茂之钳
390 lines
19 KiB
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390 lines
19 KiB
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<a href="#pub-methods">Public 成员函数</a> |
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<a href="classvde_1_1curves_1_1BezierSurface-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::BezierSurface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>Bézier 张量积曲面
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<a href="classvde_1_1curves_1_1BezierSurface.html#details">更多...</a></p>
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<p><code>#include <<a class="el" href="bezier__surface_8h_source.html">bezier_surface.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:a42924a75e61094ca1c9179f69407735a"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1BezierSurface.html#a42924a75e61094ca1c9179f69407735a">BezierSurface</a> (std::vector< std::vector< Point3D >> control_grid)</td></tr>
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<tr class="memdesc:a42924a75e61094ca1c9179f69407735a"><td class="mdescLeft"> </td><td class="mdescRight">构造 Bézier 曲面 <a href="classvde_1_1curves_1_1BezierSurface.html#a42924a75e61094ca1c9179f69407735a">更多...</a><br /></td></tr>
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<tr class="separator:a42924a75e61094ca1c9179f69407735a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a449f820a43c4b3ed267ed50bf3d523c6"><td class="memItemLeft" align="right" valign="top">Point3D </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1BezierSurface.html#a449f820a43c4b3ed267ed50bf3d523c6">evaluate</a> (double u, double v) const</td></tr>
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<tr class="memdesc:a449f820a43c4b3ed267ed50bf3d523c6"><td class="mdescLeft"> </td><td class="mdescRight">求曲面点 S(u,v) <a href="classvde_1_1curves_1_1BezierSurface.html#a449f820a43c4b3ed267ed50bf3d523c6">更多...</a><br /></td></tr>
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<tr class="separator:a449f820a43c4b3ed267ed50bf3d523c6"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:afccb4ed65d78f483d1bf159ec82bbb79"><td class="memItemLeft" align="right" valign="top">Vector3D </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1BezierSurface.html#afccb4ed65d78f483d1bf159ec82bbb79">derivative_u</a> (double u, double v) const</td></tr>
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<tr class="memdesc:afccb4ed65d78f483d1bf159ec82bbb79"><td class="mdescLeft"> </td><td class="mdescRight">u 方向偏导数 ∂S/∂u <a href="classvde_1_1curves_1_1BezierSurface.html#afccb4ed65d78f483d1bf159ec82bbb79">更多...</a><br /></td></tr>
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<tr class="separator:afccb4ed65d78f483d1bf159ec82bbb79"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a388ce9dbb5cc9487e5c33d681ee990fc"><td class="memItemLeft" align="right" valign="top">Vector3D </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1BezierSurface.html#a388ce9dbb5cc9487e5c33d681ee990fc">derivative_v</a> (double u, double v) const</td></tr>
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<tr class="memdesc:a388ce9dbb5cc9487e5c33d681ee990fc"><td class="mdescLeft"> </td><td class="mdescRight">v 方向偏导数 ∂S/∂v <a href="classvde_1_1curves_1_1BezierSurface.html#a388ce9dbb5cc9487e5c33d681ee990fc">更多...</a><br /></td></tr>
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<tr class="separator:a388ce9dbb5cc9487e5c33d681ee990fc"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8880613cba401e5a1416c23cefecab22"><td class="memItemLeft" align="right" valign="top">Vector3D </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1BezierSurface.html#a8880613cba401e5a1416c23cefecab22">normal</a> (double u, double v) const</td></tr>
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<tr class="memdesc:a8880613cba401e5a1416c23cefecab22"><td class="mdescLeft"> </td><td class="mdescRight">单位法向量 N(u,v) = (∂S/∂u × ∂S/∂v) / |…| <a href="classvde_1_1curves_1_1BezierSurface.html#a8880613cba401e5a1416c23cefecab22">更多...</a><br /></td></tr>
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<tr class="separator:a8880613cba401e5a1416c23cefecab22"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a13c65b10bc2dc6b09742e178e0bb5955"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1BezierSurface.html#a13c65b10bc2dc6b09742e178e0bb5955">degree_u</a> () const</td></tr>
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<tr class="memdesc:a13c65b10bc2dc6b09742e178e0bb5955"><td class="mdescLeft"> </td><td class="mdescRight">u 向阶次 <a href="classvde_1_1curves_1_1BezierSurface.html#a13c65b10bc2dc6b09742e178e0bb5955">更多...</a><br /></td></tr>
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<tr class="separator:a13c65b10bc2dc6b09742e178e0bb5955"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a175dd533c3cc9ff6bf08c1d257cd5c8f"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classvde_1_1curves_1_1BezierSurface.html#a175dd533c3cc9ff6bf08c1d257cd5c8f">degree_v</a> () const</td></tr>
