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id="VPContent" data-v-3b4648ff data-v-fc04087f><div class="VPDoc has-sidebar has-aside" data-v-fc04087f data-v-01c90815><!--[--><!--]--><div class="container" data-v-01c90815><div class="aside" data-v-01c90815><div class="aside-curtain" data-v-01c90815></div><div class="aside-container" data-v-01c90815><div class="aside-content" data-v-01c90815><div class="VPDocAside" data-v-01c90815 data-v-8951c20f><!--[--><!--]--><!--[--><!--]--><nav aria-labelledby="doc-outline-aria-label" class="VPDocAsideOutline" data-v-8951c20f data-v-d34649dc><div class="content" data-v-d34649dc><div class="outline-marker" data-v-d34649dc></div><div aria-level="2" class="outline-title" id="doc-outline-aria-label" role="heading" data-v-d34649dc>页面内容</div><ul class="VPDocOutlineItem root" data-v-d34649dc data-v-b9c884bb><!--[--><!--]--></ul></div></nav><!--[--><!--]--><div class="spacer" data-v-8951c20f></div><!--[--><!--]--><!----><!--[--><!--]--><!--[--><!--]--></div></div></div></div><div class="content" data-v-01c90815><div class="content-container" data-v-01c90815><!--[--><!--]--><main class="main" data-v-01c90815><div style="position:relative;" class="vp-doc _api_mp_math_plane" data-v-01c90815><div><h1 id="模块-mbcp-mp-math-plane" tabindex="-1"><strong>模块</strong> <code>mbcp.mp_math.plane</code> <a class="header-anchor" href="#模块-mbcp-mp-math-plane" aria-label="Permalink to &quot;**模块** `mbcp.mp_math.plane`&quot;">​</a></h1><p>本模块定义了三维空间中的平面类</p><h3 id="class-plane3" tabindex="-1"><em><strong>class</strong></em> <code>Plane3</code> <a class="header-anchor" href="#class-plane3" aria-label="Permalink to &quot;***class*** `Plane3`&quot;">​</a></h3><h4 id="method-init-self-a-float-b-float-c-float-d-float" tabindex="-1"><em><strong>method</strong></em> <code>__init__(self, a: float, b: float, c: float, d: float)</code> <a class="header-anchor" href="#method-init-self-a-float-b-float-c-float-d-float" aria-label="Permalink to &quot;***method*** `__init__(self, a: float, b: float, c: float, d: float)`&quot;">​</a></h4><p><strong>说明</strong>: 平面方程：ax + by + cz + d = 0</p><p><strong>参数</strong>:</p><blockquote><ul><li>a (<a href="https://docs.python.org/3/library/functions.html#float" target="_blank" rel="noreferrer"><code>float</code></a>): x系数</li><li>b (<code>float</code>): y系数</li><li>c (<code>float</code>): z系数</li><li>d (<code>float</code>): 常数项</li></ul></blockquote><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L20" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, a: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, b: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, c: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, d: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">):</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> a</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> b</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> c</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> d</span></span></code></pre></div></details><h4 id="method-approx-self-other-plane3-bool" tabindex="-1"><em><strong>method</strong></em> <code>approx(self, other: Plane3) -&gt; bool</code> <a class="header-anchor" href="#method-approx-self-other-plane3-bool" aria-label="Permalink to &quot;***method*** `approx(self, other: Plane3) -&gt; bool`&quot;">​</a></h4><p><strong>说明</strong>: 判断两个平面是否近似相等。</p><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./plane.html#class-plane3"><code>Plane3</code></a>): 另一个平面</li></ul></blockquote><p><strong>返回</strong>: <a href="https://docs.python.org/3/library/functions.html#bool" target="_blank" rel="noreferrer"><code>bool</code></a>: 是否近似相等</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L34" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> approx</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">/</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.b, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.c, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.d, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">/</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.a, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.c, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.d, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">/</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.a, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.b, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> approx(other.d, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> k)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> else</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> False</span></span></code></pre></div></details><h4 id="method-cal-angle-self-other-line3-plane3-anyangle" tabindex="-1"><em><strong>method</strong></em> <code>cal_angle(self, other: Line3 | Plane3) -&gt; AnyAngle</code> <a class="header-anchor" href="#method-cal-angle-self-other-line3-plane3-anyangle" aria-label="Permalink to &quot;***method*** `cal_angle(self, other: Line3 | Plane3) -&gt; AnyAngle`&quot;">​</a></h4><p><strong>说明</strong>: 计算平面与平面之间的夹角。