<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="generator" content="rustdoc">
<meta name="description" content="Source to the Rust file `/home/frans/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.8.2/src/structs/quaternion.rs`.">
<meta name="keywords" content="rust, rustlang, rust-lang">
<title>quaternion.rs.html -- source</title>
<link rel="stylesheet" type="text/css" href="../../../rustdoc.css">
<link rel="stylesheet" type="text/css" href="../../../main.css">
</head>
<body class="rustdoc">
<!--[if lte IE 8]>
<div class="warning">
This old browser is unsupported and will most likely display funky
things.
</div>
<![endif]-->
<nav class="sidebar">
</nav>
<nav class="sub">
<form class="search-form js-only">
<div class="search-container">
<input class="search-input" name="search"
autocomplete="off"
placeholder="Click or press ‘S’ to search, ‘?’ for more options…"
type="search">
</div>
</form>
</nav>
<section id='main' class="content source"><pre class="line-numbers"><span id="1"> 1</span>
<span id="2"> 2</span>
<span id="3"> 3</span>
<span id="4"> 4</span>
<span id="5"> 5</span>
<span id="6"> 6</span>
<span id="7"> 7</span>
<span id="8"> 8</span>
<span id="9"> 9</span>
<span id="10"> 10</span>
<span id="11"> 11</span>
<span id="12"> 12</span>
<span id="13"> 13</span>
<span id="14"> 14</span>
<span id="15"> 15</span>
<span id="16"> 16</span>
<span id="17"> 17</span>
<span id="18"> 18</span>
<span id="19"> 19</span>
<span id="20"> 20</span>
<span id="21"> 21</span>
<span id="22"> 22</span>
<span id="23"> 23</span>
<span id="24"> 24</span>
<span id="25"> 25</span>
<span id="26"> 26</span>
<span id="27"> 27</span>
<span id="28"> 28</span>
<span id="29"> 29</span>
<span id="30"> 30</span>
<span id="31"> 31</span>
<span id="32"> 32</span>
<span id="33"> 33</span>
<span id="34"> 34</span>
<span id="35"> 35</span>
<span id="36"> 36</span>
<span id="37"> 37</span>
<span id="38"> 38</span>
<span id="39"> 39</span>
<span id="40"> 40</span>
<span id="41"> 41</span>
<span id="42"> 42</span>
<span id="43"> 43</span>
<span id="44"> 44</span>
<span id="45"> 45</span>
<span id="46"> 46</span>
<span id="47"> 47</span>
<span id="48"> 48</span>
<span id="49"> 49</span>
<span id="50"> 50</span>
<span id="51"> 51</span>
<span id="52"> 52</span>
<span id="53"> 53</span>
<span id="54"> 54</span>
<span id="55"> 55</span>
<span id="56"> 56</span>
<span id="57"> 57</span>
<span id="58"> 58</span>
<span id="59"> 59</span>
<span id="60"> 60</span>
<span id="61"> 61</span>
<span id="62"> 62</span>
<span id="63"> 63</span>
<span id="64"> 64</span>
<span id="65"> 65</span>
<span id="66"> 66</span>
<span id="67"> 67</span>
<span id="68"> 68</span>
<span id="69"> 69</span>
<span id="70"> 70</span>
<span id="71"> 71</span>
<span id="72"> 72</span>
<span id="73"> 73</span>
<span id="74"> 74</span>
<span id="75"> 75</span>
<span id="76"> 76</span>
<span id="77"> 77</span>
<span id="78"> 78</span>
<span id="79"> 79</span>
<span id="80"> 80</span>
<span id="81"> 81</span>
<span id="82"> 82</span>
<span id="83"> 83</span>
<span id="84"> 84</span>
<span id="85"> 85</span>
<span id="86"> 86</span>
<span id="87"> 87</span>
<span id="88"> 88</span>
<span id="89"> 89</span>
<span id="90"> 90</span>
<span id="91"> 91</span>
<span id="92"> 92</span>
<span id="93"> 93</span>
<span id="94"> 94</span>
<span id="95"> 95</span>
<span id="96"> 96</span>
<span id="97"> 97</span>
<span id="98"> 98</span>
<span id="99"> 99</span>
<span id="100">100</span>
<span id="101">101</span>
<span id="102">102</span>
<span id="103">103</span>
<span id="104">104</span>
<span id="105">105</span>
<span id="106">106</span>
<span id="107">107</span>
<span id="108">108</span>
<span id="109">109</span>
<span id="110">110</span>
<span id="111">111</span>
<span id="112">112</span>
<span id="113">113</span>
<span id="114">114</span>
<span id="115">115</span>
<span id="116">116</span>
<span id="117">117</span>
<span id="118">118</span>
<span id="119">119</span>
<span id="120">120</span>
<span id="121">121</span>
<span id="122">122</span>
<span id="123">123</span>
<span id="124">124</span>
<span id="125">125</span>
<span id="126">126</span>
<span id="127">127</span>
<span id="128">128</span>
<span id="129">129</span>
<span id="130">130</span>
<span id="131">131</span>
<span id="132">132</span>
<span id="133">133</span>
<span id="134">134</span>
<span id="135">135</span>
<span id="136">136</span>
<span id="137">137</span>
<span id="138">138</span>
<span id="139">139</span>
<span id="140">140</span>
<span id="141">141</span>
<span id="142">142</span>
<span id="143">143</span>
<span id="144">144</span>
<span id="145">145</span>
<span id="146">146</span>
<span id="147">147</span>
<span id="148">148</span>
<span id="149">149</span>
<span id="150">150</span>
<span id="151">151</span>
<span id="152">152</span>
<span id="153">153</span>
<span id="154">154</span>
<span id="155">155</span>
<span id="156">156</span>
<span id="157">157</span>
<span id="158">158</span>
<span id="159">159</span>
<span id="160">160</span>
<span id="161">161</span>
<span id="162">162</span>
<span id="163">163</span>
<span id="164">164</span>
<span id="165">165</span>
<span id="166">166</span>
<span id="167">167</span>
<span id="168">168</span>
<span id="169">169</span>
<span id="170">170</span>
<span id="171">171</span>
<span id="172">172</span>
<span id="173">173</span>
<span id="174">174</span>
<span id="175">175</span>
<span id="176">176</span>
<span id="177">177</span>
<span id="178">178</span>
<span id="179">179</span>
<span id="180">180</span>
<span id="181">181</span>
<span id="182">182</span>
<span id="183">183</span>
<span id="184">184</span>
<span id="185">185</span>
<span id="186">186</span>
<span id="187">187</span>
<span id="188">188</span>
<span id="189">189</span>
<span id="190">190</span>
<span id="191">191</span>
<span id="192">192</span>
<span id="193">193</span>
<span id="194">194</span>
<span id="195">195</span>
<span id="196">196</span>
<span id="197">197</span>
<span id="198">198</span>
<span id="199">199</span>
<span id="200">200</span>
<span id="201">201</span>
<span id="202">202</span>
<span id="203">203</span>
<span id="204">204</span>
<span id="205">205</span>
<span id="206">206</span>
<span id="207">207</span>
<span id="208">208</span>
<span id="209">209</span>
<span id="210">210</span>
<span id="211">211</span>
<span id="212">212</span>
<span id="213">213</span>
<span id="214">214</span>
<span id="215">215</span>
<span id="216">216</span>
<span id="217">217</span>
<span id="218">218</span>
<span id="219">219</span>
<span id="220">220</span>
<span id="221">221</span>
<span id="222">222</span>
<span id="223">223</span>
<span id="224">224</span>
<span id="225">225</span>
<span id="226">226</span>
<span id="227">227</span>
<span id="228">228</span>
<span id="229">229</span>
<span id="230">230</span>
<span id="231">231</span>
<span id="232">232</span>
<span id="233">233</span>
<span id="234">234</span>
<span id="235">235</span>
<span id="236">236</span>
<span id="237">237</span>
<span id="238">238</span>
<span id="239">239</span>
<span id="240">240</span>
<span id="241">241</span>
<span id="242">242</span>
<span id="243">243</span>
<span id="244">244</span>
<span id="245">245</span>
<span id="246">246</span>
<span id="247">247</span>
<span id="248">248</span>
<span id="249">249</span>
<span id="250">250</span>
<span id="251">251</span>
<span id="252">252</span>
<span id="253">253</span>
<span id="254">254</span>
<span id="255">255</span>
<span id="256">256</span>
<span id="257">257</span>
<span id="258">258</span>
<span id="259">259</span>
