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45 lines
80 KiB
JavaScript
45 lines
80 KiB
JavaScript
import{_ as n,c as i,j as s,a as t,a4 as e,o as a}from"./chunks/framework.DpC1ZpOZ.js";const rs=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),l={name:"en/api/mp_math/line.md"},h=e('<h1 id="module-mbcp-mp-math-line" tabindex="-1"><strong>Module</strong> <code>mbcp.mp_math.line</code> <a class="header-anchor" href="#module-mbcp-mp-math-line" aria-label="Permalink to "**Module** `mbcp.mp_math.line`""></a></h1><p>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 "***class*** `Line3`""></a></h3><hr><h4 id="method-init-self-point-point3-direction-vector3" tabindex="-1"><em><strong>method</strong></em> <code>__init__(self, point: Point3, direction: Vector3)</code> <a class="header-anchor" href="#method-init-self-point-point3-direction-vector3" aria-label="Permalink to "***method*** `__init__(self, point: Point3, direction: Vector3)`""></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 (<a href="./point.html#class-point3"><code>Point3</code></a>): 直线上的一点</li><li>direction (<a href="./vector.html#class-vector3"><code>Vector3</code></a>): 方向向量</li></ul></blockquote><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L19" target="_blank">View on GitHub</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, point: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Point3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, direction: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Vector3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">):</span></span>\n<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>\n<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><hr><h4 id="method-approx-self-other-line3-epsilon-float-approx-bool" tabindex="-1"><em><strong>method</strong></em> <code>approx(self, other: Line3, epsilon: float = APPROX) -> bool</code> <a class="header-anchor" href="#method-approx-self-other-line3-epsilon-float-approx-bool" aria-label="Permalink to "***method*** `approx(self, other: Line3, epsilon: float = APPROX) -> bool`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一条直线</li><li>epsilon (<a href="https://docs.python.org/3/library/functions.html#float" target="_blank" rel="noreferrer"><code>float</code></a>): 误差</li></ul></blockquote><p><strong>Return</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>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L29" target="_blank">View on GitHub</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;">'Line3'</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;">) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>\n<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><hr><h4 id="method-cal-angle-self-other-line3-anyangle" tabindex="-1"><em><strong>method</strong></em> <code>cal_angle(self, other: Line3) -> AnyAngle</code> <a class="header-anchor" href="#method-cal-angle-self-other-line3-anyangle" aria-label="Permalink to "***method*** `cal_angle(self, other: Line3) -> AnyAngle`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一条直线</li></ul></blockquote><p><strong>Return</strong>: <a href="./angle.html#class-anyangle"><code>AnyAngle</code></a>: 夹角</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L40" target="_blank">View on GitHub</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;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'AnyAngle'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>\n<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><hr><h4 id="method-cal-distance-self-other-line3-point3-float" tabindex="-1"><em><strong>method</strong></em> 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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;">'Line3 | Point3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">float</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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>
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<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>
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||
<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>
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||
<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>
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||
<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;">'Unsupported type.'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span></code></pre></div></details><hr><h4 id="method-cal-intersection-self-other-line3-point3" tabindex="-1"><em><strong>method</strong></em> <code>cal_intersection(self, other: Line3) -> Point3</code> <a class="header-anchor" href="#method-cal-intersection-self-other-line3-point3" aria-label="Permalink to "***method*** \`cal_intersection(self, other: Line3) -> Point3\`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一条直线</li></ul></blockquote><p><strong>Return</strong>: <a href="./point.html#class-point3"><code>Point3</code></a>: 交点</p><p><strong>Raises</strong>:</p><blockquote><ul><li><a href="https://docs.python.org/3/library/exceptions.html#TypeError" target="_blank" rel="noreferrer"><code>ValueError</code></a> 直线平行</li><li><code>ValueError</code> 直线不共面</li></ul></blockquote><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L92" target="_blank">View on GitHub</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</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Point3'</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;">.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;">'Lines are parallel and do not intersect.'</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;">'Lines are not coplanar and do not intersect.'</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><hr><h4 id="method-cal-perpendicular-self-point-point3-line3" tabindex="-1"><em><strong>method</strong></em> <code>cal_perpendicular(self, point: Point3) -> Line3</code> <a class="header-anchor" href="#method-cal-perpendicular-self-point-point3-line3" aria-label="Permalink to "***method*** \`cal_perpendicular(self, point: Point3) -> Line3\`""></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 (<a href="./point.html#class-point3"><code>Point3</code></a>): 指定点</li></ul></blockquote><p><strong>Return</strong>: <a href="./line.html#class-line3"><code>Line3</code></a>: 垂线</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L110" target="_blank">View on GitHub</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_perpendicular</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, point: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Point3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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||
