mbcp/assets/en_api_mp_math_line.md.CIOnk8LF.js

import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n(`<h1 id="mbcp-mp-math-line" tabindex="-1">mbcp.mp_math.line <a class="header-anchor" href="#mbcp-mp-math-line" aria-label="Permalink to &quot;mbcp.mp_math.line&quot;">​</a></h1><p><strong>Description</strong>: 本模块定义了三维空间中的直线类</p><h3 id="class-line3" tabindex="-1"><em><strong>class</strong></em> <code>Line3</code> <a class="header-anchor" href="#class-line3" aria-label="Permalink to &quot;***class*** \`Line3\`&quot;">​</a></h3><h4 id="def-init-self-point-point3-direction-vector3" tabindex="-1"><em><strong>def</strong></em> <code>__init__(self, point: Point3, direction: Vector3)</code> <a class="header-anchor" href="#def-init-self-point-point3-direction-vector3" aria-label="Permalink to &quot;***def*** \`__init__(self, point: Point3, direction: Vector3)\`&quot;">​</a></h4><p><strong>Description</strong>: 三维空间中的直线。由一个点和一个方向向量确定。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>point: 直线上的一点</li><li>direction: 直线的方向向量</li></ul></blockquote><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L19" target="_blank" rel="noreferrer">View on GitHub</a></p><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, point: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Point3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, direction: </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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        三维空间中的直线。由一个点和一个方向向量确定。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            point: 直线上的一点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            direction: 直线的方向向量</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">    self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> point</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">    self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> direction</span></span></code></pre></div></details><h4 id="def-approx-self-other-line3-epsilon-float-approx-bool" tabindex="-1"><em><strong>def</strong></em> <code>approx(self, other: Line3, epsilon: float = APPROX) -&gt; bool</code> <a class="header-anchor" href="#def-approx-self-other-line3-epsilon-float-approx-bool" aria-label="Permalink to &quot;***def*** \`approx(self, other: Line3, epsilon: float = APPROX) -&gt; bool\`&quot;">​</a></h4><p><strong>Description</strong>: 判断两条直线是否近似相等。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li><li>epsilon: 误差</li></ul></blockquote><p><strong>Return</strong>: 是否近似相等</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L29" target="_blank" rel="noreferrer">View on GitHub</a></p><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;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, epsilon: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">APPROX</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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        判断两条直线是否近似相等。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            epsilon: 误差</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            是否近似相等</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.is_approx_parallel(other, epsilon) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</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;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point).is_approx_parallel(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction, epsilon)</span></span></code></pre></div></details><h4 id="def-cal-angle-self-other-line3-anyangle" tabindex="-1"><em><strong>def</strong></em> <code>cal_angle(self, other: Line3) -&gt; AnyAngle</code> <a class="header-anchor" href="#def-cal-angle-self-other-line3-anyangle" aria-label="Permalink to &quot;***def*** \`cal_angle(self, other: Line3) -&gt; AnyAngle\`&quot;">​</a></h4><p><strong>Description</strong>: 计算直线和直线之间的夹角。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li></ul></blockquote><p><strong>Return</strong>: 夹角弧度</p><p><strong>Raises</strong>:</p><blockquote><ul><li>TypeError 不支持的类型</li></ul></blockquote><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L40" target="_blank" rel="noreferrer">View on GitHub</a></p><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&#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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        计算直线和直线之间的夹角。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            夹角弧度</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Raises:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            TypeError: 不支持的类型</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.direction.cal_angle(other.direction)</span></span></code></pre></div></details><h4 id="def-cal-distance-self-other-line3-point3-float" tabindex="-1"><em><strong>def</strong></em> <code>cal_distance(self, other: Line3 | Point3) -&gt; float</code> <a class="header-anchor" href="#def-cal-distance-self-other-line3-point3-float" aria-label="Permalink to &quot;***def*** \`cal_distance(self, other: Line3 | Point3) -&gt; float\`&quot;">​</a></h4><p><strong>Description</strong>: 计算直线和直线或点之间的距离。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 平行直线或点</li></ul></blockquote><p><strong>Return</strong>: 距离</p><p><strong>Raises</strong>:</p><blockquote><ul><li>TypeError 不支持的类型</li></ul></blockquote><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L52" target="_blank" rel="noreferrer">View on GitHub</a></p><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;Line3 | 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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        计算直线和直线或点之间的距离。