<span id="260">260</span>
<span id="261">261</span>
<span id="262">262</span>
<span id="263">263</span>
<span id="264">264</span>
<span id="265">265</span>
<span id="266">266</span>
<span id="267">267</span>
<span id="268">268</span>
<span id="269">269</span>
<span id="270">270</span>
<span id="271">271</span>
<span id="272">272</span>
<span id="273">273</span>
<span id="274">274</span>
<span id="275">275</span>
<span id="276">276</span>
<span id="277">277</span>
<span id="278">278</span>
<span id="279">279</span>
<span id="280">280</span>
<span id="281">281</span>
<span id="282">282</span>
<span id="283">283</span>
<span id="284">284</span>
<span id="285">285</span>
<span id="286">286</span>
<span id="287">287</span>
<span id="288">288</span>
<span id="289">289</span>
<span id="290">290</span>
<span id="291">291</span>
<span id="292">292</span>
<span id="293">293</span>
<span id="294">294</span>
<span id="295">295</span>
<span id="296">296</span>
<span id="297">297</span>
<span id="298">298</span>
<span id="299">299</span>
<span id="300">300</span>
<span id="301">301</span>
<span id="302">302</span>
<span id="303">303</span>
<span id="304">304</span>
<span id="305">305</span>
<span id="306">306</span>
<span id="307">307</span>
<span id="308">308</span>
<span id="309">309</span>
<span id="310">310</span>
<span id="311">311</span>
<span id="312">312</span>
<span id="313">313</span>
<span id="314">314</span>
<span id="315">315</span>
<span id="316">316</span>
<span id="317">317</span>
<span id="318">318</span>
<span id="319">319</span>
<span id="320">320</span>
<span id="321">321</span>
<span id="322">322</span>
<span id="323">323</span>
<span id="324">324</span>
<span id="325">325</span>
<span id="326">326</span>
<span id="327">327</span>
<span id="328">328</span>
<span id="329">329</span>
<span id="330">330</span>
<span id="331">331</span>
<span id="332">332</span>
<span id="333">333</span>
<span id="334">334</span>
<span id="335">335</span>
<span id="336">336</span>
<span id="337">337</span>
<span id="338">338</span>
<span id="339">339</span>
<span id="340">340</span>
<span id="341">341</span>
<span id="342">342</span>
<span id="343">343</span>
<span id="344">344</span>
<span id="345">345</span>
<span id="346">346</span>
<span id="347">347</span>
<span id="348">348</span>
<span id="349">349</span>
<span id="350">350</span>
<span id="351">351</span>
<span id="352">352</span>
<span id="353">353</span>
<span id="354">354</span>
<span id="355">355</span>
<span id="356">356</span>
<span id="357">357</span>
<span id="358">358</span>
<span id="359">359</span>
<span id="360">360</span>
<span id="361">361</span>
<span id="362">362</span>
<span id="363">363</span>
<span id="364">364</span>
<span id="365">365</span>
<span id="366">366</span>
<span id="367">367</span>
<span id="368">368</span>
<span id="369">369</span>
<span id="370">370</span>
<span id="371">371</span>
<span id="372">372</span>
<span id="373">373</span>
<span id="374">374</span>
<span id="375">375</span>
<span id="376">376</span>
<span id="377">377</span>
<span id="378">378</span>
<span id="379">379</span>
<span id="380">380</span>
<span id="381">381</span>
<span id="382">382</span>
<span id="383">383</span>
<span id="384">384</span>
<span id="385">385</span>
<span id="386">386</span>
<span id="387">387</span>
<span id="388">388</span>
<span id="389">389</span>
<span id="390">390</span>
<span id="391">391</span>
<span id="392">392</span>
<span id="393">393</span>
<span id="394">394</span>
<span id="395">395</span>
<span id="396">396</span>
<span id="397">397</span>
<span id="398">398</span>
<span id="399">399</span>
<span id="400">400</span>
<span id="401">401</span>
<span id="402">402</span>
<span id="403">403</span>
<span id="404">404</span>
<span id="405">405</span>
<span id="406">406</span>
<span id="407">407</span>
<span id="408">408</span>
<span id="409">409</span>
<span id="410">410</span>
<span id="411">411</span>
<span id="412">412</span>
<span id="413">413</span>
<span id="414">414</span>
<span id="415">415</span>
<span id="416">416</span>
<span id="417">417</span>
<span id="418">418</span>
<span id="419">419</span>
<span id="420">420</span>
<span id="421">421</span>
<span id="422">422</span>
<span id="423">423</span>
<span id="424">424</span>
<span id="425">425</span>
<span id="426">426</span>
<span id="427">427</span>
<span id="428">428</span>
<span id="429">429</span>
<span id="430">430</span>
<span id="431">431</span>
<span id="432">432</span>
<span id="433">433</span>
<span id="434">434</span>
<span id="435">435</span>
<span id="436">436</span>
<span id="437">437</span>
<span id="438">438</span>
<span id="439">439</span>
<span id="440">440</span>
<span id="441">441</span>
<span id="442">442</span>
<span id="443">443</span>
<span id="444">444</span>
<span id="445">445</span>
<span id="446">446</span>
<span id="447">447</span>
<span id="448">448</span>
<span id="449">449</span>
<span id="450">450</span>
<span id="451">451</span>
<span id="452">452</span>
<span id="453">453</span>
<span id="454">454</span>
<span id="455">455</span>
<span id="456">456</span>
<span id="457">457</span>
<span id="458">458</span>
<span id="459">459</span>
<span id="460">460</span>
<span id="461">461</span>
<span id="462">462</span>
<span id="463">463</span>
<span id="464">464</span>
<span id="465">465</span>
<span id="466">466</span>
<span id="467">467</span>
<span id="468">468</span>
<span id="469">469</span>
<span id="470">470</span>
<span id="471">471</span>
<span id="472">472</span>
<span id="473">473</span>
<span id="474">474</span>
<span id="475">475</span>
<span id="476">476</span>
<span id="477">477</span>
<span id="478">478</span>
<span id="479">479</span>
<span id="480">480</span>
<span id="481">481</span>
<span id="482">482</span>
<span id="483">483</span>
<span id="484">484</span>
<span id="485">485</span>
<span id="486">486</span>
<span id="487">487</span>
<span id="488">488</span>
<span id="489">489</span>
<span id="490">490</span>
<span id="491">491</span>
<span id="492">492</span>
<span id="493">493</span>
<span id="494">494</span>
<span id="495">495</span>
<span id="496">496</span>
<span id="497">497</span>
<span id="498">498</span>
<span id="499">499</span>
<span id="500">500</span>
<span id="501">501</span>
<span id="502">502</span>
<span id="503">503</span>
<span id="504">504</span>
<span id="505">505</span>
<span id="506">506</span>
<span id="507">507</span>
<span id="508">508</span>
<span id="509">509</span>
<span id="510">510</span>
<span id="511">511</span>
<span id="512">512</span>
<span id="513">513</span>
<span id="514">514</span>
<span id="515">515</span>
<span id="516">516</span>
<span id="517">517</span>
<span id="518">518</span>
<span id="519">519</span>
<span id="520">520</span>
<span id="521">521</span>
<span id="522">522</span>
<span id="523">523</span>
<span id="524">524</span>
<span id="525">525</span>
<span id="526">526</span>
<span id="527">527</span>
<span id="528">528</span>
<span id="529">529</span>
<span id="530">530</span>
<span id="531">531</span>
<span id="532">532</span>
<span id="533">533</span>
<span id="534">534</span>
<span id="535">535</span>
<span id="536">536</span>
<span id="537">537</span>
<span id="538">538</span>
<span id="539">539</span>
<span id="540">540</span>
<span id="541">541</span>
<span id="542">542</span>
<span id="543">543</span>
<span id="544">544</span>
<span id="545">545</span>
<span id="546">546</span>
<span id="547">547</span>
<span id="548">548</span>
<span id="549">549</span>
<span id="550">550</span>
<span id="551">551</span>
