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<li>x ← x + Δx，重复直到收敛或 max_iter</li>
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</ol>
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<p>自由度分析： DOF = 2·N_free_points - Σ(约束方程数) DOF > 0 → 欠约束（解不唯一） DOF = 0 → 恰定（应有唯一解） DOF < 0 → 过约束（最小二乘意义下求解）</p>
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<div class="fragment"><div class="line">ConstraintSolver solver;</div>
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<div class="line"><span class="keywordtype">int</span> p0 = solver.add_point(0, 0); <span class="comment">// 原点</span></div>
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<div class="line"><span class="keywordtype">int</span> p1 = solver.add_point(100, 0);</div>
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<div class="line"><span class="keywordtype">int</span> p2 = solver.add_point(100, 50);</div>
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<div class="line">solver.add_line(p0, p1); <span class="comment">// 底边</span></div>
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<div class="line">solver.fix_point(p0); <span class="comment">// 原点固定</span></div>
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<div class="line">solver.add_constraint(<a class="code" href="group__sketch.html#ggaad27ecad61ea382a4ea2f61366fdd1b3ac1b5fa03ecdb95d4a45dd1c40b02527f">ConstraintType::Horizontal</a>, {p0, p1});</div>
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<div class="line">solver.add_constraint(<a class="code" href="group__sketch.html#ggaad27ecad61ea382a4ea2f61366fdd1b3a0aa6f4210bf373c95eda00232e93cd98">ConstraintType::Distance</a>, {p0, p2}, 100.0);</div>
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<div class="line"> </div>
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<div class="line"><span class="keyword">auto</span> result = solver.solve();</div>
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<div class="line"><span class="keywordflow">if</span> (result.converged) {</div>
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<div class="line"> <span class="keyword">auto</span> p = result.points;</div>
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<div class="line">}</div>
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<div class="ttc" id="agroup__sketch_html_ggaad27ecad61ea382a4ea2f61366fdd1b3a0aa6f4210bf373c95eda00232e93cd98"><div class="ttname"><a href="group__sketch.html#ggaad27ecad61ea382a4ea2f61366fdd1b3a0aa6f4210bf373c95eda00232e93cd98">vde::sketch::ConstraintType::Distance</a></div><div class="ttdeci">@ Distance</div><div class="ttdoc">距离约束: |p1-p0| - d = 0 [1 eq]</div></div>
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<div class="ttc" id="agroup__sketch_html_ggaad27ecad61ea382a4ea2f61366fdd1b3ac1b5fa03ecdb95d4a45dd1c40b02527f"><div class="ttname"><a href="group__sketch.html#ggaad27ecad61ea382a4ea2f61366fdd1b3ac1b5fa03ecdb95d4a45dd1c40b02527f">vde::sketch::ConstraintType::Horizontal</a></div><div class="ttdeci">@ Horizontal</div><div class="ttdoc">水平线: y1 - y0 = 0 [1 eq]</div></div>
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</div><!-- fragment -->
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<p class="definition">在文件 <a class="el" href="constraint__solver_8h_source.html">constraint_solver.h</a> 第 <a class="el" href="constraint__solver_8h_source.html#l00124">124</a> 行定义.</p>
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</div><h2 class="groupheader">成员函数说明</h2>
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<a id="ad4e765480991df078531640548ea665b"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ad4e765480991df078531640548ea665b">◆ </a></span>add_circle()</h2>
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<div class="memitem">
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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">int vde::sketch::ConstraintSolver::add_circle </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>center</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">double </td>
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<td class="paramname"><em>radius</em> </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></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>添加圆 </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">center</td><td>圆心点 ID </td></tr>
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<tr><td class="paramname">radius</td><td>半径 </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>返回</dt><dd>圆 ID </dd></dl>
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</div>
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</div>
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<a id="aa6842123b8a570cf802a26276a540d85"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aa6842123b8a570cf802a26276a540d85">◆ </a></span>add_constraint()</h2>
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<div class="memitem">
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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">void vde::sketch::ConstraintSolver::add_constraint </td>
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<td>(</td>
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<td class="paramtype"><a class="el" href="group__sketch.html#gaad27ecad61ea382a4ea2f61366fdd1b3">ConstraintType</a> </td>
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<td class="paramname"><em>type</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">const std::vector< int > & </td>
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<td class="paramname"><em>elements</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">double </td>
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<td class="paramname"><em>val</em> = <code>0.0</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></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>添加约束 </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">type</td><td>约束类型 </td></tr>
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<tr><td class="paramname">elements</td><td>约束涉及的元素 ID 列表 </td></tr>
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<tr><td class="paramname">val</td><td>约束值（距离、角度等），默认 0</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>不同类型 elements 的语义： Horizontal/Vertical: {p0, p1} Parallel/Perpendicular: {l0_p0, l0_p1, l1_p0, l1_p1} Distance: {p0, p1}, val = 距离 Angle: {l0_p0, l0_p1, l1_p0, l1_p1}, val = 角度（度） Radius: {circle_id}, val = 半径 Tangent: {line_p0, line_p1, circle_id} Coincident: {p0, p1} </dd></dl>
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</div>
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<a id="ac19676b3a70a8fa2a5e0379f0c5f721c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ac19676b3a70a8fa2a5e0379f0c5f721c">◆ </a></span>add_line()</h2>
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<div class="memitem">
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<td class="memname">int vde::sketch::ConstraintSolver::add_line </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>p0</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>p1</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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</table>
