<!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 of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/geometry/similarity_construction.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>similarity_construction.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="icon" href="https://nalgebra.org/img/favicon.ico"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../nalgebra/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
<a href="#2" id="2">2</a>
<a href="#3" id="3">3</a>
<a href="#4" id="4">4</a>
<a href="#5" id="5">5</a>
<a href="#6" id="6">6</a>
<a href="#7" id="7">7</a>
<a href="#8" id="8">8</a>
<a href="#9" id="9">9</a>
<a href="#10" id="10">10</a>
<a href="#11" id="11">11</a>
<a href="#12" id="12">12</a>
<a href="#13" id="13">13</a>
<a href="#14" id="14">14</a>
<a href="#15" id="15">15</a>
<a href="#16" id="16">16</a>
<a href="#17" id="17">17</a>
<a href="#18" id="18">18</a>
<a href="#19" id="19">19</a>
<a href="#20" id="20">20</a>
<a href="#21" id="21">21</a>
<a href="#22" id="22">22</a>
<a href="#23" id="23">23</a>
<a href="#24" id="24">24</a>
<a href="#25" id="25">25</a>
<a href="#26" id="26">26</a>
<a href="#27" id="27">27</a>
<a href="#28" id="28">28</a>
<a href="#29" id="29">29</a>
<a href="#30" id="30">30</a>
<a href="#31" id="31">31</a>
<a href="#32" id="32">32</a>
<a href="#33" id="33">33</a>
<a href="#34" id="34">34</a>
<a href="#35" id="35">35</a>
<a href="#36" id="36">36</a>
<a href="#37" id="37">37</a>
<a href="#38" id="38">38</a>
<a href="#39" id="39">39</a>
<a href="#40" id="40">40</a>
<a href="#41" id="41">41</a>
<a href="#42" id="42">42</a>
<a href="#43" id="43">43</a>
<a href="#44" id="44">44</a>
<a href="#45" id="45">45</a>
<a href="#46" id="46">46</a>
<a href="#47" id="47">47</a>
<a href="#48" id="48">48</a>
<a href="#49" id="49">49</a>
<a href="#50" id="50">50</a>
<a href="#51" id="51">51</a>
<a href="#52" id="52">52</a>
<a href="#53" id="53">53</a>
<a href="#54" id="54">54</a>
<a href="#55" id="55">55</a>
<a href="#56" id="56">56</a>
<a href="#57" id="57">57</a>
<a href="#58" id="58">58</a>
<a href="#59" id="59">59</a>
<a href="#60" id="60">60</a>
<a href="#61" id="61">61</a>
<a href="#62" id="62">62</a>
<a href="#63" id="63">63</a>
<a href="#64" id="64">64</a>
<a href="#65" id="65">65</a>
<a href="#66" id="66">66</a>
<a href="#67" id="67">67</a>
<a href="#68" id="68">68</a>
<a href="#69" id="69">69</a>
<a href="#70" id="70">70</a>
<a href="#71" id="71">71</a>
<a href="#72" id="72">72</a>
<a href="#73" id="73">73</a>
<a href="#74" id="74">74</a>
<a href="#75" id="75">75</a>
<a href="#76" id="76">76</a>
<a href="#77" id="77">77</a>
<a href="#78" id="78">78</a>
<a href="#79" id="79">79</a>
<a href="#80" id="80">80</a>
<a href="#81" id="81">81</a>
<a href="#82" id="82">82</a>
<a href="#83" id="83">83</a>
<a href="#84" id="84">84</a>
<a href="#85" id="85">85</a>
<a href="#86" id="86">86</a>
<a href="#87" id="87">87</a>
<a href="#88" id="88">88</a>
<a href="#89" id="89">89</a>
<a href="#90" id="90">90</a>
<a href="#91" id="91">91</a>
<a href="#92" id="92">92</a>
<a href="#93" id="93">93</a>
<a href="#94" id="94">94</a>
<a href="#95" id="95">95</a>
<a href="#96" id="96">96</a>
<a href="#97" id="97">97</a>
<a href="#98" id="98">98</a>
<a href="#99" id="99">99</a>
<a href="#100" id="100">100</a>
<a href="#101" id="101">101</a>
<a href="#102" id="102">102</a>
<a href="#103" id="103">103</a>
<a href="#104" id="104">104</a>
<a href="#105" id="105">105</a>