<span id="552">552</span>
<span id="553">553</span>
<span id="554">554</span>
<span id="555">555</span>
<span id="556">556</span>
<span id="557">557</span>
<span id="558">558</span>
<span id="559">559</span>
<span id="560">560</span>
<span id="561">561</span>
<span id="562">562</span>
<span id="563">563</span>
<span id="564">564</span>
<span id="565">565</span>
<span id="566">566</span>
<span id="567">567</span>
<span id="568">568</span>
<span id="569">569</span>
<span id="570">570</span>
<span id="571">571</span>
<span id="572">572</span>
<span id="573">573</span>
<span id="574">574</span>
<span id="575">575</span>
<span id="576">576</span>
<span id="577">577</span>
<span id="578">578</span>
<span id="579">579</span>
<span id="580">580</span>
<span id="581">581</span>
<span id="582">582</span>
<span id="583">583</span>
<span id="584">584</span>
<span id="585">585</span>
<span id="586">586</span>
<span id="587">587</span>
<span id="588">588</span>
<span id="589">589</span>
<span id="590">590</span>
<span id="591">591</span>
<span id="592">592</span>
<span id="593">593</span>
<span id="594">594</span>
<span id="595">595</span>
<span id="596">596</span>
<span id="597">597</span>
<span id="598">598</span>
</pre><pre class='rust '>
<span class='doccomment'>//! Quaternion definition.</span>
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>fmt</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>mem</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>slice</span>::{<span class='ident'>Iter</span>, <span class='ident'>IterMut</span>};
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Add</span>, <span class='ident'>Sub</span>, <span class='ident'>Mul</span>, <span class='ident'>Div</span>, <span class='ident'>Neg</span>, <span class='ident'>AddAssign</span>, <span class='ident'>SubAssign</span>, <span class='ident'>MulAssign</span>, <span class='ident'>DivAssign</span>, <span class='ident'>Index</span>, <span class='ident'>IndexMut</span>};
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>iter</span>::{<span class='ident'>FromIterator</span>, <span class='ident'>IntoIterator</span>};
<span class='kw'>use</span> <span class='ident'>rand</span>::{<span class='ident'>Rand</span>, <span class='ident'>Rng</span>};
<span class='kw'>use</span> <span class='ident'>num</span>::{<span class='ident'>Zero</span>, <span class='ident'>One</span>};
<span class='kw'>use</span> <span class='ident'>structs</span>::{<span class='ident'>Vector3</span>, <span class='ident'>Point3</span>, <span class='ident'>Rotation3</span>, <span class='ident'>Matrix3</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>operations</span>::{<span class='ident'>ApproxEq</span>, <span class='ident'>Inverse</span>, <span class='ident'>PartialOrder</span>, <span class='ident'>PartialOrdering</span>, <span class='ident'>Axpy</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>structure</span>::{<span class='ident'>Cast</span>, <span class='ident'>Indexable</span>, <span class='ident'>Iterable</span>, <span class='ident'>IterableMut</span>, <span class='ident'>Dimension</span>, <span class='ident'>Shape</span>, <span class='ident'>BaseFloat</span>, <span class='ident'>BaseNum</span>,
<span class='ident'>Bounded</span>, <span class='ident'>Repeat</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>geometry</span>::{<span class='ident'>Norm</span>, <span class='ident'>Rotation</span>, <span class='ident'>RotationMatrix</span>, <span class='ident'>Rotate</span>, <span class='ident'>RotationTo</span>, <span class='ident'>Transform</span>};
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span><span class='op'>=</span><span class='string'>"arbitrary"</span>)]</span>
<span class='kw'>use</span> <span class='ident'>quickcheck</span>::{<span class='ident'>Arbitrary</span>, <span class='ident'>Gen</span>};
<span class='doccomment'>/// A quaternion. See `UnitQuaternion` for a quaternion that can be used as a rotation.</span>
<span class='attribute'>#[<span class='ident'>repr</span>(<span class='ident'>C</span>)]</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Eq</span>, <span class='ident'>PartialEq</span>, <span class='ident'>RustcEncodable</span>, <span class='ident'>RustcDecodable</span>, <span class='ident'>Clone</span>, <span class='ident'>Hash</span>, <span class='ident'>Debug</span>, <span class='ident'>Copy</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// The scalar component of the quaternion.</span>
<span class='kw'>pub</span> <span class='ident'>w</span>: <span class='ident'>N</span>,
<span class='doccomment'>/// The first vector component of the quaternion.</span>
<span class='kw'>pub</span> <span class='ident'>i</span>: <span class='ident'>N</span>,
<span class='doccomment'>/// The second vector component of the quaternion.</span>
<span class='kw'>pub</span> <span class='ident'>j</span>: <span class='ident'>N</span>,
<span class='doccomment'>/// The third vector component of the quaternion.</span>
<span class='kw'>pub</span> <span class='ident'>k</span>: <span class='ident'>N</span>
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Creates a new quaternion from its components.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new</span>(<span class='ident'>w</span>: <span class='ident'>N</span>, <span class='ident'>i</span>: <span class='ident'>N</span>, <span class='ident'>j</span>: <span class='ident'>N</span>, <span class='ident'>k</span>: <span class='ident'>N</span>) <span class='op'>-></span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>Quaternion</span> {
<span class='ident'>w</span>: <span class='ident'>w</span>,
<span class='ident'>i</span>: <span class='ident'>i</span>,
<span class='ident'>j</span>: <span class='ident'>j</span>,
<span class='ident'>k</span>: <span class='ident'>k</span>
}
}
<span class='doccomment'>/// The vector part `(i, j, k)` of this quaternion.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>vector</span><span class='op'><</span><span class='lifetime'>'a</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='comment'>// FIXME: do this require a `repr(C)` ?</span>
<span class='kw'>unsafe</span> {
<span class='ident'>mem</span>::<span class='ident'>transmute</span>(<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>i</span>)
}
}
<span class='doccomment'>/// The scalar part `w` of this quaternion.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>scalar</span><span class='op'><</span><span class='lifetime'>'a</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>N</span> {
<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>w</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Copy</span><span class='op'>></span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Compute the conjugate of this quaternion.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>conjugate</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>Quaternion</span> { <span class='ident'>w</span>: <span class='self'>self</span>.<span class='ident'>w</span>, <span class='ident'>i</span>: <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>i</span>, <span class='ident'>j</span>: <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>j</span>, <span class='ident'>k</span>: <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>k</span> }
}
<span class='doccomment'>/// Replaces this quaternion by its conjugate.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>conjugate_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) {
<span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>=</span> <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>i</span>;