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 平行直线或点</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            距离</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Raises:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            TypeError: 不支持的类型</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">        if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> ==</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other:</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;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.is_parallel(other):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">            return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (other.point </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;">.point).cross(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction).length </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;">.direction.length</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">        elif</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> not</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.is_coplanar(other):</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;">.direction.cross(other.direction) </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;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point) </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;">.direction.cross(other.direction).length)</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;"> 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:#24292E;--shiki-dark:#E1E4E8;"> (other </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;">.point).cross(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction).length </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;">.direction.length</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:#032F62;--shiki-dark:#9ECBFF;">&#39;Unsupported type.&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span></code></pre></div></details><h4 id="def-cal-intersection-self-other-line3-point3" tabindex="-1"><em><strong>def</strong></em> <code>cal_intersection(self, other: Line3) -&gt; Point3</code> <a class="header-anchor" href="#def-cal-intersection-self-other-line3-point3" aria-label="Permalink to &quot;***def*** \`cal_intersection(self, other: Line3) -&gt; Point3\`&quot;">​</a></h4><p><strong>Description</strong>: 计算两条直线的交点。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li></ul></blockquote><p><strong>Return</strong>: 交点</p><p><strong>Raises</strong>:</p><blockquote><ul><li>ValueError 直线平行</li><li>ValueError 直线不共面</li></ul></blockquote><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L83" target="_blank" rel="noreferrer">View on GitHub</a></p><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</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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        计算两条直线的交点。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            交点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Raises:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            ValueError: 直线平行</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            ValueError: 直线不共面</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.is_parallel(other):</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;Lines are parallel and do not intersect.&#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:#D73A49;--shiki-dark:#F97583;"> not</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.is_coplanar(other):</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;Lines are not coplanar and do not intersect.&#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;">.point </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;">.direction.cross(other.direction) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.direction.cross(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point) </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;">.direction.cross(other.direction).length </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;">.direction</span></span></code></pre></div></details><h4 id="def-cal-perpendicular-self-point-point3-line3" tabindex="-1"><em><strong>def</strong></em> <code>cal_perpendicular(self, point: Point3) -&gt; Line3</code> <a class="header-anchor" href="#def-cal-perpendicular-self-point-point3-line3" aria-label="Permalink to &quot;***def*** \`cal_perpendicular(self, point: Point3) -&gt; Line3\`&quot;">​</a></h4><p><strong>Description</strong>: 计算直线经过指定点p的垂线。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>point: 指定点</li></ul></blockquote><p><strong>Return</strong>: 垂线</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L101" target="_blank" rel="noreferrer">View on GitHub</a></p><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_perpendicular</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;Line3&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        计算直线经过指定点p的垂线。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            point: 指定点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            垂线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">    return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> Line3(point, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction.cross(point </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;">.point))</span></span></code></pre></div></details><h4 id="def-get-point-self-t-realnumber-point3" tabindex="-1"><em><strong>def</strong></em> <code>get_point(self, t: RealNumber) -&gt; Point3</code> <a class="header-anchor" href="#def-get-point-self-t-realnumber-point3" aria-label="Permalink to &quot;***def*** \`get_point(self, t: RealNumber) -&gt; Point3\`&quot;">​</a></h4><p><strong>Description</strong>: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>t: 参数t</li></ul></blockquote><p><strong>Return</strong>: 点</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L111" target="_blank" rel="noreferrer">View on GitHub</a></p><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;"> get_point</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, t: RealNumber) -&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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            t: 参数t</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t </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;">.direction</span></span></code></pre></div></details><h4 id="def-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc" tabindex="-1"><em><strong>def</strong></em> <code>get_parametric_equations(self) -&gt; tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]</code> <a class="header-anchor" href="#def-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc" aria-label="Permalink to &quot;***def*** \`get_parametric_equations(self) -&gt; tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]\`&quot;">​</a></h4><p><strong>Description</strong>: 获取直线的参数方程。</p><p><strong>Return</strong>: x(t), y(t), z(t)</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L121" target="_blank" rel="noreferrer">View on GitHub</a></p><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;"> get_parametric_equations</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self) -&gt; tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        获取直线的参数方程。