<a href="#106" id="106">106</a>
<a href="#107" id="107">107</a>
<a href="#108" id="108">108</a>
<a href="#109" id="109">109</a>
<a href="#110" id="110">110</a>
<a href="#111" id="111">111</a>
<a href="#112" id="112">112</a>
<a href="#113" id="113">113</a>
<a href="#114" id="114">114</a>
<a href="#115" id="115">115</a>
<a href="#116" id="116">116</a>
<a href="#117" id="117">117</a>
<a href="#118" id="118">118</a>
<a href="#119" id="119">119</a>
<a href="#120" id="120">120</a>
<a href="#121" id="121">121</a>
<a href="#122" id="122">122</a>
<a href="#123" id="123">123</a>
<a href="#124" id="124">124</a>
<a href="#125" id="125">125</a>
<a href="#126" id="126">126</a>
<a href="#127" id="127">127</a>
<a href="#128" id="128">128</a>
<a href="#129" id="129">129</a>
<a href="#130" id="130">130</a>
<a href="#131" id="131">131</a>
<a href="#132" id="132">132</a>
<a href="#133" id="133">133</a>
<a href="#134" id="134">134</a>
<a href="#135" id="135">135</a>
<a href="#136" id="136">136</a>
<a href="#137" id="137">137</a>
<a href="#138" id="138">138</a>
<a href="#139" id="139">139</a>
<a href="#140" id="140">140</a>
<a href="#141" id="141">141</a>
<a href="#142" id="142">142</a>
<a href="#143" id="143">143</a>
<a href="#144" id="144">144</a>
<a href="#145" id="145">145</a>
<a href="#146" id="146">146</a>
<a href="#147" id="147">147</a>
<a href="#148" id="148">148</a>
<a href="#149" id="149">149</a>
<a href="#150" id="150">150</a>
<a href="#151" id="151">151</a>
<a href="#152" id="152">152</a>
<a href="#153" id="153">153</a>
<a href="#154" id="154">154</a>
<a href="#155" id="155">155</a>
<a href="#156" id="156">156</a>
<a href="#157" id="157">157</a>
<a href="#158" id="158">158</a>
<a href="#159" id="159">159</a>
<a href="#160" id="160">160</a>
<a href="#161" id="161">161</a>
<a href="#162" id="162">162</a>
<a href="#163" id="163">163</a>
<a href="#164" id="164">164</a>
<a href="#165" id="165">165</a>
<a href="#166" id="166">166</a>
<a href="#167" id="167">167</a>
<a href="#168" id="168">168</a>
<a href="#169" id="169">169</a>
<a href="#170" id="170">170</a>
<a href="#171" id="171">171</a>
<a href="#172" id="172">172</a>
<a href="#173" id="173">173</a>
<a href="#174" id="174">174</a>
<a href="#175" id="175">175</a>
<a href="#176" id="176">176</a>
<a href="#177" id="177">177</a>
<a href="#178" id="178">178</a>
<a href="#179" id="179">179</a>
<a href="#180" id="180">180</a>
<a href="#181" id="181">181</a>
<a href="#182" id="182">182</a>
<a href="#183" id="183">183</a>
<a href="#184" id="184">184</a>
<a href="#185" id="185">185</a>
<a href="#186" id="186">186</a>
<a href="#187" id="187">187</a>
<a href="#188" id="188">188</a>
<a href="#189" id="189">189</a>
<a href="#190" id="190">190</a>
<a href="#191" id="191">191</a>
<a href="#192" id="192">192</a>
<a href="#193" id="193">193</a>
<a href="#194" id="194">194</a>
<a href="#195" id="195">195</a>
<a href="#196" id="196">196</a>
<a href="#197" id="197">197</a>
<a href="#198" id="198">198</a>
<a href="#199" id="199">199</a>
<a href="#200" id="200">200</a>
<a href="#201" id="201">201</a>
<a href="#202" id="202">202</a>
<a href="#203" id="203">203</a>
<a href="#204" id="204">204</a>
<a href="#205" id="205">205</a>
<a href="#206" id="206">206</a>
<a href="#207" id="207">207</a>
<a href="#208" id="208">208</a>
<a href="#209" id="209">209</a>
<a href="#210" id="210">210</a>
<a href="#211" id="211">211</a>
<a href="#212" id="212">212</a>
<a href="#213" id="213">213</a>
<a href="#214" id="214">214</a>