<span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>=</span> <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>j</span>;
<span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>=</span> <span class='op'>-</span><span class='self'>self</span>.<span class='ident'>k</span>;
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span> <span class='op'>+</span> <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Inverse</span> <span class='kw'>for</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>res</span> <span class='op'>=</span> <span class='op'>*</span><span class='self'>self</span>;
<span class='kw'>if</span> <span class='ident'>res</span>.<span class='ident'>inverse_mut</span>() {
<span class='prelude-val'>Some</span>(<span class='ident'>res</span>)
}
<span class='kw'>else</span> {
<span class='prelude-val'>None</span>
}
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='kw'>let</span> <span class='ident'>norm_squared</span> <span class='op'>=</span> <span class='ident'>Norm</span>::<span class='ident'>norm_squared</span>(<span class='self'>self</span>);
<span class='kw'>if</span> <span class='ident'>ApproxEq</span>::<span class='ident'>approx_eq</span>(<span class='kw-2'>&</span><span class='ident'>norm_squared</span>, <span class='kw-2'>&</span>::<span class='ident'>zero</span>()) {
<span class='bool-val'>false</span>
}
<span class='kw'>else</span> {
<span class='self'>self</span>.<span class='ident'>conjugate_mut</span>();
<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>/</span> <span class='ident'>norm_squared</span>;
<span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>/</span> <span class='ident'>norm_squared</span>;
<span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>/</span> <span class='ident'>norm_squared</span>;
<span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>/</span> <span class='ident'>norm_squared</span>;
<span class='bool-val'>true</span>
}
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>norm_squared</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>k</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>normalize</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>norm</span>();
<span class='ident'>Quaternion</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>/</span> <span class='ident'>n</span>, <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>/</span> <span class='ident'>n</span>, <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>/</span> <span class='ident'>n</span>, <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>/</span> <span class='ident'>n</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>normalize_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='ident'>Norm</span>::<span class='ident'>norm</span>(<span class='self'>self</span>);
<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>/</span> <span class='ident'>n</span>;
<span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>/</span> <span class='ident'>n</span>;
<span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>/</span> <span class='ident'>n</span>;
<span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>/</span> <span class='ident'>n</span>;
<span class='ident'>n</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>
<span class='kw'>where</span> <span class='ident'>N</span>: <span class='ident'>Copy</span> <span class='op'>+</span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Sub</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Add</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>Quaternion</span>::<span class='ident'>new</span>(
<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>w</span> <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>i</span> <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>j</span> <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>k</span>,
<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>i</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>w</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>k</span> <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>j</span>,
<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>j</span> <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>k</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>w</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>i</span>,
<span class='self'>self</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>k</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>j</span> <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>j</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>i</span> <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>k</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>w</span>)
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='ident'>MulAssign</span><span class='op'><</span><span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>
<span class='kw'>where</span> <span class='ident'>N</span>: <span class='ident'>Copy</span> <span class='op'>+</span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Sub</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Add</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul_assign</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>=</span> <span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='ident'>right</span>;
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>Div</span><span class='op'><</span><span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>div</span>(<span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='self'>self</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>inverse</span>().<span class='ident'>expect</span>(<span class='string'>"Unable to invert the denominator."</span>)
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>DivAssign</span><span class='op'><</span><span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>div_assign</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>*=</span> <span class='ident'>right</span>.<span class='ident'>inverse</span>().<span class='ident'>expect</span>(<span class='string'>"Unable to invert the denominator."</span>)
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>fmt</span>::<span class='ident'>Display</span><span class='op'>></span> <span class='ident'>fmt</span>::<span class='ident'>Display</span> <span class='kw'>for</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>fmt</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>f</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>fmt</span>::<span class='ident'>Formatter</span>) <span class='op'>-></span> <span class='ident'>fmt</span>::<span class='prelude-ty'>Result</span> {
<span class='macro'>write</span><span class='macro'>!</span>(<span class='ident'>f</span>, <span class='string'>"Quaternion {} − ({}, {}, {})"</span>, <span class='self'>self</span>.<span class='ident'>w</span>, <span class='self'>self</span>.<span class='ident'>i</span>, <span class='self'>self</span>.<span class='ident'>j</span>, <span class='self'>self</span>.<span class='ident'>k</span>)
}
}
<span class='macro'>rand_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='doccomment'>/// A unit quaternion that can represent a 3D rotation.</span>