<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><hr><h4 id="method-get-point-self-t-realnumber-point3" tabindex="-1"><em><strong>method</strong></em> <code>get_point(self, t: RealNumber) -> Point3</code> <a class="header-anchor" href="#method-get-point-self-t-realnumber-point3" aria-label="Permalink to "***method*** \`get_point(self, t: RealNumber) -> Point3\`""></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 (<a href="./mp_math_typing.html#var-realnumber"><code>RealNumber</code></a>): 参数t</li></ul></blockquote><p><strong>Return</strong>: <a href="./point.html#class-point3"><code>Point3</code></a>: 点</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L120" target="_blank">View on GitHub</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;"> get_point</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, t: RealNumber) -> </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Point3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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||
<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><hr><h4 id="method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc" tabindex="-1"><em><strong>method</strong></em> <code>get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]</code> <a class="header-anchor" href="#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc" aria-label="Permalink to "***method*** \`get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]\`""></a></h4><p><strong>Description</strong>: 获取直线的参数方程。</p><p><strong>Return</strong>: <a href="https://docs.python.org/3/library/stdtypes.html#tuple" target="_blank" rel="noreferrer"><code>tuple</code></a>[<a href="./mp_math_typing.html#var-onesinglevarfunc"><code>OneSingleVarFunc</code></a>, <code>OneSingleVarFunc</code>, <code>OneSingleVarFunc</code>]: 参数方程</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L130" target="_blank">View on GitHub</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;"> get_parametric_equations</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:</span></span>
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||
<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><hr><h4 id="method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool" tabindex="-1"><em><strong>method</strong></em> <code>is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool</code> <a class="header-anchor" href="#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool" aria-label="Permalink to "***method*** \`is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool\`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一条直线</li><li>epsilon (<a href="https://docs.python.org/3/library/functions.html#float" target="_blank" rel="noreferrer"><code>float</code></a>): 误差</li></ul></blockquote><p><strong>Return</strong>: <a href="https://docs.python.org/3/library/functions.html#bool" target="_blank" rel="noreferrer"><code>bool</code></a>: 是否近似平行</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L140" target="_blank">View on GitHub</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_approx_parallel</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3'</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;">) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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><hr><h4 id="method-is-parallel-self-other-line3-bool" tabindex="-1"><em><strong>method</strong></em> <code>is_parallel(self, other: Line3) -> bool</code> <a class="header-anchor" href="#method-is-parallel-self-other-line3-bool" aria-label="Permalink to "***method*** \`is_parallel(self, other: Line3) -> bool\`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一</li></ul></blockquote><p><strong>Return</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>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L151" target="_blank">View on GitHub</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;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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><hr><h4 id="method-is-collinear-self-other-line3-bool" tabindex="-1"><em><strong>method</strong></em> <code>is_collinear(self, other: Line3) -> bool</code> <a class="header-anchor" href="#method-is-collinear-self-other-line3-bool" aria-label="Permalink to "***method*** \`is_collinear(self, other: Line3) -> bool\`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一</li></ul></blockquote><p><strong>Return</strong>: <a href="https://docs.python.org/3/library/functions.html#bool" target="_blank" rel="noreferrer"><code>bool</code></a>: 是否共线</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L161" target="_blank">View on GitHub</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_collinear</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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><hr><h4 id="method-is-point-on-self-point-point3-bool" tabindex="-1"><em><strong>method</strong></em> <code>is_point_on(self, point: Point3) -> bool</code> <a class="header-anchor" href="#method-is-point-on-self-point-point3-bool" aria-label="Permalink to "***method*** \`is_point_on(self, point: Point3) -> bool\`""></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 (<a href="./point.html#class-point3"><code>Point3</code></a>): 点</li></ul></blockquote><p><strong>Return</strong>: <a href="https://docs.python.org/3/library/functions.html#bool" target="_blank" rel="noreferrer"><code>bool</code></a>: 是否在直线上</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L171" target="_blank">View on GitHub</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_point_on</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, point: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Point3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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><hr><h4 