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            x(t), y(t), z(t)</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">    return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">lambda</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</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:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction.x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">lambda</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</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:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction.y </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">lambda</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.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;">.direction.z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> t)</span></span></code></pre></div></details><h4 id="def-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool" tabindex="-1"><em><strong>def</strong></em> <code>is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -&gt; bool</code> <a class="header-anchor" href="#def-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool" aria-label="Permalink to &quot;***def*** \`is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -&gt; bool\`&quot;">​</a></h4><p><strong>Description</strong>: 判断两条直线是否近似平行。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li><li>epsilon: 误差</li></ul></blockquote><p><strong>Return</strong>: 是否近似平行</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L131" target="_blank" rel="noreferrer">View on GitHub</a></p><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_approx_parallel</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;">, epsilon: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">1e-06</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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        判断两条直线是否近似平行。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            epsilon: 误差</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            是否近似平行</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.direction.is_approx_parallel(other.direction, epsilon)</span></span></code></pre></div></details><h4 id="def-is-parallel-self-other-line3-bool" tabindex="-1"><em><strong>def</strong></em> <code>is_parallel(self, other: Line3) -&gt; bool</code> <a class="header-anchor" href="#def-is-parallel-self-other-line3-bool" aria-label="Permalink to &quot;***def*** \`is_parallel(self, other: Line3) -&gt; bool\`&quot;">​</a></h4><p><strong>Description</strong>: 判断两条直线是否平行。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li></ul></blockquote><p><strong>Return</strong>: 是否平行</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L142" target="_blank" rel="noreferrer">View on GitHub</a></p><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;Line3&#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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        判断两条直线是否平行。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            是否平行</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.direction.is_parallel(other.direction)</span></span></code></pre></div></details><h4 id="def-is-collinear-self-other-line3-bool" tabindex="-1"><em><strong>def</strong></em> <code>is_collinear(self, other: Line3) -&gt; bool</code> <a class="header-anchor" href="#def-is-collinear-self-other-line3-bool" aria-label="Permalink to &quot;***def*** \`is_collinear(self, other: Line3) -&gt; bool\`&quot;">​</a></h4><p><strong>Description</strong>: 判断两条直线是否共线。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li></ul></blockquote><p><strong>Return</strong>: 是否共线</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L152" target="_blank" rel="noreferrer">View on GitHub</a></p><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_collinear</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:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        判断两条直线是否共线。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            是否共线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.is_parallel(other) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</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;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point).is_parallel(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction)</span></span></code></pre></div></details><h4 id="def-is-point-on-self-point-point3-bool" tabindex="-1"><em><strong>def</strong></em> <code>is_point_on(self, point: Point3) -&gt; bool</code> <a class="header-anchor" href="#def-is-point-on-self-point-point3-bool" aria-label="Permalink to &quot;***def*** \`is_point_on(self, point: Point3) -&gt; bool\`&quot;">​</a></h4><p><strong>Description</strong>: 判断点是否在直线上。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>point: 点</li></ul></blockquote><p><strong>Return</strong>: 是否在直线上</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L162" target="_blank" rel="noreferrer">View on GitHub</a></p><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_point_on</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:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        判断点是否在直线上。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            point: 点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            是否在直线上</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">    return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (point </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;">.point).is_parallel(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction)</span></span></code></pre></div></details><h4 id="def-is-coplanar-self-other-line3-bool" tabindex="-1"><em><strong>def</strong></em> <code>is_coplanar(self, other: Line3) -&gt; bool</code> <a class="header-anchor" href="#def-is-coplanar-self-other-line3-bool" aria-label="Permalink to &quot;***def*** \`is_coplanar(self, other: Line3) -&gt; bool\`&quot;">​</a></h4><p><strong>Description</strong>: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li></ul></blockquote><p><strong>Return</strong>: 是否共面</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L172" target="_blank" rel="noreferrer">View on GitHub</a></p><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_coplanar</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:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        判断两条直线是否共面。