<span class='attribute'>#[<span class='ident'>repr</span>(<span class='ident'>C</span>)]</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Eq</span>, <span class='ident'>PartialEq</span>, <span class='ident'>RustcEncodable</span>, <span class='ident'>RustcDecodable</span>, <span class='ident'>Clone</span>, <span class='ident'>Hash</span>, <span class='ident'>Debug</span>, <span class='ident'>Copy</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>q</span>: <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Creates a new unit quaternion from the axis-angle representation of a rotation.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new</span>(<span class='ident'>axisangle</span>: <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>sqang</span> <span class='op'>=</span> <span class='ident'>Norm</span>::<span class='ident'>norm_squared</span>(<span class='kw-2'>&</span><span class='ident'>axisangle</span>);
<span class='kw'>if</span> ::<span class='ident'>is_zero</span>(<span class='kw-2'>&</span><span class='ident'>sqang</span>) {
::<span class='ident'>one</span>()
}
<span class='kw'>else</span> {
<span class='kw'>let</span> <span class='ident'>ang</span> <span class='op'>=</span> <span class='ident'>sqang</span>.<span class='ident'>sqrt</span>();
<span class='kw'>let</span> (<span class='ident'>s</span>, <span class='ident'>c</span>) <span class='op'>=</span> (<span class='ident'>ang</span> <span class='op'>/</span> <span class='ident'>Cast</span>::<span class='ident'>from</span>(<span class='number'>2.0</span>)).<span class='ident'>sin_cos</span>();
<span class='kw'>let</span> <span class='ident'>s_ang</span> <span class='op'>=</span> <span class='ident'>s</span> <span class='op'>/</span> <span class='ident'>ang</span>;
<span class='kw'>unsafe</span> {
<span class='ident'>UnitQuaternion</span>::<span class='ident'>new_with_unit_quaternion</span>(
<span class='ident'>Quaternion</span>::<span class='ident'>new</span>(
<span class='ident'>c</span>,
<span class='ident'>axisangle</span>.<span class='ident'>x</span> <span class='op'>*</span> <span class='ident'>s_ang</span>,
<span class='ident'>axisangle</span>.<span class='ident'>y</span> <span class='op'>*</span> <span class='ident'>s_ang</span>,
<span class='ident'>axisangle</span>.<span class='ident'>z</span> <span class='op'>*</span> <span class='ident'>s_ang</span>)
)
}
}
}
<span class='doccomment'>/// Creates a new unit quaternion from a quaternion.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The input quaternion will be normalized.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new_with_quaternion</span>(<span class='ident'>q</span>: <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>UnitQuaternion</span> { <span class='ident'>q</span>: <span class='ident'>q</span>.<span class='ident'>normalize</span>() }
}
<span class='doccomment'>/// Creates a new unit quaternion from Euler angles.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new_with_euler_angles</span>(<span class='ident'>roll</span>: <span class='ident'>N</span>, <span class='ident'>pitch</span>: <span class='ident'>N</span>, <span class='ident'>yaw</span>: <span class='ident'>N</span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>_0_5</span>: <span class='ident'>N</span> <span class='op'>=</span> <span class='ident'>Cast</span>::<span class='ident'>from</span>(<span class='number'>0.5</span>);
<span class='kw'>let</span> (<span class='ident'>sr</span>, <span class='ident'>cr</span>) <span class='op'>=</span> (<span class='ident'>roll</span> <span class='op'>*</span> <span class='ident'>_0_5</span>).<span class='ident'>sin_cos</span>();
<span class='kw'>let</span> (<span class='ident'>sp</span>, <span class='ident'>cp</span>) <span class='op'>=</span> (<span class='ident'>pitch</span> <span class='op'>*</span> <span class='ident'>_0_5</span>).<span class='ident'>sin_cos</span>();
<span class='kw'>let</span> (<span class='ident'>sy</span>, <span class='ident'>cy</span>) <span class='op'>=</span> (<span class='ident'>yaw</span> <span class='op'>*</span> <span class='ident'>_0_5</span>).<span class='ident'>sin_cos</span>();
<span class='kw'>unsafe</span> {
<span class='ident'>UnitQuaternion</span>::<span class='ident'>new_with_unit_quaternion</span>(
<span class='ident'>Quaternion</span>::<span class='ident'>new</span>(
<span class='ident'>cr</span> <span class='op'>*</span> <span class='ident'>cp</span> <span class='op'>*</span> <span class='ident'>cy</span> <span class='op'>+</span> <span class='ident'>sr</span> <span class='op'>*</span> <span class='ident'>sp</span> <span class='op'>*</span> <span class='ident'>sy</span>,
<span class='ident'>sr</span> <span class='op'>*</span> <span class='ident'>cp</span> <span class='op'>*</span> <span class='ident'>cy</span> <span class='op'>-</span> <span class='ident'>cr</span> <span class='op'>*</span> <span class='ident'>sp</span> <span class='op'>*</span> <span class='ident'>sy</span>,
<span class='ident'>cr</span> <span class='op'>*</span> <span class='ident'>sp</span> <span class='op'>*</span> <span class='ident'>cy</span> <span class='op'>+</span> <span class='ident'>sr</span> <span class='op'>*</span> <span class='ident'>cp</span> <span class='op'>*</span> <span class='ident'>sy</span>,
<span class='ident'>cr</span> <span class='op'>*</span> <span class='ident'>cp</span> <span class='op'>*</span> <span class='ident'>sy</span> <span class='op'>-</span> <span class='ident'>sr</span> <span class='op'>*</span> <span class='ident'>sp</span> <span class='op'>*</span> <span class='ident'>cy</span>)
)
}
}
<span class='doccomment'>/// Builds a rotation matrix from this quaternion.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>to_rotation_matrix</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Rotation3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>_2</span>: <span class='ident'>N</span> <span class='op'>=</span> <span class='ident'>Cast</span>::<span class='ident'>from</span>(<span class='number'>2.0</span>);
<span class='kw'>let</span> <span class='ident'>ww</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span>;
<span class='kw'>let</span> <span class='ident'>ii</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>i</span>;
<span class='kw'>let</span> <span class='ident'>jj</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>j</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>j</span>;
<span class='kw'>let</span> <span class='ident'>kk</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>k</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>k</span>;
<span class='kw'>let</span> <span class='ident'>ij</span> <span class='op'>=</span> <span class='ident'>_2</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>j</span>;
<span class='kw'>let</span> <span class='ident'>wk</span> <span class='op'>=</span> <span class='ident'>_2</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>k</span>;
<span class='kw'>let</span> <span class='ident'>wj</span> <span class='op'>=</span> <span class='ident'>_2</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>j</span>;
<span class='kw'>let</span> <span class='ident'>ik</span> <span class='op'>=</span> <span class='ident'>_2</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>i</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>k</span>;
<span class='kw'>let</span> <span class='ident'>jk</span> <span class='op'>=</span> <span class='ident'>_2</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>j</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>k</span>;
<span class='kw'>let</span> <span class='ident'>wi</span> <span class='op'>=</span> <span class='ident'>_2</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>i</span>;
<span class='kw'>unsafe</span> {
<span class='ident'>Rotation3</span>::<span class='ident'>new_with_matrix</span>(
<span class='ident'>Matrix3</span>::<span class='ident'>new</span>(
