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Rodrigues’ rotation formula: Difference between revisions

Rodrigues’ rotation formula (view source)

Revision as of 16:05, 4 November 2021

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<pre>2.23222107330823 1.39513817081764 -8.37082902490585</pre>
 
=={{header|Phix}}==
{{trans|JavaScript}}
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">norm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">normalize</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">norm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">dotProduct</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v2</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">crossProduct</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v2</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">v11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v13</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">v21</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v22</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v23</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">v2</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">v12</span><span style="color: #0000FF;">*</span><span style="color: #000000;">v23</span><span style="color: #0000FF;">-</span><span style="color: #000000;">v13</span><span style="color: #0000FF;">*</span><span style="color: #000000;">v22</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v13</span><span style="color: #0000FF;">*</span><span style="color: #000000;">v21</span><span style="color: #0000FF;">-</span><span style="color: #000000;">v11</span><span style="color: #0000FF;">*</span><span style="color: #000000;">v23</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v11</span><span style="color: #0000FF;">*</span><span style="color: #000000;">v22</span><span style="color: #0000FF;">-</span><span style="color: #000000;">v12</span><span style="color: #0000FF;">*</span><span style="color: #000000;">v21</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">getAngle</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">arccos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dotProduct</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v2</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">norm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v1</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">norm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v2</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">matrixMultiply</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">dotProduct</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">dotProduct</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">dotProduct</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">aRotate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">ca</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">sa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">ca</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span><span style="color: #000000;">v</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">ca</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ca</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ca</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">z</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">matrixMultiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">v1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">v2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">30</span><span style="color: #0000FF;">};</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">getAngle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v2</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">cp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">crossProduct</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">ncp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">normalize</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cp</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">aRotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ncp</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">);</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">np</span>
<!--</lang>-->
{{out}}
<pre>
{2.232221073,1.395138171,-8.370829025}
</pre>
 
=={{header|Raku}}==
Petelomax
7,813

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