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<!DOCTYPE html>
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<section id="vector-operations">
<h1><a class="toc-backref" href="#id1" role="doc-backlink">Vector Operations</a><a class="headerlink" href="#vector-operations" title="Permalink to this heading">¶</a></h1>
<p>The vector object has the properties of 3D vectors in math and science.</p>
<p><code class="docutils literal notranslate"><span class="pre">r</span> <span class="pre">=</span> <span class="pre">vector(x,y,z)</span></code> or <code class="docutils literal notranslate"><span class="pre">r=vec(x,y,z)</span></code> produce the 3D vector < x, y, z >.</p>
<nav class="contents" id="contents">
<p class="topic-title">Contents</p>
<ul class="simple">
<li><p><a class="reference internal" href="#vector-operations" id="id1">Vector Operations</a></p>
<ul>
<li><p><a class="reference internal" href="#vector-addition-and-subtraction" id="id2">Vector Addition and Subtraction</a></p></li>
<li><p><a class="reference internal" href="#scalar-multiplication" id="id3">Scalar Multiplication</a></p></li>
<li><p><a class="reference internal" href="#magnitude" id="id4">Magnitude</a></p></li>
<li><p><a class="reference internal" href="#unit-vector" id="id5">Unit Vector</a></p></li>
<li><p><a class="reference internal" href="#dot-product" id="id6">Dot Product</a></p></li>
<li><p><a class="reference internal" href="#angle-between-vectors" id="id7">Angle Between Vectors</a></p></li>
<li><p><a class="reference internal" href="#projections" id="id8">Projections</a></p></li>
<li><p><a class="reference internal" href="#random-vector" id="id9">Random Vector</a></p></li>
<li><p><a class="reference internal" href="#rotating-a-vector" id="id10">Rotating a Vector</a></p></li>
</ul>
</li>
</ul>
</nav>
<section id="vector-addition-and-subtraction">
<h2><a class="toc-backref" href="#id2" role="doc-backlink">Vector Addition and Subtraction</a><a class="headerlink" href="#vector-addition-and-subtraction" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="mi">30</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="p">)</span> <span class="c1"># displays < 1, 22, 33 ></span>
</pre></div>
</div>
</section>
<section id="scalar-multiplication">
<h2><a class="toc-backref" href="#id3" role="doc-backlink">Scalar Multiplication</a><a class="headerlink" href="#scalar-multiplication" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">a</span>
<span class="nb">print</span><span class="p">(</span><span class="n">c</span><span class="p">)</span> <span class="c1"># displays < 2, 4, 6 ></span>
</pre></div>
</div>
</section>
<section id="magnitude">
<h2><a class="toc-backref" href="#id4" role="doc-backlink">Magnitude</a><a class="headerlink" href="#magnitude" title="Permalink to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">mag</span></code> can be invoked as a function or an attribute:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="mi">30</span><span class="p">)</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">mag</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">d</span><span class="p">)</span> <span class="c1"># displays 3.74166</span>
<span class="n">e</span> <span class="o">=</span> <span class="n">b</span><span class="o">.</span><span class="n">mag</span>
<span class="nb">print</span><span class="p">(</span><span class="n">e</span><span class="p">)</span> <span class="c1"># displays 37.4166</span>
</pre></div>
</div>
</section>
<section id="unit-vector">
<h2><a class="toc-backref" href="#id5" role="doc-backlink">Unit Vector</a><a class="headerlink" href="#unit-vector" title="Permalink to this heading">¶</a></h2>
<p>There are two names for the function that calculates a unit vector: hat() and norm(). Both can be invoked as functions or attributes:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="mi">30</span><span class="p">)</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">hat</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="c1"># displays < 0.267261, 0.534522, 0.801784 ></span>
<span class="n">g</span> <span class="o">=</span> <span class="n">norm</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">g</span><span class="p">)</span> <span class="c1"># displays < 0.267261, 0.534522, 0.801784 ></span>
<span class="n">h</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">hat</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">b</span><span class="o">.</span><span class="n">norm</span>
</pre></div>
</div>
<p>For convenience, <code class="docutils literal notranslate"><span class="pre">hat(</span> <span class="pre">vec(0,0,0)</span> <span class="pre">)</span> <span class="pre">=</span> <span class="pre">vec(0,</span> <span class="pre">0,</span> <span class="pre">0)</span></code> to avoid runtime errors.</p>
</section>
<section id="dot-product">