<span class='ident'>ww</span> <span class='op'>+</span> <span class='ident'>ii</span> <span class='op'>-</span> <span class='ident'>jj</span> <span class='op'>-</span> <span class='ident'>kk</span>, <span class='ident'>ij</span> <span class='op'>-</span> <span class='ident'>wk</span>, <span class='ident'>wj</span> <span class='op'>+</span> <span class='ident'>ik</span>,
<span class='ident'>wk</span> <span class='op'>+</span> <span class='ident'>ij</span>, <span class='ident'>ww</span> <span class='op'>-</span> <span class='ident'>ii</span> <span class='op'>+</span> <span class='ident'>jj</span> <span class='op'>-</span> <span class='ident'>kk</span>, <span class='ident'>jk</span> <span class='op'>-</span> <span class='ident'>wi</span>,
<span class='ident'>ik</span> <span class='op'>-</span> <span class='ident'>wj</span>, <span class='ident'>wi</span> <span class='op'>+</span> <span class='ident'>jk</span>, <span class='ident'>ww</span> <span class='op'>-</span> <span class='ident'>ii</span> <span class='op'>-</span> <span class='ident'>jj</span> <span class='op'>+</span> <span class='ident'>kk</span>
)
)
}
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Creates a new unit quaternion from a quaternion.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is unsafe because the input quaternion will not be normalized.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>unsafe</span> <span class='kw'>fn</span> <span class='ident'>new_with_unit_quaternion</span>(<span class='ident'>q</span>: <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>UnitQuaternion</span> {
<span class='ident'>q</span>: <span class='ident'>q</span>
}
}
<span class='doccomment'>/// The `Quaternion` representation of this unit quaternion.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>quaternion</span><span class='op'><</span><span class='lifetime'>'a</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Quaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>q</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span><span class='op'>></span> <span class='ident'>One</span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>one</span>() <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>unsafe</span> {
<span class='ident'>UnitQuaternion</span>::<span class='ident'>new_with_unit_quaternion</span>(<span class='ident'>Quaternion</span>::<span class='ident'>new</span>(::<span class='ident'>one</span>(), ::<span class='ident'>zero</span>(), ::<span class='ident'>zero</span>(), ::<span class='ident'>zero</span>()))
}
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>Copy</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Inverse</span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>cpy</span> <span class='op'>=</span> <span class='op'>*</span><span class='self'>self</span>;
<span class='ident'>cpy</span>.<span class='ident'>inverse_mut</span>();
<span class='prelude-val'>Some</span>(<span class='ident'>cpy</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>conjugate_mut</span>();
<span class='bool-val'>true</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>Rand</span> <span class='op'>+</span> <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>Rand</span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>rand</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(<span class='ident'>rng</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>UnitQuaternion</span>::<span class='ident'>new</span>(<span class='ident'>rng</span>.<span class='ident'>gen</span>())
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>approx_epsilon</span>(_: <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='ident'>ApproxEq</span>::<span class='ident'>approx_epsilon</span>(<span class='prelude-val'>None</span>::<span class='op'><</span><span class='ident'>N</span><span class='op'>></span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>approx_ulps</span>(_: <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>) <span class='op'>-></span> <span class='ident'>u32</span> {
<span class='ident'>ApproxEq</span>::<span class='ident'>approx_ulps</span>(<span class='prelude-val'>None</span>::<span class='op'><</span><span class='ident'>N</span><span class='op'>></span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>approx_eq_eps</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>eps</span>: <span class='kw-2'>&</span><span class='ident'>N</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>ApproxEq</span>::<span class='ident'>approx_eq_eps</span>(<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>q</span>, <span class='kw-2'>&</span><span class='ident'>other</span>.<span class='ident'>q</span>, <span class='ident'>eps</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>approx_eq_ulps</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>ulps</span>: <span class='ident'>u32</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>ApproxEq</span>::<span class='ident'>approx_eq_ulps</span>(<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>q</span>, <span class='kw-2'>&</span><span class='ident'>other</span>.<span class='ident'>q</span>, <span class='ident'>ulps</span>)
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span> <span class='op'>+</span> <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Div</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>div</span>(<span class='self'>self</span>, <span class='ident'>other</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>UnitQuaternion</span> { <span class='ident'>q</span>: <span class='self'>self</span>.<span class='ident'>q</span> <span class='op'>/</span> <span class='ident'>other</span>.<span class='ident'>q</span> }
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span> <span class='op'>+</span> <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='ident'>DivAssign</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>div_assign</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>other</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='self'>self</span>.<span class='ident'>q</span> <span class='op'>/=</span> <span class='ident'>other</span>.<span class='ident'>q</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span><span class='op'>></span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>UnitQuaternion</span> { <span class='ident'>q</span>: <span class='self'>self</span>.<span class='ident'>q</span> <span class='op'>*</span> <span class='ident'>right</span>.<span class='ident'>q</span> }
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span><span class='op'>></span> <span class='ident'>MulAssign</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul_assign</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='self'>self</span>.<span class='ident'>q</span> <span class='op'>*=</span> <span class='ident'>right</span>.<span class='ident'>q</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span><span class='op'>></span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>_2</span>: <span class='ident'>N</span> <span class='op'>=</span> ::<span class='ident'>one</span>::<span class='op'><</span><span class='ident'>N</span><span class='op'>></span>() <span class='op'>+</span> ::<span class='ident'>one</span>();
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>t</span> <span class='op'>=</span> ::<span class='ident'>cross</span>(<span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>vector</span>(), <span class='kw-2'>&</span><span class='ident'>right</span>);