<a href="#215" id="215">215</a>
<a href="#216" id="216">216</a>
<a href="#217" id="217">217</a>
<a href="#218" id="218">218</a>
<a href="#219" id="219">219</a>
<a href="#220" id="220">220</a>
<a href="#221" id="221">221</a>
<a href="#222" id="222">222</a>
<a href="#223" id="223">223</a>
<a href="#224" id="224">224</a>
<a href="#225" id="225">225</a>
<a href="#226" id="226">226</a>
<a href="#227" id="227">227</a>
<a href="#228" id="228">228</a>
<a href="#229" id="229">229</a>
<a href="#230" id="230">230</a>
<a href="#231" id="231">231</a>
<a href="#232" id="232">232</a>
<a href="#233" id="233">233</a>
<a href="#234" id="234">234</a>
<a href="#235" id="235">235</a>
<a href="#236" id="236">236</a>
<a href="#237" id="237">237</a>
<a href="#238" id="238">238</a>
<a href="#239" id="239">239</a>
<a href="#240" id="240">240</a>
<a href="#241" id="241">241</a>
<a href="#242" id="242">242</a>
<a href="#243" id="243">243</a>
<a href="#244" id="244">244</a>
<a href="#245" id="245">245</a>
<a href="#246" id="246">246</a>
<a href="#247" id="247">247</a>
<a href="#248" id="248">248</a>
<a href="#249" id="249">249</a>
<a href="#250" id="250">250</a>
<a href="#251" id="251">251</a>
<a href="#252" id="252">252</a>
<a href="#253" id="253">253</a>
<a href="#254" id="254">254</a>
<a href="#255" id="255">255</a>
<a href="#256" id="256">256</a>
<a href="#257" id="257">257</a>
<a href="#258" id="258">258</a>
<a href="#259" id="259">259</a>
<a href="#260" id="260">260</a>
<a href="#261" id="261">261</a>
<a href="#262" id="262">262</a>
<a href="#263" id="263">263</a>
<a href="#264" id="264">264</a>
<a href="#265" id="265">265</a>
<a href="#266" id="266">266</a>
<a href="#267" id="267">267</a>
<a href="#268" id="268">268</a>
<a href="#269" id="269">269</a>
<a href="#270" id="270">270</a>
<a href="#271" id="271">271</a>
<a href="#272" id="272">272</a>
<a href="#273" id="273">273</a>
<a href="#274" id="274">274</a>
<a href="#275" id="275">275</a>
<a href="#276" id="276">276</a>
<a href="#277" id="277">277</a>
<a href="#278" id="278">278</a>
<a href="#279" id="279">279</a>
<a href="#280" id="280">280</a>
<a href="#281" id="281">281</a>
<a href="#282" id="282">282</a>
<a href="#283" id="283">283</a>
<a href="#284" id="284">284</a>
<a href="#285" id="285">285</a>
<a href="#286" id="286">286</a>
<a href="#287" id="287">287</a>
<a href="#288" id="288">288</a>
<a href="#289" id="289">289</a>
<a href="#290" id="290">290</a>
<a href="#291" id="291">291</a>
<a href="#292" id="292">292</a>
<a href="#293" id="293">293</a>
<a href="#294" id="294">294</a>
<a href="#295" id="295">295</a>
<a href="#296" id="296">296</a>
<a href="#297" id="297">297</a>
<a href="#298" id="298">298</a>
<a href="#299" id="299">299</a>
<a href="#300" id="300">300</a>
<a href="#301" id="301">301</a>
<a href="#302" id="302">302</a>
<a href="#303" id="303">303</a>
<a href="#304" id="304">304</a>
<a href="#305" id="305">305</a>
<a href="#306" id="306">306</a>
<a href="#307" id="307">307</a>
<a href="#308" id="308">308</a>
<a href="#309" id="309">309</a>
<a href="#310" id="310">310</a>
<a href="#311" id="311">311</a>
<a href="#312" id="312">312</a>
<a href="#313" id="313">313</a>
<a href="#314" id="314">314</a>
<a href="#315" id="315">315</a>
<a href="#316" id="316">316</a>
<a href="#317" id="317">317</a>
<a href="#318" id="318">318</a>
<a href="#319" id="319">319</a>
<a href="#320" id="320">320</a>
<a href="#321" id="321">321</a>
<a href="#322" id="322">322</a>