<h2><a class="toc-backref" href="#id6" role="doc-backlink">Dot Product</a><a class="headerlink" href="#dot-product" title="Permalink to this heading">¶</a></h2>
<p>Both dot and cross products can be invoked as functions or attributes:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a1</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">b1</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">dot</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="c1"># displays 2</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">cross</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="c1"># displays < 0, 0, 6 ></span>
<span class="n">m</span> <span class="o">=</span> <span class="n">a1</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">b1</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">a1</span><span class="o">.</span><span class="n">cross</span><span class="p">(</span><span class="n">b1</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="angle-between-vectors">
<h2><a class="toc-backref" href="#id7" role="doc-backlink">Angle Between Vectors</a><a class="headerlink" href="#angle-between-vectors" title="Permalink to this heading">¶</a></h2>
<p>The diff_angle() function returns the angle between two vectors in radians:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a1</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">b1</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">diff_angle</span><span class="p">(</span><span class="n">a1</span><span class="p">,</span><span class="n">b1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="c1"># displays 1.24905</span>
<span class="n">q</span> <span class="o">=</span> <span class="n">a1</span><span class="o">.</span><span class="n">diff_angle</span><span class="p">(</span><span class="n">b1</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="projections">
<h2><a class="toc-backref" href="#id8" role="doc-backlink">Projections</a><a class="headerlink" href="#projections" title="Permalink to this heading">¶</a></h2>
<p>For convenience, the proj() function calculates the vector projection of one vector onto another:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">B</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">C</span> <span class="o">=</span> <span class="n">proj</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">B</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">C</span><span class="p">)</span> <span class="c1"># displays < 0, 1, 0 ></span>
</pre></div>
</div>
<p>Note that <code class="docutils literal notranslate"><span class="pre">proj(A,B)</span> <span class="pre">=</span> <span class="pre">dot(</span> <span class="pre">A,</span> <span class="pre">hat(B)</span> <span class="pre">)</span> <span class="pre">*</span> <span class="pre">hat(B)</span></code></p>
<p>The comp() function calculates the scalar projection of A along B:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">B</span> <span class="o">=</span> <span class="n">vector</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="n">C</span> <span class="o">=</span> <span class="n">comp</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">B</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">C</span><span class="p">)</span> <span class="c1"># displays 1.</span>
</pre></div>
</div>
<p>Note that <code class="docutils literal notranslate"><span class="pre">comp(A,B)</span> <span class="pre">=</span> <span class="pre">dot(</span> <span class="pre">A,</span> <span class="pre">hat(B)</span> <span class="pre">)</span></code></p>
</section>
<section id="random-vector">
<h2><a class="toc-backref" href="#id9" role="doc-backlink">Random Vector</a><a class="headerlink" href="#random-vector" title="Permalink to this heading">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">vector.random()</span></code> produces a vector whose components are random numbers in the range -1 to +1.</p>
</section>
<section id="rotating-a-vector">
<h2><a class="toc-backref" href="#id10" role="doc-backlink">Rotating a Vector</a><a class="headerlink" href="#rotating-a-vector" title="Permalink to this heading">¶</a></h2>
<dl class="py function">
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">myvec2</span> <span class="pre">=</span> <span class="pre">rotate(</span> <span class="pre">myvec1,</span> <span class="pre">angle=a,</span> <span class="pre">axis=vector(x,y,z)</span> <span class="pre">)</span></span></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>firstargument</strong> (<em>vector</em>) – Vector to be rotated (<em>myvec1</em> in example above).</p></li>
<li><p><strong>angle</strong> (<em>scalar</em>) – Angle of rotation in radians.</p></li>
<li><p><strong>axis</strong> (<em>vector</em>) – Axis of rotation. Default < 0, 0, 1 >.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
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