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<tr class="memdesc:a175dd533c3cc9ff6bf08c1d257cd5c8f"><td class="mdescLeft"> </td><td class="mdescRight">v 向阶次 <a href="classvde_1_1curves_1_1BezierSurface.html#a175dd533c3cc9ff6bf08c1d257cd5c8f">更多...</a><br /></td></tr>
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<tr class="separator:a175dd533c3cc9ff6bf08c1d257cd5c8f"><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>Bézier 张量积曲面 </p>
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<p>由 (m+1)×(n+1) 控制点网格定义，m = degree_u，n = degree_v。 参数域 (u,v) ∈ [0,1]×[0,1]，四个角点插值网格四角。</p>
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<p>求值公式：S(u,v) = Σ_i Σ_j P_{ij} · B_i^m(u) · B_j^n(v) </p>
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<p class="definition">在文件 <a class="el" href="bezier__surface_8h_source.html">bezier_surface.h</a> 第 <a class="el" href="bezier__surface_8h_source.html#l00019">19</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="a42924a75e61094ca1c9179f69407735a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a42924a75e61094ca1c9179f69407735a">◆ </a></span>BezierSurface()</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">vde::curves::BezierSurface::BezierSurface </td>
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<td>(</td>
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<td class="paramtype">std::vector< std::vector< Point3D >> </td>
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<td class="paramname"><em>control_grid</em></td><td>)</td>
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<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>构造 Bézier 曲面 </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_grid</td><td>控制点网格，grid[i][j] 对应 u 方向第 i 个、v 方向第 j 个控制点 </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>grid 必须矩整（所有行等长）；grid.size() = degree_u+1, grid[0].size() = degree_v+1 <div class="fragment"><div class="line"><span class="comment">// 3x3 控制网格 → 双二次 Bézier 曲面</span></div>
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<div class="line"><a class="code" href="classvde_1_1curves_1_1BezierSurface.html#a42924a75e61094ca1c9179f69407735a">BezierSurface</a> surf({{p00,p01,p02}, {p10,p11,p12}, {p20,p21,p22}});</div>
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<div class="ttc" id="aclassvde_1_1curves_1_1BezierSurface_html_a42924a75e61094ca1c9179f69407735a"><div class="ttname"><a href="classvde_1_1curves_1_1BezierSurface.html#a42924a75e61094ca1c9179f69407735a">vde::curves::BezierSurface::BezierSurface</a></div><div class="ttdeci">BezierSurface(std::vector< std::vector< Point3D >> control_grid)</div><div class="ttdoc">构造 Bézier 曲面</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="a13c65b10bc2dc6b09742e178e0bb5955"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a13c65b10bc2dc6b09742e178e0bb5955">◆ </a></span>degree_u()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="mlabels">
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<tr>
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<td class="mlabels-left">
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<table class="memname">
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<tr>
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<td class="memname">int vde::curves::BezierSurface::degree_u </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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</tr>
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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>u 向阶次 </p>
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<dl class="section return"><dt>返回</dt><dd>u 方向阶次（控制点行数 - 1） </dd></dl>
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<p class="definition">在文件 <a class="el" href="bezier__surface_8h_source.html">bezier_surface.h</a> 第 <a class="el" href="bezier__surface_8h_source.html#l00071">71</a> 行定义.</p>
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</div>
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</div>
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<a id="a175dd533c3cc9ff6bf08c1d257cd5c8f"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a175dd533c3cc9ff6bf08c1d257cd5c8f">◆ </a></span>degree_v()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="mlabels">
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<tr>
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<td class="mlabels-left">
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<table class="memname">
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<tr>
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<td class="memname">int vde::curves::BezierSurface::degree_v </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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</tr>
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</table>
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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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</tr>
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</table>
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</div><div class="memdoc">
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<p>v 向阶次 </p>