<a href="#323" id="323">323</a>
<a href="#324" id="324">324</a>
<a href="#325" id="325">325</a>
<a href="#326" id="326">326</a>
<a href="#327" id="327">327</a>
<a href="#328" id="328">328</a>
<a href="#329" id="329">329</a>
<a href="#330" id="330">330</a>
<a href="#331" id="331">331</a>
<a href="#332" id="332">332</a>
<a href="#333" id="333">333</a>
<a href="#334" id="334">334</a>
<a href="#335" id="335">335</a>
<a href="#336" id="336">336</a>
<a href="#337" id="337">337</a>
<a href="#338" id="338">338</a>
<a href="#339" id="339">339</a>
<a href="#340" id="340">340</a>
<a href="#341" id="341">341</a>
<a href="#342" id="342">342</a>
<a href="#343" id="343">343</a>
<a href="#344" id="344">344</a>
<a href="#345" id="345">345</a>
<a href="#346" id="346">346</a>
<a href="#347" id="347">347</a>
<a href="#348" id="348">348</a>
<a href="#349" id="349">349</a>
<a href="#350" id="350">350</a>
<a href="#351" id="351">351</a>
<a href="#352" id="352">352</a>
<a href="#353" id="353">353</a>
<a href="#354" id="354">354</a>
<a href="#355" id="355">355</a>
<a href="#356" id="356">356</a>
<a href="#357" id="357">357</a>
<a href="#358" id="358">358</a>
<a href="#359" id="359">359</a>
<a href="#360" id="360">360</a>
<a href="#361" id="361">361</a>
<a href="#362" id="362">362</a>
<a href="#363" id="363">363</a>
<a href="#364" id="364">364</a>
<a href="#365" id="365">365</a>
<a href="#366" id="366">366</a>
<a href="#367" id="367">367</a>
<a href="#368" id="368">368</a>
<a href="#369" id="369">369</a>
<a href="#370" id="370">370</a>
<a href="#371" id="371">371</a>
<a href="#372" id="372">372</a>
<a href="#373" id="373">373</a>
<a href="#374" id="374">374</a>
<a href="#375" id="375">375</a>
<a href="#376" id="376">376</a>
<a href="#377" id="377">377</a>
<a href="#378" id="378">378</a>
<a href="#379" id="379">379</a>
<a href="#380" id="380">380</a>
<a href="#381" id="381">381</a>
<a href="#382" id="382">382</a>
<a href="#383" id="383">383</a>
<a href="#384" id="384">384</a>
<a href="#385" id="385">385</a>
<a href="#386" id="386">386</a>
<a href="#387" id="387">387</a>
<a href="#388" id="388">388</a>
<a href="#389" id="389">389</a>
<a href="#390" id="390">390</a>
<a href="#391" id="391">391</a>
<a href="#392" id="392">392</a>
<a href="#393" id="393">393</a>
<a href="#394" id="394">394</a>
<a href="#395" id="395">395</a>
<a href="#396" id="396">396</a>
<a href="#397" id="397">397</a>
<a href="#398" id="398">398</a>
<a href="#399" id="399">399</a>
<a href="#400" id="400">400</a>
<a href="#401" id="401">401</a>
</pre><pre class="rust"><code><span class="attr">#[cfg(feature = <span class="string">"arbitrary"</span>)]
</span><span class="kw">use </span><span class="kw">crate</span>::base::storage::Owned;
<span class="attr">#[cfg(feature = <span class="string">"arbitrary"</span>)]
</span><span class="kw">use </span>quickcheck::{Arbitrary, Gen};
<span class="kw">use </span>num::One;
<span class="attr">#[cfg(feature = <span class="string">"rand-no-std"</span>)]
</span><span class="kw">use </span>rand::{
distributions::{Distribution, Standard},
Rng,
};
<span class="kw">use </span>simba::scalar::SupersetOf;
<span class="kw">use </span>simba::simd::SimdRealField;
<span class="kw">use </span><span class="kw">crate</span>::base::{Vector2, Vector3};
<span class="kw">use crate</span>::{
AbstractRotation, Isometry, Point, Point3, Rotation2, Rotation3, Scalar, Similarity,
Translation, UnitComplex, UnitQuaternion,
};