</p><div class="tip custom-block"><p class="custom-block-title">TIP</p><p>平面间夹角计算公式:</p><mjx-container tabindex="0" class="MathJax" jax="SVG" display="true" style="direction:ltr;display:block;text-align:center;margin:1em 0;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-2.17ex;" xmlns="http://www.w3.org/2000/svg" width="22.011ex" 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style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;overflow:hidden;width:100%;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>θ</mi><mo>=</mo><mi>arccos</mi><mo data-mjx-texclass="NONE">⁡</mo><mo stretchy="false">(</mo><mfrac><mrow><mi>n</mi><mn>1</mn><mo>⋅</mo><mi>n</mi><mn>2</mn></mrow><mrow><mo data-mjx-texclass="ORD" stretchy="false">|</mo><mi>n</mi><mn>1</mn><mo data-mjx-texclass="ORD" stretchy="false">|</mo><mo>⋅</mo><mo data-mjx-texclass="ORD" stretchy="false">|</mo><mi>n</mi><mn>2</mn><mo data-mjx-texclass="ORD" stretchy="false">|</mo></mrow></mfrac><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><p>其中 <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="2.489ex" height="1.532ex" role="img" focusable="false" viewBox="0 -666 1100 677" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 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style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="2.489ex" height="1.532ex" role="img" focusable="false" viewBox="0 -666 1100 677" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z" style="stroke-width:3;"></path></g><g data-mml-node="mn" 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mn>2</mn></math></mjx-assistive-mml></mjx-container> 分别为两个平面的法向量</p></div><div class="tip custom-block"><p class="custom-block-title">TIP</p><p>平面与直线夹角计算公式:</p><mjx-container tabindex="0" class="MathJax" jax="SVG" display="true" style="direction:ltr;display:block;text-align:center;margin:1em 0;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-2.17ex;" xmlns="http://www.w3.org/2000/svg" width="19.568ex" height="5.269ex" role="img" focusable="false" viewBox="0 -1370 8649 2329" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 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transform="translate(1378.2,0)"><path data-c="22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z" style="stroke-width:3;"></path></g><g data-mml-node="mo" transform="translate(1878.4,0) translate(0 -0.5)"><path data-c="7C" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z" style="stroke-width:3;"></path></g><g data-mml-node="mi" transform="translate(2156.4,0)"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 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1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;overflow:hidden;width:100%;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>θ</mi><mo>=</mo><mi>arccos</mi><mo data-mjx-texclass="NONE">⁡</mo><mo stretchy="false">(</mo><mfrac><mrow><mi>n</mi><mo>⋅</mo><mi>d</mi></mrow><mrow><mo data-mjx-texclass="ORD" stretchy="false">|</mo><mi>n</mi><mo data-mjx-texclass="ORD" stretchy="false">|</mo><mo>⋅</mo><mo data-mjx-texclass="ORD" stretchy="false">|</mo><mi>d</mi><mo data-mjx-texclass="ORD" stretchy="false">|</mo></mrow></mfrac><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><p>其中 <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 为平面的法向量，<mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.176ex" height="1.593ex" role="img" focusable="false" viewBox="0 -694 520 704" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></mjx-assistive-mml></mjx-container> 为直线的方向向量</p></div><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./line.html#class-line3"><code>Line3</code></a> | <a href="./plane.html#class-plane3"><code>Plane3</code></a>): 另一个平面或直线</li></ul></blockquote><p><strong>返回</strong>: <a href="./angle.html#class-anyangle"><code>AnyAngle</code></a>: 夹角</p><p><strong>引发</strong>:</p><blockquote><ul><li><a href="https://docs.python.org/3/library/exceptions.html#TypeError" target="_blank" rel="noreferrer"><code>TypeError</code></a> 不支持的类型</li></ul></blockquote><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L54" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> cal_angle</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3 | Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;AnyAngle&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other, Line3):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal.cal_angle(other.direction).complementary</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other, Plane3):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> AnyAngle(math.acos(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.normal </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal.length </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.normal.length)), </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70;">is_radian</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">True</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> else</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> raise</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> TypeError</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">f</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Unsupported type: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">{type</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other)</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">}</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span></code></pre></div></details><h4 id="method-cal-distance-self-other-plane3-point3-float" tabindex="-1"><em><strong>method</strong></em> <code>cal_distance(self, other: Plane3 | Point3) -&gt; float</code> <a class="header-anchor" href="#method-cal-distance-self-other-plane3-point3-float" aria-label="Permalink to &quot;***method*** `cal_distance(self, other: Plane3 | Point3) -&gt; float`&quot;">​</a></h4><p><strong>说明</strong>: 计算平面与平面或点之间的距离。