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<dl class="section return"><dt>返回</dt><dd>v 方向阶次（控制点列数 - 1） </dd></dl>
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<p class="definition">在文件 <a class="el" href="bezier__surface_8h_source.html">bezier_surface.h</a> 第 <a class="el" href="bezier__surface_8h_source.html#l00077">77</a> 行定义.</p>
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</div>
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</div>
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<a id="afccb4ed65d78f483d1bf159ec82bbb79"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#afccb4ed65d78f483d1bf159ec82bbb79">◆ </a></span>derivative_u()</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">Vector3D vde::curves::BezierSurface::derivative_u </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>u</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>v</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> 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>u 方向偏导数 ∂S/∂u </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">u</td><td>u 参数 </td></tr>
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<tr><td class="paramname">v</td><td>v 参数 </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>u 方向切向量 </dd></dl>
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<dl class="section note"><dt>注解</dt><dd>通过降阶 Bézier 曲线计算：对 v 求值后沿 u 求导 </dd></dl>
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</div>
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</div>
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<a id="a388ce9dbb5cc9487e5c33d681ee990fc"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a388ce9dbb5cc9487e5c33d681ee990fc">◆ </a></span>derivative_v()</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">Vector3D vde::curves::BezierSurface::derivative_v </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>u</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>v</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> 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>v 方向偏导数 ∂S/∂v </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">u</td><td>u 参数 </td></tr>
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<tr><td class="paramname">v</td><td>v 参数 </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>v 方向切向量 </dd></dl>
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||
</div>
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</div>
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<a id="a449f820a43c4b3ed267ed50bf3d523c6"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a449f820a43c4b3ed267ed50bf3d523c6">◆ </a></span>evaluate()</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">Point3D vde::curves::BezierSurface::evaluate </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>u</em>, </td>
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||
</tr>
|
||
<tr>
|
||
<td class="paramkey"></td>
|
||
<td></td>
|
||
<td class="paramtype">double </td>
|
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<td class="paramname"><em>v</em> </td>
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||
</tr>
|
||
<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>求曲面点 S(u,v) </p>
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<dl class="params"><dt>参数</dt><dd>
|
||
<table class="params">
|
||
<tr><td class="paramname">u</td><td>u 参数，范围 [0, 1] </td></tr>
|
||
<tr><td class="paramname">v</td><td>v 参数，范围 [0, 1] </td></tr>
|
||
</table>
|
||
</dd>
|
||
</dl>
|
||
<dl class="section return"><dt>返回</dt><dd>曲面上对应 (u,v) 的 3D 坐标 </dd></dl>
|
||
<dl class="section note"><dt>注解</dt><dd>张量积求值：先按 v 方向对每行做 de Casteljau，再沿 u 方向对结果做一次 </dd></dl>
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||
|
||
</div>
|
||
</div>
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<a id="a8880613cba401e5a1416c23cefecab22"></a>
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||
<h2 class="memtitle"><span class="permalink"><a href="#a8880613cba401e5a1416c23cefecab22">◆ </a></span>normal()</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">Vector3D vde::curves::BezierSurface::normal </td>
|
||
<td>(</td>
|
||
<td class="paramtype">double </td>
|
||
<td class="paramname"><em>u</em>, </td>
|
||
</tr>
|
||
<tr>
|
||
<td class="paramkey"></td>
|
||
<td></td>
|
||
<td class="paramtype">double </td>
|
||
<td class="paramname"><em>v</em> </td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>)</td>
|
||
<td></td><td> const</td>
|
||
</tr>
|
||
</table>
|
||
</div><div class="memdoc">
|
||
|
||
<p>单位法向量 N(u,v) = (∂S/∂u × ∂S/∂v) / |…| </p>
|
||
<dl class="params"><dt>参数</dt><dd>
|
||
<table class="params">
|
||
<tr><td class="paramname">u</td><td>u 参数 </td></tr>
|
||
<tr><td class="paramname">v</td><td>v 参数 </td></tr>
|
||
</table>
|
||
</dd>
|
||
</dl>
|
||
<dl class="section return"><dt>返回</dt><dd>归一化法向量（指向曲面的特选侧） </dd></dl>
|
||
<dl class="section note"><dt>注解</dt><dd>当两个偏导数平行时返回零向量（奇异点） </dd></dl>
|
||
|
||
</div>
|
||
</div>
|
||
<hr/>该类的文档由以下文件生成:<ul>
|
||
<li>include/vde/curves/<a class="el" href="bezier__surface_8h_source.html">bezier_surface.h</a></li>
|
||
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