<span class="kw">impl</span><T: SimdRealField, R, <span class="kw">const </span>D: usize> Default <span class="kw">for </span>Similarity<T, R, D>
<span class="kw">where
</span>T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
<span class="kw">fn </span>default() -> <span class="self">Self </span>{
<span class="self">Self</span>::identity()
}
}
<span class="kw">impl</span><T: SimdRealField, R, <span class="kw">const </span>D: usize> Similarity<T, R, D>
<span class="kw">where
</span>T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
<span class="doccomment">/// Creates a new identity similarity.
///
/// # Example
/// ```
/// # use nalgebra::{Similarity2, Point2, Similarity3, Point3};
///
/// let sim = Similarity2::identity();
/// let pt = Point2::new(1.0, 2.0);
/// assert_eq!(sim * pt, pt);
///
/// let sim = Similarity3::identity();
/// let pt = Point3::new(1.0, 2.0, 3.0);
/// assert_eq!(sim * pt, pt);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>identity() -> <span class="self">Self </span>{
<span class="self">Self</span>::from_isometry(Isometry::identity(), T::one())
}
}
<span class="kw">impl</span><T: SimdRealField, R, <span class="kw">const </span>D: usize> One <span class="kw">for </span>Similarity<T, R, D>
<span class="kw">where
</span>T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
<span class="doccomment">/// Creates a new identity similarity.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>one() -> <span class="self">Self </span>{
<span class="self">Self</span>::identity()
}
}
<span class="attr">#[cfg(feature = <span class="string">"rand-no-std"</span>)]
</span><span class="kw">impl</span><T: <span class="kw">crate</span>::RealField, R, <span class="kw">const </span>D: usize> Distribution<Similarity<T, R, D>> <span class="kw">for </span>Standard
<span class="kw">where
</span>R: AbstractRotation<T, D>,
Standard: Distribution<T> + Distribution<R>,
{
<span class="doccomment">/// Generate an arbitrary random variate for testing purposes.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>sample<<span class="lifetime">'a</span>, G: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>G) -> Similarity<T, R, D> {
<span class="kw">let </span><span class="kw-2">mut </span>s = rng.gen();
<span class="kw">while </span><span class="macro">relative_eq!</span>(s, T::zero()) {
s = rng.gen()
}
Similarity::from_isometry(rng.gen(), s)
}
}
<span class="kw">impl</span><T: SimdRealField, R, <span class="kw">const </span>D: usize> Similarity<T, R, D>
<span class="kw">where
</span>T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
<span class="doccomment">/// The similarity that applies the scaling factor `scaling`, followed by the rotation `r` with
/// its axis passing through the point `p`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity2, Point2, UnitComplex};
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
/// let pt = Point2::new(3.0, 2.0);
/// let sim = Similarity2::rotation_wrt_point(rot, pt, 4.0);
///
/// assert_relative_eq!(sim * Point2::new(1.0, 2.0), Point2::new(-3.0, 3.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>rotation_wrt_point(r: R, p: Point<T, D>, scaling: T) -> <span class="self">Self </span>{
<span class="kw">let </span>shift = r.transform_vector(<span class="kw-2">&</span>-<span class="kw-2">&</span>p.coords);
<span class="self">Self</span>::from_parts(Translation::from(shift + p.coords), r, scaling)
}
}
<span class="attr">#[cfg(feature = <span class="string">"arbitrary"</span>)]