</p><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./plane.html#class-plane3"><code>Plane3</code></a> | <a href="./point.html#class-point3"><code>Point3</code></a>): 另一个平面或点</li></ul></blockquote><p><strong>返回</strong>: <a href="https://docs.python.org/3/library/functions.html#float" target="_blank" rel="noreferrer"><code>float</code></a>: 距离</p><p><strong>引发</strong>:</p><blockquote><ul><li><a href="https://docs.python.org/3/library/exceptions.html#TypeError" target="_blank" rel="noreferrer"><code>TypeError</code></a> 不支持的类型</li></ul></blockquote><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L81" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> cal_distance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3 | Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other, Plane3):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other, Point3):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> abs</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">**</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 2</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> +</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">**</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 2</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> +</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">**</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 2</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">**</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0.5</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> else</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> raise</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> TypeError</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">f</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Unsupported type: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">{type</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other)</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">}</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span></code></pre></div></details><h4 id="method-cal-intersection-line3-self-other-plane3-line3" tabindex="-1"><em><strong>method</strong></em> <code>cal_intersection_line3(self, other: Plane3) -&gt; Line3</code> <a class="header-anchor" href="#method-cal-intersection-line3-self-other-plane3-line3" aria-label="Permalink to &quot;***method*** `cal_intersection_line3(self, other: Plane3) -&gt; Line3`&quot;">​</a></h4><p><strong>说明</strong>: 计算两平面的交线。</p><div class="tip custom-block"><p class="custom-block-title">TIP</p><p>计算两平面交线的一般步骤:</p><ol><li>求两平面的法向量的叉乘得到方向向量</li></ol><mjx-container tabindex="0" class="MathJax" jax="SVG" display="true" style="direction:ltr;display:block;text-align:center;margin:1em 0;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="11.937ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 5276 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 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display="block"><mi>d</mi><mo>=</mo><mi>n</mi><mn>1</mn><mo>×</mo><mi>n</mi><mn>2</mn></math></mjx-assistive-mml></mjx-container><ol start="2"><li>寻找直线上的一点，依次假设<mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.442ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2405.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 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1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示</li></ol><mjx-container tabindex="0" class="MathJax" jax="SVG" display="true" style="direction:ltr;display:block;text-align:center;margin:1em 0;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-3.281ex;" xmlns="http://www.w3.org/2000/svg" width="13.363ex" height="7.692ex" role="img" focusable="false" viewBox="0 -1950 5906.6 3400" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mrow"><g data-mml-node="mo"><path data-c="23A7" d="M712 899L718 893V876V865Q718 854 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0px;border:0px;display:block;overflow:hidden;width:100%;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi>x</mi><mo>−</mo><msub><mi>x</mi><mn>0</mn></msub></mrow><mi>m</mi></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>−</mo><msub><mi>y</mi><mn>0</mn></msub></mrow><mi>n</mi></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>−</mo><msub><mi>z</mi><mn>0</mn></msub></mrow><mi>p</mi></mfrac></math></mjx-assistive-mml></mjx-container></div><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./plane.html#class-plane3"><code>Plane3</code></a>): 另一个平面</li></ul></blockquote><p><strong>返回</strong>: <a href="./line.html#class-line3"><code>Line3</code></a>: 交线</p><p><strong>引发</strong>:</p><blockquote><ul><li><a href="https://docs.python.org/3/library/exceptions.html#ValueError" target="_blank" rel="noreferrer"><code>ValueError</code></a> 平面平行且无交线</li></ul></blockquote><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L98" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> cal_intersection_line3</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal.is_parallel(other.normal):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> raise</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> ValueError</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Planes are parallel and have no intersection.