<span class='ident'>t</span>.<span class='ident'>x</span> <span class='op'>=</span> <span class='ident'>t</span>.<span class='ident'>x</span> <span class='op'>*</span> <span class='ident'>_2</span>;
<span class='ident'>t</span>.<span class='ident'>y</span> <span class='op'>=</span> <span class='ident'>t</span>.<span class='ident'>y</span> <span class='op'>*</span> <span class='ident'>_2</span>;
<span class='ident'>t</span>.<span class='ident'>z</span> <span class='op'>=</span> <span class='ident'>t</span>.<span class='ident'>z</span> <span class='op'>*</span> <span class='ident'>_2</span>;
<span class='ident'>Vector3</span>::<span class='ident'>new</span>(<span class='ident'>t</span>.<span class='ident'>x</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span>, <span class='ident'>t</span>.<span class='ident'>y</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span>, <span class='ident'>t</span>.<span class='ident'>z</span> <span class='op'>*</span> <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span>) <span class='op'>+</span> ::<span class='ident'>cross</span>(<span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>vector</span>(), <span class='kw-2'>&</span><span class='ident'>t</span>) <span class='op'>+</span> <span class='ident'>right</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span><span class='op'>></span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
::<span class='ident'>origin</span>::<span class='op'><</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>() <span class='op'>+</span> <span class='self'>self</span> <span class='op'>*</span> <span class='op'>*</span><span class='ident'>right</span>.<span class='ident'>as_vector</span>()
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>inverse_quaternion</span> <span class='op'>=</span> <span class='ident'>right</span>;
<span class='ident'>inverse_quaternion</span>.<span class='ident'>inverse_mut</span>();
<span class='ident'>inverse_quaternion</span> <span class='op'>*</span> <span class='self'>self</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
::<span class='ident'>origin</span>::<span class='op'><</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>() <span class='op'>+</span> <span class='op'>*</span><span class='self'>self</span>.<span class='ident'>as_vector</span>() <span class='op'>*</span> <span class='ident'>right</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>MulAssign</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul_assign</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>=</span> <span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='ident'>right</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>MulAssign</span><span class='op'><</span><span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul_assign</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>right</span>: <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>=</span> <span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='ident'>right</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>_2</span> <span class='op'>=</span> ::<span class='ident'>one</span>::<span class='op'><</span><span class='ident'>N</span><span class='op'>></span>() <span class='op'>+</span> ::<span class='ident'>one</span>();
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>v</span> <span class='op'>=</span> <span class='op'>*</span><span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>vector</span>();
<span class='kw'>let</span> <span class='ident'>ang</span> <span class='op'>=</span> <span class='ident'>_2</span> <span class='op'>*</span> <span class='ident'>v</span>.<span class='ident'>normalize_mut</span>().<span class='ident'>atan2</span>(<span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span>);
<span class='kw'>if</span> ::<span class='ident'>is_zero</span>(<span class='kw-2'>&</span><span class='ident'>ang</span>) {
::<span class='ident'>zero</span>()
}
<span class='kw'>else</span> {
<span class='ident'>Vector3</span>::<span class='ident'>new</span>(<span class='ident'>v</span>.<span class='ident'>x</span> <span class='op'>*</span> <span class='ident'>ang</span>, <span class='ident'>v</span>.<span class='ident'>y</span> <span class='op'>*</span> <span class='ident'>ang</span>, <span class='ident'>v</span>.<span class='ident'>z</span> <span class='op'>*</span> <span class='ident'>ang</span>)
}
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse_rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>-</span><span class='self'>self</span>.<span class='ident'>rotation</span>()
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>=</span> <span class='ident'>Rotation</span>::<span class='ident'>append_rotation</span>(<span class='self'>self</span>, <span class='ident'>amount</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='ident'>UnitQuaternion</span>::<span class='ident'>new</span>(<span class='op'>*</span><span class='ident'>amount</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>prepend_rotation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>=</span> <span class='ident'>Rotation</span>::<span class='ident'>prepend_rotation</span>(<span class='self'>self</span>, <span class='ident'>amount</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>prepend_rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>UnitQuaternion</span>::<span class='ident'>new</span>(<span class='op'>*</span><span class='ident'>amount</span>) <span class='op'>*</span> <span class='op'>*</span><span class='self'>self</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>set_rotation</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>v</span>: <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>=</span> <span class='ident'>UnitQuaternion</span>::<span class='ident'>new</span>(<span class='ident'>v</span>)
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>RotationMatrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Rotation3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>to_rotation_matrix</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Rotation3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='self'>self</span>.<span class='ident'>to_rotation_matrix</span>()
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Rotate</span><span class='op'><</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>rotate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='op'>*</span><span class='ident'>v</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse_rotate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='ident'>v</span> <span class='op'>*</span> <span class='op'>*</span><span class='self'>self</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Rotate</span><span class='op'><</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>rotate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>p</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='op'>*</span><span class='ident'>p</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse_rotate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>p</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='ident'>p</span> <span class='op'>*</span> <span class='op'>*</span><span class='self'>self</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span> <span class='op'>+</span> <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='ident'>RotationTo</span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>AngleType</span> <span class='op'>=</span> <span class='ident'>N</span>;