</span><span class="kw">impl</span><T, R, <span class="kw">const </span>D: usize> Arbitrary <span class="kw">for </span>Similarity<T, R, D>
<span class="kw">where
</span>T: <span class="kw">crate</span>::RealField + Arbitrary + Send,
T::Element: <span class="kw">crate</span>::RealField,
R: AbstractRotation<T, D> + Arbitrary + Send,
Owned<T, <span class="kw">crate</span>::Const<D>>: Send,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>arbitrary(rng: <span class="kw-2">&mut </span>Gen) -> <span class="self">Self </span>{
<span class="kw">let </span><span class="kw-2">mut </span>s: T = Arbitrary::arbitrary(rng);
<span class="kw">while </span>s.is_zero() {
s = Arbitrary::arbitrary(rng)
}
<span class="self">Self</span>::from_isometry(Arbitrary::arbitrary(rng), s)
}
}
<span class="comment">/*
*
* Constructors for various static dimensions.
*
*/
// 2D similarity.
</span><span class="kw">impl</span><T: SimdRealField> Similarity<T, Rotation2<T>, <span class="number">2</span>>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// Creates a new similarity from a translation, a rotation, and an uniform scaling factor.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{SimilarityMatrix2, Vector2, Point2};
/// let sim = SimilarityMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
///
/// assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>new(translation: Vector2<T>, angle: T, scaling: T) -> <span class="self">Self </span>{
<span class="self">Self</span>::from_parts(
Translation::from(translation),
Rotation2::new(angle),
scaling,
)
}
<span class="doccomment">/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::SimilarityMatrix2;
/// let sim = SimilarityMatrix2::<f64>::identity();
/// let sim2 = sim.cast::<f32>();
/// assert_eq!(sim2, SimilarityMatrix2::<f32>::identity());
/// ```
</span><span class="kw">pub fn </span>cast<To: Scalar>(<span class="self">self</span>) -> Similarity<To, Rotation2<To>, <span class="number">2</span>>
<span class="kw">where
</span>Similarity<To, Rotation2<To>, <span class="number">2</span>>: SupersetOf<<span class="self">Self</span>>,
{
<span class="kw">crate</span>::convert(<span class="self">self</span>)
}
}
<span class="kw">impl</span><T: SimdRealField> Similarity<T, UnitComplex<T>, <span class="number">2</span>>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// Creates a new similarity from a translation and a rotation angle.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity2, Vector2, Point2};
/// let sim = Similarity2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
///
/// assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>new(translation: Vector2<T>, angle: T, scaling: T) -> <span class="self">Self </span>{
<span class="self">Self</span>::from_parts(
Translation::from(translation),
UnitComplex::new(angle),
scaling,
)
}
<span class="doccomment">/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Similarity2;
/// let sim = Similarity2::<f64>::identity();
/// let sim2 = sim.cast::<f32>();
/// assert_eq!(sim2, Similarity2::<f32>::identity());
/// ```
</span><span class="kw">pub fn </span>cast<To: Scalar>(<span class="self">self</span>) -> Similarity<To, UnitComplex<To>, <span class="number">2</span>>
<span class="kw">where
</span>Similarity<To, UnitComplex<To>, <span class="number">2</span>>: SupersetOf<<span class="self">Self</span>>,
{
<span class="kw">crate</span>::convert(<span class="self">self</span>)
}
}
<span class="comment">// 3D rotation.