&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> direction </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal.cross(other.normal)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> x, y, z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> A </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.array([[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c], [other.b, other.c]])</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> B </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.array([</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">other.d])</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> y, z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.linalg.solve(A, B)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> A </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.array([[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c], [other.a, other.c]])</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> B </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.array([</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">other.d])</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> x, z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.linalg.solve(A, B)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> and</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">!=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> A </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.array([[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b], [other.a, other.b]])</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> B </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.array([</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">other.d])</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> x, y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> np.linalg.solve(A, B)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> Line3(Point3(x, y, z), direction)</span></span></code></pre></div></details><h4 id="method-cal-intersection-point3-self-other-line3-point3" tabindex="-1"><em><strong>method</strong></em> <code>cal_intersection_point3(self, other: Line3) -&gt; Point3</code> <a class="header-anchor" href="#method-cal-intersection-point3-self-other-line3-point3" aria-label="Permalink to &quot;***method*** `cal_intersection_point3(self, other: Line3) -&gt; Point3`&quot;">​</a></h4><p><strong>说明</strong>: 计算平面与直线的交点。</p><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./line.html#class-line3"><code>Line3</code></a>): 直线</li></ul></blockquote><p><strong>返回</strong>: <a href="./point.html#class-point3"><code>Point3</code></a>: 交点</p><p><strong>引发</strong>:</p><blockquote><ul><li><a href="https://docs.python.org/3/library/exceptions.html#ValueError" target="_blank" rel="noreferrer"><code>ValueError</code></a> 平面与直线平行或重合</li></ul></blockquote><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L142" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> cal_intersection_point3</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.direction </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">==</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> raise</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> ValueError</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;The plane and the line are parallel or coincident.&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> x, y, z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.get_parametric_equations()</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> -</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point.x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point.y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point.z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.d) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.direction.x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.direction.y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.direction.z)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> Point3(x(t), y(t), z(t))</span></span></code></pre></div></details><h4 id="method-cal-parallel-plane3-self-point-point3-plane3" tabindex="-1"><em><strong>method</strong></em> <code>cal_parallel_plane3(self, point: Point3) -&gt; Plane3</code> <a class="header-anchor" href="#method-cal-parallel-plane3-self-point-point3-plane3" aria-label="Permalink to &quot;***method*** `cal_parallel_plane3(self, point: Point3) -&gt; Plane3`&quot;">​</a></h4><p><strong>说明</strong>: 计算平行于该平面且过指定点的平面。</p><p><strong>参数</strong>:</p><blockquote><ul><li>point (<a href="./point.html#class-point3"><code>Point3</code></a>): 指定点</li></ul></blockquote><p><strong>返回</strong>: <a href="./plane.html#class-plane3"><code>Plane3</code></a>: 平面</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L162" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> cal_parallel_plane3</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, point: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> Plane3.from_point_and_normal(point, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal)</span></span></code></pre></div></details><h4 id="method-is-parallel-self-other-plane3-bool" tabindex="-1"><em><strong>method</strong></em> <code>is_parallel(self, other: Plane3) -&gt; bool</code> <a class="header-anchor" href="#method-is-parallel-self-other-plane3-bool" aria-label="Permalink to &quot;***method*** `is_parallel(self, other: Plane3) -&gt; bool`&quot;">​</a></h4><p><strong>说明</strong>: 判断两个平面是否平行。