id="method-is-coplanar-self-other-line3-bool" tabindex="-1"><em><strong>method</strong></em> <code>is_coplanar(self, other: Line3) -> bool</code> <a class="header-anchor" href="#method-is-coplanar-self-other-line3-bool" aria-label="Permalink to "***method*** \`is_coplanar(self, other: Line3) -> bool\`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一</li></ul></blockquote><p><strong>Return</strong>: <a href="https://docs.python.org/3/library/functions.html#bool" target="_blank" rel="noreferrer"><code>bool</code></a>: 是否共面</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L181" target="_blank">View on GitHub</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_coplanar</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, other: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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><hr><h4 id="method-simplify-self" tabindex="-1"><em><strong>method</strong></em> <code>simplify(self)</code> <a class="header-anchor" href="#method-simplify-self" aria-label="Permalink to "***method*** \`simplify(self)\`""></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> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L192" target="_blank">View on GitHub</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;"> simplify</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self):</span></span>
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<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>
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||
<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>
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||
<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>
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<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>
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||
<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>
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<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>
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||
<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><hr><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-points-cls-p1-point3-p2-point3-line3" tabindex="-1"><em><strong>method</strong></em> <code>from_two_points(cls, p1: Point3, p2: Point3) -> Line3</code> <a class="header-anchor" href="#method-from-two-points-cls-p1-point3-p2-point3-line3" aria-label="Permalink to "***method*** \`from_two_points(cls, p1: Point3, p2: Point3) -> Line3\`""></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 (<a href="./point.html#class-point3"><code>Point3</code></a>): 点1</li><li>p2 (<a href="./point.html#class-point3"><code>Point3</code></a>): 点2</li></ul></blockquote><p><strong>Return</strong>: <a href="./line.html#class-line3"><code>Line3</code></a>: 直线</p><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L211" target="_blank">View on GitHub</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>
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||
<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;">'Point3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, p2: </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Point3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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>
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<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><hr><h4 id="method-self-other-line3-line3-point3-none" tabindex="-1"><em><strong>method</strong></em> <code>self & other: Line3 => Line3 | Point3 | None</code> <a class="header-anchor" href="#method-self-other-line3-line3-point3-none" aria-label="Permalink to "***method*** \`self & other: Line3 => Line3 | Point3 | None\`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一条直线</li></ul></blockquote><p><strong>Return</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><details><summary><b>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L223" target="_blank">View on GitHub</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 style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -> </span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">'Line3 | Point3 | None'</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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>
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||
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span></span>
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||
<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><hr><h4 id="method-self-other-bool" tabindex="-1"><em><strong>method</strong></em> <code>self == other => bool</code> <a class="header-anchor" href="#method-self-other-bool" aria-label="Permalink to "***method*** \`self == other => bool\`""></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 (<a href="./line.html#class-line3"><code>Line3</code></a>): 另一条直线</li></ul></blockquote><p><strong>Return</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>Source code</b> or <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/line.py#L238" target="_blank">View on GitHub</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) -> </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">bool</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
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<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>`,97);function ts(as,es,ns,ls,hs,os){return a(),i("div",null,[h,s("div",o,[p,r,s("ul",null,[d,s("li",null,[t("平行/异面 = "),s("mjx-container",k,[(a(),i("svg",c,m)),y])]),s("li",null,[t("相交 = 0 其中，"),s("mjx-container",E,[(a(),i("svg",Q,T)),b]),t("和"),s("mjx-container",f,[(a(),i("svg",F,C)),x]),t("分别为两条直线上的点，"),s("mjx-container",w,[(a(),i("svg",v,A)),B]),t("为直线的方向向量。")])])]),s("div",L,[H,V,s("mjx-container",P,[(a(),i("svg",M,S)),R]),s("p",null,[t("其中，"),s("mjx-container",j,[(a(),i("svg",Z,G)),N]),t("为直线上的点，"),s("mjx-container",I,[(a(),i("svg",z,J)),$]),t("为点，"),s("mjx-container",U,[(a(),i("svg",K,Y)),ss]),t("为直线的方向向量。")])]),is])}const ds=n(l,[["render",ts]]);export{rs as __pageData,ds as default};
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