</span><span class="macro">macro_rules! </span>similarity_construction_impl(
(<span class="macro-nonterminal">$Rot</span>: ident) => {
<span class="kw">impl</span><T: SimdRealField> Similarity<T, <span class="macro-nonterminal">$Rot</span><T>, <span class="number">3</span>>
<span class="kw">where </span>T::Element: SimdRealField {
<span class="doccomment">/// Creates a new similarity from a translation, rotation axis-angle, and scaling
/// factor.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
/// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
/// let translation = Vector3::new(1.0, 2.0, 3.0);
/// // Point and vector being transformed in the tests.
/// let pt = Point3::new(4.0, 5.0, 6.0);
/// let vec = Vector3::new(4.0, 5.0, 6.0);
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let sim = Similarity3::new(translation, axisangle, 3.0);
/// assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
/// assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);
///
/// // Similarity with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
/// let sim = SimilarityMatrix3::new(translation, axisangle, 3.0);
/// assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
/// assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>new(translation: Vector3<T>, axisangle: Vector3<T>, scaling: T) -> <span class="self">Self
</span>{
<span class="self">Self</span>::from_isometry(Isometry::<<span class="kw">_</span>, <span class="macro-nonterminal">$Rot</span><T>, <span class="number">3</span>>::new(translation, axisangle), scaling)
}
<span class="doccomment">/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Similarity3;
/// let sim = Similarity3::<f64>::identity();
/// let sim2 = sim.cast::<f32>();
/// assert_eq!(sim2, Similarity3::<f32>::identity());
/// ```
</span><span class="kw">pub fn </span>cast<To: Scalar>(<span class="self">self</span>) -> Similarity<To, <span class="macro-nonterminal">$Rot</span><To>, <span class="number">3</span>>
<span class="kw">where
</span>Similarity<To, <span class="macro-nonterminal">$Rot</span><To>, <span class="number">3</span>>: SupersetOf<<span class="self">Self</span>>,
{
<span class="kw">crate</span>::convert(<span class="self">self</span>)
}
<span class="doccomment">/// Creates an similarity that corresponds to a scaling factor and a local frame of
/// an observer standing at the point `eye` and looking toward `target`.
///
/// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
/// `eye`.
///
/// # Arguments
/// * eye - The observer position.
/// * target - The target position.
/// * up - Vertical direction. The only requirement of this parameter is to not be collinear
/// to `eye - at`. Non-collinearity is not checked.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
/// let eye = Point3::new(1.0, 2.0, 3.0);
/// let target = Point3::new(2.0, 2.0, 3.0);
/// let up = Vector3::y();
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let sim = Similarity3::face_towards(&eye, &target, &up, 3.0);
/// assert_eq!(sim * Point3::origin(), eye);
/// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
///
/// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
/// let sim = SimilarityMatrix3::face_towards(&eye, &target, &up, 3.0);
/// assert_eq!(sim * Point3::origin(), eye);
/// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>face_towards(eye: <span class="kw-2">&</span>Point3<T>,
target: <span class="kw-2">&</span>Point3<T>,
up: <span class="kw-2">&</span>Vector3<T>,
scaling: T)
-> <span class="self">Self </span>{
<span class="self">Self</span>::from_isometry(Isometry::<<span class="kw">_</span>, <span class="macro-nonterminal">$Rot</span><T>, <span class="number">3</span>>::face_towards(eye, target, up), scaling)
}
<span class="doccomment">/// Deprecated: Use [`SimilarityMatrix3::face_towards`](Self::face_towards) instead.