</p><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./plane.html#class-plane3"><code>Plane3</code></a>): 另一个平面</li></ul></blockquote><p><strong>返回</strong>: <a href="https://docs.python.org/3/library/functions.html#bool" target="_blank" rel="noreferrer"><code>bool</code></a>: 是否平行</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L172" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> is_parallel</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal.is_parallel(other.normal)</span></span></code></pre></div></details><p><a href="https://docs.python.org/3/library/functions.html#property" target="_blank" rel="noreferrer"><code>@property</code></a></p><h4 id="method-normal-self-vector3" tabindex="-1"><em><strong>method</strong></em> <code>normal(self) -&gt; Vector3</code> <a class="header-anchor" href="#method-normal-self-vector3" aria-label="Permalink to &quot;***method*** `normal(self) -&gt; Vector3`&quot;">​</a></h4><p><strong>说明</strong>: 平面的法向量。</p><p><strong>返回</strong>: <a href="./vector.html#class-vector3"><code>Vector3</code></a>: 法向量</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L183" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">@</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">property</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> normal</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Vector3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> Vector3(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.a, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.b, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.c)</span></span></code></pre></div></details><p><a href="https://docs.python.org/3/library/functions.html#classmethod" target="_blank" rel="noreferrer"><code>@classmethod</code></a></p><h4 id="method-from-point-and-normal-cls-point-point3-normal-vector3-plane3" tabindex="-1"><em><strong>method</strong></em> <code>from_point_and_normal(cls, point: Point3, normal: Vector3) -&gt; Plane3</code> <a class="header-anchor" href="#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3" aria-label="Permalink to &quot;***method*** `from_point_and_normal(cls, point: Point3, normal: Vector3) -&gt; Plane3`&quot;">​</a></h4><p><strong>说明</strong>: 工厂函数 由点和法向量构造平面(点法式构造)。</p><p><strong>参数</strong>:</p><blockquote><ul><li>point (<a href="./point.html#class-point3"><code>Point3</code></a>): 平面上一点</li><li>normal (<a href="./vector.html#class-vector3"><code>Vector3</code></a>): 法向量</li></ul></blockquote><p><strong>返回</strong>: <a href="./plane.html#class-plane3"><code>Plane3</code></a>: 平面</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L192" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">@</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">classmethod</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> from_point_and_normal</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(cls, point: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, normal: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Vector3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> a, b, c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (normal.x, normal.y, normal.z)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> d </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> -</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">a </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> point.x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> b </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> point.y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> c </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> point.z</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> cls</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(a, b, c, d)</span></span></code></pre></div></details><p><a href="https://docs.python.org/3/library/functions.html#classmethod" target="_blank" rel="noreferrer"><code>@classmethod</code></a></p><h4 id="method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3" tabindex="-1"><em><strong>method</strong></em> <code>from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -&gt; Plane3</code> <a class="header-anchor" href="#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3" aria-label="Permalink to &quot;***method*** `from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -&gt; Plane3`&quot;">​</a></h4><p><strong>说明</strong>: 工厂函数 由三点构造平面。</p><p><strong>参数</strong>:</p><blockquote><ul><li>p1 (<a href="./point.html#class-point3"><code>Point3</code></a>): 点1</li><li>p2 (<code>Point3</code>): 点2</li><li>p3 (<code>Point3</code>): 点3</li></ul></blockquote><p><strong>返回</strong>: 平面</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L206" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">@</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">classmethod</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> from_three_points</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(cls, p1: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, p2: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, p3: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v1 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> p2 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> p1</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v2 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> p3 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> p1</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> normal </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v1.cross(v2)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> cls</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.from_point_and_normal(p1, normal)</span></span></code></pre></div></details><p><a href="https://docs.python.org/3/library/functions.html#classmethod" target="_blank" rel="noreferrer"><code>@classmethod</code></a></p><h4 id="method-from-two-lines-cls-l1-line3-l2-line3-plane3" tabindex="-1"><em><strong>method</strong></em> <code>from_two_lines(cls, l1: Line3, l2: Line3) -&gt; Plane3</code> <a class="header-anchor" href="#method-from-two-lines-cls-l1-line3-l2-line3-plane3" aria-label="Permalink to &quot;***method*** `from_two_lines(cls, l1: Line3, l2: Line3) -&gt; Plane3`&quot;">​</a></h4><p><strong>说明</strong>: 工厂函数 由两直线构造平面。</p><p><strong>参数</strong>:</p><blockquote><ul><li>l1 (<a href="./line.html#class-line3"><code>Line3</code></a>): 直线</li><li>l2 (<code>Line3</code>): 直线</li></ul></blockquote><p><strong>返回</strong>: 平面</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L224" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">@</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">classmethod</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> from_two_lines</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(cls, l1: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, l2: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v1 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> l1.direction</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v2 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> l2.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> l1.point</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v2 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">==</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> zero_vector3:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v2 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> l2.get_point(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">1</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> l1.point</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> cls</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.from_point_and_normal(l1.point, v1.cross(v2))</span></span></code></pre></div></details><p><a href="https://docs.python.org/3/library/functions.html#classmethod" target="_blank" rel="noreferrer"><code>@classmethod</code></a></p><h4 id="method-from-point-and-line-cls-point-point3-line-line3-plane3" tabindex="-1"><em><strong>method</strong></em> <code>from_point_and_line(cls, point: Point3, line: Line3) -&gt; Plane3</code> <a class="header-anchor" href="#method-from-point-and-line-cls-point-point3-line-line3-plane3" aria-label="Permalink to &quot;***method*** `from_point_and_line(cls, point: Point3, line: Line3) -&gt; Plane3`&quot;">​</a></h4><p><strong>说明</strong>: 工厂函数 由点和直线构造平面。</p><p><strong>参数</strong>:</p><blockquote><ul><li>point (<a href="./point.html#class-point3"><code>Point3</code></a>): 平面上一点</li><li>line (<a href="./line.html#class-line3"><code>Line3</code></a>): 直线</li></ul></blockquote><p><strong>返回</strong>: 平面</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L240" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">@</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">classmethod</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> from_point_and_line</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(cls, point: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, line: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> cls</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.from_point_and_normal(point, line.direction)</span></span></code></pre></div></details><p><code>@overload</code></p><h4 id="method-self-other-line3-point3-none" tabindex="-1"><em><strong>method</strong></em> <code>self &amp; other: Line3 =&gt; Point3 | None</code> <a class="header-anchor" href="#method-self-other-line3-point3-none" aria-label="Permalink to &quot;***method*** `self &amp; other: Line3 =&gt; Point3 | None`&quot;">​</a></h4><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L277" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">@overload</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __and__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3 | None&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> ...</span></span></code></pre></div></details><p><code>@overload</code></p><h4 id="method-self-other-plane3-line3-none" tabindex="-1"><em><strong>method</strong></em> <code>self &amp; other: Plane3 =&gt; Line3 | None</code> <a class="header-anchor" href="#method-self-other-plane3-line3-none" aria-label="Permalink to &quot;***method*** `self &amp; other: Plane3 =&gt; Line3 | None`&quot;">​</a></h4><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L281" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;">@overload</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __and__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Plane3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3 | None&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> ...