<span class='kw'>type</span> <span class='ident'>DeltaRotationType</span> <span class='op'>=</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>angle_to</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='kw'>let</span> <span class='ident'>delta</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>rotation_to</span>(<span class='ident'>other</span>);
<span class='kw'>let</span> <span class='ident'>_2</span> <span class='op'>=</span> ::<span class='ident'>one</span>::<span class='op'><</span><span class='ident'>N</span><span class='op'>></span>() <span class='op'>+</span> ::<span class='ident'>one</span>();
<span class='ident'>_2</span> <span class='op'>*</span> <span class='ident'>delta</span>.<span class='ident'>q</span>.<span class='ident'>vector</span>().<span class='ident'>norm</span>().<span class='ident'>atan2</span>(<span class='ident'>delta</span>.<span class='ident'>q</span>.<span class='ident'>w</span>)
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>rotation_to</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='ident'>other</span> <span class='op'>/</span> <span class='op'>*</span><span class='self'>self</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Transform</span><span class='op'><</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>transform</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='op'>*</span><span class='ident'>v</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse_transform</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='ident'>v</span> <span class='op'>*</span> <span class='op'>*</span><span class='self'>self</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>>></span> <span class='ident'>Transform</span><span class='op'><</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>transform</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>p</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='self'>self</span> <span class='op'>*</span> <span class='op'>*</span><span class='ident'>p</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>inverse_transform</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>p</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='op'>*</span><span class='ident'>p</span> <span class='op'>*</span> <span class='op'>*</span><span class='self'>self</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>fmt</span>::<span class='ident'>Display</span><span class='op'>></span> <span class='ident'>fmt</span>::<span class='ident'>Display</span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>fmt</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>f</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>fmt</span>::<span class='ident'>Formatter</span>) <span class='op'>-></span> <span class='ident'>fmt</span>::<span class='prelude-ty'>Result</span> {
<span class='macro'>write</span><span class='macro'>!</span>(<span class='ident'>f</span>, <span class='string'>"Unit quaternion {} − ({}, {}, {})"</span>, <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>w</span>, <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>i</span>, <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>j</span>, <span class='self'>self</span>.<span class='ident'>q</span>.<span class='ident'>k</span>)
}
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span><span class='op'>=</span><span class='string'>"arbitrary"</span>)]</span>
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>Arbitrary</span> <span class='op'>+</span> <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>Arbitrary</span> <span class='kw'>for</span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>arbitrary</span><span class='op'><</span><span class='ident'>G</span>: <span class='ident'>Gen</span><span class='op'>></span>(<span class='ident'>g</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>G</span>) <span class='op'>-></span> <span class='ident'>UnitQuaternion</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>UnitQuaternion</span>::<span class='ident'>new</span>(<span class='ident'>Arbitrary</span>::<span class='ident'>arbitrary</span>(<span class='ident'>g</span>))
}
}
<span class='macro'>pord_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>vec_axis_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>vec_cast_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>conversion_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='number'>4</span>);
<span class='macro'>index_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>);
<span class='macro'>indexable_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='number'>4</span>);
<span class='macro'>at_fast_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='number'>4</span>);
<span class='macro'>repeat_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>val</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>dim_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='number'>3</span>);
<span class='macro'>container_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>);
<span class='macro'>add_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>sub_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>scalar_add_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>scalar_sub_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>scalar_mul_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>scalar_div_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>neg_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>zero_one_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>approx_eq_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>from_iterator_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>iterator</span>, <span class='ident'>iterator</span>, <span class='ident'>iterator</span>, <span class='ident'>iterator</span>);
<span class='macro'>bounded_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>axpy_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>iterable_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='number'>4</span>);
<span class='macro'>iterable_mut_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='number'>4</span>);
<span class='macro'>arbitrary_impl</span><span class='macro'>!</span>(<span class='ident'>Quaternion</span>, <span class='ident'>w</span>, <span class='ident'>i</span>, <span class='ident'>j</span>, <span class='ident'>k</span>);
<span class='macro'>dim_impl</span><span class='macro'>!</span>(<span class='ident'>UnitQuaternion</span>, <span class='number'>3</span>);
</pre>
</section>
<section id='search' class="content hidden"></section>
<section class="footer"></section>
<aside id="help" class="hidden">
<div>
<h1 class="hidden">Help</h1>
<div class="shortcuts">
<h2>Keyboard Shortcuts</h2>
<dl>
<dt>?</dt>
<dd>Show this help dialog</dd>
<dt>S</dt>
<dd>Focus the search field</dd>
<dt>⇤</dt>
<dd>Move up in search results</dd>
<dt>⇥</dt>
<dd>Move down in search results</dd>
<dt>⏎</dt>
<dd>Go to active search result</dd>
<dt>+</dt>
<dd>Collapse/expand all sections</dd>
</dl>
</div>
<div class="infos">
<h2>Search Tricks</h2>
<p>
Prefix searches with a type followed by a colon (e.g.
<code>fn:</code>) to restrict the search to a given type.
</p>
<p>
Accepted types are: <code>fn</code>, <code>mod</code>,
<code>struct</code>, <code>enum</code>,
<code>trait</code>, <code>type</code>, <code>macro</code>,
and <code>const</code>.
</p>
<p>
Search functions by type signature (e.g.
<code>vec -> usize</code> or <code>* -> vec</code>)
</p>
</div>
</div>
</aside>
<script>
window.rootPath = "../../../";
window.currentCrate = "nalgebra";
window.playgroundUrl = "";
</script>
<script src="../../../jquery.js"></script>
<script src="../../../main.js"></script>
<script defer src="../../../search-index.js"></script>
</body>
</html>