</span><span class="attr">#[deprecated(note=<span class="string">"renamed to `face_towards`"</span>)]
</span><span class="kw">pub fn </span>new_observer_frames(eye: <span class="kw-2">&</span>Point3<T>,
target: <span class="kw-2">&</span>Point3<T>,
up: <span class="kw-2">&</span>Vector3<T>,
scaling: T)
-> <span class="self">Self </span>{
<span class="self">Self</span>::face_towards(eye, target, up, scaling)
}
<span class="doccomment">/// Builds a right-handed look-at view matrix including scaling factor.
///
/// This conforms to the common notion of right handed look-at matrix from the computer
/// graphics community.
///
/// # Arguments
/// * eye - The eye position.
/// * target - The target position.
/// * up - A vector approximately aligned with required the vertical axis. The only
/// requirement of this parameter is to not be collinear to `target - eye`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
/// let eye = Point3::new(1.0, 2.0, 3.0);
/// let target = Point3::new(2.0, 2.0, 3.0);
/// let up = Vector3::y();
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let iso = Similarity3::look_at_rh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);
///
/// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
/// let iso = SimilarityMatrix3::look_at_rh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>look_at_rh(eye: <span class="kw-2">&</span>Point3<T>,
target: <span class="kw-2">&</span>Point3<T>,
up: <span class="kw-2">&</span>Vector3<T>,
scaling: T)
-> <span class="self">Self </span>{
<span class="self">Self</span>::from_isometry(Isometry::<<span class="kw">_</span>, <span class="macro-nonterminal">$Rot</span><T>, <span class="number">3</span>>::look_at_rh(eye, target, up), scaling)
}
<span class="doccomment">/// Builds a left-handed look-at view matrix including a scaling factor.
///
/// This conforms to the common notion of left handed look-at matrix from the computer
/// graphics community.
///
/// # Arguments
/// * eye - The eye position.
/// * target - The target position.
/// * up - A vector approximately aligned with required the vertical axis. The only
/// requirement of this parameter is to not be collinear to `target - eye`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
/// let eye = Point3::new(1.0, 2.0, 3.0);
/// let target = Point3::new(2.0, 2.0, 3.0);
/// let up = Vector3::y();
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let sim = Similarity3::look_at_lh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);
///
/// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
/// let sim = SimilarityMatrix3::look_at_lh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>look_at_lh(eye: <span class="kw-2">&</span>Point3<T>,
target: <span class="kw-2">&</span>Point3<T>,
up: <span class="kw-2">&</span>Vector3<T>,
scaling: T)
-> <span class="self">Self </span>{
<span class="self">Self</span>::from_isometry(Isometry::<<span class="kw">_</span>, <span class="macro-nonterminal">$Rot</span><T>, <span class="number">3</span>>::look_at_lh(eye, target, up), scaling)
}
}
}
);
<span class="macro">similarity_construction_impl!</span>(Rotation3);
<span class="macro">similarity_construction_impl!</span>(UnitQuaternion);
</code></pre></div>
</section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="nalgebra" data-themes="" data-resource-suffix="" data-rustdoc-version="1.67.1 (d5a82bbd2 2023-02-07)" data-search-js="search-444266647c4dba98.js" data-settings-js="settings-bebeae96e00e4617.js" data-settings-css="settings-af96d9e2fc13e081.css" ></div></body></html>