</span></span></code></pre></div></details><h4 id="method-self-other" tabindex="-1"><em><strong>method</strong></em> <code>self &amp; other</code> <a class="header-anchor" href="#method-self-other" aria-label="Permalink to &quot;***method*** `self &amp; other`&quot;">​</a></h4><p><strong>说明</strong>: 取两平面的交集（人话：交线）</p><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./line.html#class-line3"><code>Line3</code></a> | <a href="./plane.html#class-plane3"><code>Plane3</code></a>): 另一个平面或直线</li></ul></blockquote><p><strong>返回</strong>: <a href="./line.html#class-line3"><code>Line3</code></a> | <a href="./point.html#class-point3"><code>Point3</code></a> | <a href="https://docs.python.org/3/library/constants.html#None" target="_blank" rel="noreferrer"><code>None</code></a>: 交集</p><p><strong>引发</strong>:</p><blockquote><ul><li><a href="https://docs.python.org/3/library/exceptions.html#TypeError" target="_blank" rel="noreferrer"><code>TypeError</code></a> 不支持的类型</li></ul></blockquote><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L284" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __and__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other, Plane3):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal.is_parallel(other.normal):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> None</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.cal_intersection_line3(other)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other, Line3):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.normal </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.direction </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">==</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> None</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.cal_intersection_point3(other)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> else</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> raise</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> TypeError</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">f</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&quot;unsupported operand type(s) for &amp;: &#39;Plane3&#39; and &#39;</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">{type</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(other)</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">}</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;&quot;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span></code></pre></div></details><h4 id="method-self-other-bool" tabindex="-1"><em><strong>method</strong></em> <code>self == other =&gt; bool</code> <a class="header-anchor" href="#method-self-other-bool" aria-label="Permalink to &quot;***method*** `self == other =&gt; bool`&quot;">​</a></h4><p><strong>说明</strong>: 判断两个平面是否等价。</p><p><strong>参数</strong>:</p><blockquote><ul><li>other (<a href="./plane.html#class-plane3"><code>Plane3</code></a>): 另一个平面</li></ul></blockquote><p><strong>返回</strong>: <a href="https://docs.python.org/3/library/functions.html#bool" target="_blank" rel="noreferrer"><code>bool</code></a>: 是否等价</p><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L305" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __eq__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other) -&gt; </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.approx(other)</span></span></code></pre></div></details><h4 id="method-self-other-line3-point3" tabindex="-1"><em><strong>method</strong></em> <code>self &amp; other: Line3 =&gt; Point3</code> <a class="header-anchor" href="#method-self-other-line3-point3" aria-label="Permalink to &quot;***method*** `self &amp; other: Line3 =&gt; Point3`&quot;">​</a></h4><details><summary><b>源代码</b> 或 <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/plane.py#L315" target="_blank">在GitHub上查看</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __rand__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.cal_intersection_point3(other)</span></span></code></pre></div></details></div></div></main><footer class="VPDocFooter" data-v-01c90815 data-v-28deee4a><!--[--><!--]--><div class="edit-info" data-v-28deee4a><div class="edit-link" data-v-28deee4a><a class="VPLink link vp-external-link-icon no-icon edit-link-button" href="https://github.com/snowykami/mbcp/tree/main/mbcp//mp_math/plane.py" target="_blank" rel="noreferrer" data-v-28deee4a><!--[--><span class="vpi-square-pen edit-link-icon" data-v-28deee4a></span> 在 GitHub 上编辑此页<!--]--></a></div><!----></div><nav class="prev-next" aria-labelledby="doc-footer-aria-label" data-v-28deee4a><span class="visually-hidden" id="doc-footer-aria-label" data-v-28deee4a>Pager</span><div class="pager" data-v-28deee4a><a class="VPLink link pager-link prev" href="/api/mp_math/mp_math_typing.html" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>上一页</span><span class="title" data-v-28deee4a>mbcp.mp_math.mp_math_typing</span><!--]--></a></div><div class="pager" data-v-28deee4a><a class="VPLink link pager-link next" href="/api/mp_math/point.html" data-v-28deee4a><!--[--><span class="desc" data-v-28deee4a>下一页</span><span class="title" data-v-28deee4a>mbcp.mp_math.point</span><!--]--></a></div></nav></footer><!--[--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter has-sidebar" data-v-3b4648ff data-v-d69bcf5d><div class="container" data-v-d69bcf5d><p class="message" data-v-d69bcf5d>文档由 <a href="https://vitepress.dev/">VitePress</a> 构建 | API引用由 <a href="https://github.com/LiteyukiStudio/litedoc">litedoc</a> 生成</p><p class="copyright" data-v-d69bcf5d>Copyright (C) 2020-2024 SnowyKami. All Rights Reserved</p></div></footer><!--[--><!--]--></div></div>
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