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            是否共面</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.direction.cross(other.direction) </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;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">==</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span></span></code></pre></div></details><h4 id="def-simplify-self" tabindex="-1"><em><strong>def</strong></em> <code>simplify(self)</code> <a class="header-anchor" href="#def-simplify-self" aria-label="Permalink to &quot;***def*** \`simplify(self)\`&quot;">​</a></h4><p><strong>Description</strong>: 简化直线方程，等价相等。 自体简化，不返回值。</p><p>按照可行性一次对x y z 化 0 处理，并对向量单位化</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L183" target="_blank" rel="noreferrer">View on GitHub</a></p><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;"> simplify</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self):</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        简化直线方程，等价相等。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        自体简化，不返回值。</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        按照可行性一次对x y z 化 0 处理，并对向量单位化</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">    self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction.normalize()</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;">.direction.x </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:#005CC5;--shiki-dark:#79B8FF;">        self</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:#005CC5;--shiki-dark:#79B8FF;"> 0</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;">.direction.y </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:#005CC5;--shiki-dark:#79B8FF;">        self</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:#005CC5;--shiki-dark:#79B8FF;"> 0</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;">.direction.z </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:#005CC5;--shiki-dark:#79B8FF;">        self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.point.z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 0</span></span></code></pre></div></details><p><code>@classmethod</code></p><h4 id="def-from-two-points-cls-p1-point3-p2-point3-line3" tabindex="-1"><em><strong>def</strong></em> <code>from_two_points(cls, p1: Point3, p2: Point3) -&gt; Line3</code> <a class="header-anchor" href="#def-from-two-points-cls-p1-point3-p2-point3-line3" aria-label="Permalink to &quot;***def*** \`from_two_points(cls, p1: Point3, p2: Point3) -&gt; Line3\`&quot;">​</a></h4><p><strong>Description</strong>: 工厂函数 由两点构造直线。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>p1: 点1</li><li>p2: 点2</li></ul></blockquote><p><strong>Return</strong>: 直线</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L202" target="_blank" rel="noreferrer">View on GitHub</a></p><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_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;">) -&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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        工厂函数 由两点构造直线。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            p1: 点1</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            p2: 点2</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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:#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:#D73A49;--shiki-dark:#F97583;">    return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> cls</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(p1, direction)</span></span></code></pre></div></details><h4 id="def-and-self-other-line3-line3-point3-none" tabindex="-1"><em><strong>def</strong></em> <code>__and__(self, other: Line3) -&gt; Line3 | Point3 | None</code> <a class="header-anchor" href="#def-and-self-other-line3-line3-point3-none" aria-label="Permalink to &quot;***def*** \`__and__(self, other: Line3) -&gt; Line3 | Point3 | None\`&quot;">​</a></h4><p><strong>Description</strong>: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other: 另一条直线</li></ul></blockquote><p><strong>Return</strong>: 交点</p><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L214" target="_blank" rel="noreferrer">View on GitHub</a></p><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 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;Line3 | Point3 | None&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other: 另一条直线</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            交点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.is_collinear(other):</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>
<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;">.is_parallel(other) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">or</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> not</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.is_coplanar(other):</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;">    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;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.cal_intersection(other)</span></span></code></pre></div></details><h4 id="def-eq-self-other-bool" tabindex="-1"><em><strong>def</strong></em> <code>__eq__(self, other) -&gt; bool</code> <a class="header-anchor" href="#def-eq-self-other-bool" aria-label="Permalink to &quot;***def*** \`__eq__(self, other) -&gt; bool\`&quot;">​</a></h4><p><strong>Description</strong>: 判断两条直线是否等价。</p><p>v1 // v2 ∧ (p1 - p2) // v1</p><p><strong>Arguments</strong>:</p><blockquote><ul><li>other:</li></ul></blockquote><details><summary><b>Source code</b></summary><p><a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L229" target="_blank" rel="noreferrer">View on GitHub</a></p><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:#032F62;--shiki-dark:#9ECBFF;">    &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        判断两条直线是否等价。</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        v1 // v2 ∧ (p1 - p2) // v1</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">            other:</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        Returns:</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">        &quot;&quot;&quot;</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;">.direction.is_parallel(other.direction) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">and</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;">.point </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> other.point).is_parallel(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.direction)</span></span></code></pre></div></details>`,107),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const c=s(t,[["render",p]]);export{E as __pageData,c as default};