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</div><div class="memdoc">
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<p>添加线段 </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">p0</td><td>起点 ID </td></tr>
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<tr><td class="paramname">p1</td><td>终点 ID </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>返回</dt><dd>线段 ID </dd></dl>
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<a id="a2e7b997e006b4daa6c2243bf2131fc85"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a2e7b997e006b4daa6c2243bf2131fc85">◆ </a></span>add_point()</h2>
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<div class="memitem">
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<td class="memname">int vde::sketch::ConstraintSolver::add_point </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>y</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">bool </td>
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<td class="paramname"><em>fixed</em> = <code>false</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></td>
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</div><div class="memdoc">
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<p>添加自由点 </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">x</td><td>X 坐标 </td></tr>
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<tr><td class="paramname">y</td><td>Y 坐标 </td></tr>
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<tr><td class="paramname">fixed</td><td>是否固定（true 则排除变量） </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>返回</dt><dd>点 ID </dd></dl>
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</div>
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</div>
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<a id="a91d17aa7e2f52755b4af5dd424b34120"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a91d17aa7e2f52755b4af5dd424b34120">◆ </a></span>degrees_of_freedom()</h2>
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<td class="memname">int vde::sketch::ConstraintSolver::degrees_of_freedom </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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<p>计算自由度 </p>
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<dl class="section return"><dt>返回</dt><dd>DOF = 2·N_free - Σ(约束方程数)</dd></dl>
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<dl class="section note"><dt>注解</dt><dd>DOF < 0 时系统过约束，求解器仍然工作但解非精确满足所有约束 </dd></dl>
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<a id="a4053dee188a1d77c9633d7606e304dba"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a4053dee188a1d77c9633d7606e304dba">◆ </a></span>fix_point()</h2>
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<td class="memname">void vde::sketch::ConstraintSolver::fix_point </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>pid</em></td><td>)</td>
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<td></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>标记点为固定（硬约束） </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">pid</td><td>点 ID </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>固定点不参与变量优化，从自由度中排除 </dd></dl>
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<p class="definition">在文件 <a class="el" href="constraint__solver_8h_source.html">constraint_solver.h</a> 第 <a class="el" href="constraint__solver_8h_source.html#l00173">173</a> 行定义.</p>
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<a id="a11d82c59907150da286cafe0f52cc62a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a11d82c59907150da286cafe0f52cc62a">◆ </a></span>get_point()</h2>
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<td class="memname">Point2D vde::sketch::ConstraintSolver::get_point </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>id</em></td><td>)</td>
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<td> const</td>
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<p>查询点坐标 </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">id</td><td>点 ID </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>返回</dt><dd>Point2D 当前坐标 </dd></dl>
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</div>
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</div>
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<a id="a9d03d290c64a652a98245552583919f9"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a9d03d290c64a652a98245552583919f9">◆ </a></span>points()</h2>
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<td class="memname">const std::vector<<a class="el" href="structvde_1_1sketch_1_1SketchPoint.html">SketchPoint</a>>& vde::sketch::ConstraintSolver::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>
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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>当前点集访问 </p>
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<dl class="section return"><dt>返回</dt><dd><a class="el" href="structvde_1_1sketch_1_1SketchPoint.html" title="草图点元素">SketchPoint</a> 数组只读引用 </dd></dl>
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<p class="definition">在文件 <a class="el" href="constraint__solver_8h_source.html">constraint_solver.h</a> 第 <a class="el" href="constraint__solver_8h_source.html#l00201">201</a> 行定义.</p>
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<a id="a4ee3bc183f2d651f89c584675b8c10d9"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a4ee3bc183f2d651f89c584675b8c10d9">◆ </a></span>solve()</h2>
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<td class="memname"><a class="el" href="structvde_1_1sketch_1_1SolverResult.html">SolverResult</a> vde::sketch::ConstraintSolver::solve </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>max_iter</em> = <code>100</code>, </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">double </td>
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<td class="paramname"><em>tol</em> = <code>1e-8</code> </td>
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<tr>
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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>执行约束求解 </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">max_iter</td><td>最大 Gauss-Newton 迭代次数，默认 100 </td></tr>
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<tr><td class="paramname">tol</td><td>收敛容差（梯度范数 < tol 时停止），默认 1e-8 </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>返回</dt><dd><a class="el" href="structvde_1_1sketch_1_1SolverResult.html" title="求解器返回结果">SolverResult</a> 求解结果</dd></dl>
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<dl class="section note"><dt>注解</dt><dd>收敛判断：||J^T r|| < tol </dd>
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<dd>
|
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欠约束时（DOF > 0）解不唯一；过约束时（DOF < 0）为最小二乘解 </dd></dl>
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</div>
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</div>
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<hr/>该类的文档由以下文件生成:<ul>
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<li>include/vde/sketch/<a class="el" href="constraint__solver_8h_source.html">constraint_solver.h</a></li>
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</ul>
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