<!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/mrh/.cargo/registry/src/github.com-1ecc6299db9ec823/cgmath-0.17.0/src/euler.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>euler.rs.html -- source</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc source"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../cgmath/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><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>
</pre><div class="example-wrap"><pre class="rust ">
<span class="comment">// Copyright 2016 The CGMath Developers. For a full listing of the authors,</span>
<span class="comment">// refer to the Cargo.toml file at the top-level directory of this distribution.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span>
<span class="comment">// you may not use this file except in compliance with the License.</span>
<span class="comment">// You may obtain a copy of the License at</span>
<span class="comment">//</span>
<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span>
<span class="comment">//</span>
<span class="comment">// Unless required by applicable law or agreed to in writing, software</span>
<span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span>
<span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span>
<span class="comment">// See the License for the specific language governing permissions and</span>
<span class="comment">// limitations under the License.</span>
<span class="kw">use</span> <span class="ident">rand</span>::<span class="ident">distributions</span>::{<span class="ident">Distribution</span>, <span class="ident">Standard</span>};
<span class="kw">use</span> <span class="ident">rand</span>::<span class="ident">Rng</span>;
<span class="kw">use</span> <span class="ident">num_traits</span>::<span class="ident">cast</span>;
<span class="kw">use</span> <span class="ident">structure</span>::<span class="kw-2">*</span>;
<span class="kw">use</span> <span class="ident">angle</span>::<span class="ident">Rad</span>;
<span class="kw">use</span> <span class="ident">approx</span>;
<span class="kw">use</span> <span class="ident">quaternion</span>::<span class="ident">Quaternion</span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"mint"</span>)]</span>
<span class="kw">use</span> <span class="ident">mint</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">BaseFloat</span>;
<span class="doccomment">/// A set of [Euler angles] representing a rotation in three-dimensional space.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This type is marked as `#[repr(C)]`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The axis rotation sequence is XYZ. That is, the rotation is first around</span>
<span class="doccomment">/// the X axis, then the Y axis, and lastly the Z axis (using intrinsic</span>
<span class="doccomment">/// rotations). Since all three rotation axes are used, the angles are</span>
<span class="doccomment">/// Tait–Bryan angles rather than proper Euler angles.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Ranges</span>
<span class="doccomment">///</span>
<span class="doccomment">/// - x: [-pi, pi]</span>
<span class="doccomment">/// - y: [-pi/2, pi/2]</span>
<span class="doccomment">/// - z: [-pi, pi]</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Defining rotations using Euler angles</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Note that while [Euler angles] are intuitive to define, they are prone to</span>
<span class="doccomment">/// [gimbal lock] and are challenging to interpolate between. Instead we</span>
<span class="doccomment">/// recommend that you convert them to a more robust representation, such as a</span>
<span class="doccomment">/// quaternion or a rotation matrix. To this end, `From<Euler<A>>` conversions</span>
<span class="doccomment">/// are provided for the following types:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// - [`Basis3`](struct.Basis3.html)</span>
<span class="doccomment">/// - [`Matrix3`](struct.Matrix3.html)</span>
<span class="doccomment">/// - [`Matrix4`](struct.Matrix4.html)</span>
<span class="doccomment">/// - [`Quaternion`](struct.Quaternion.html)</span>
<span class="doccomment">///</span>
<span class="doccomment">/// For example, to define a quaternion that applies the following:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// 1. a 90° rotation around the _x_ axis</span>
<span class="doccomment">/// 2. a 45° rotation around the _y_ axis</span>
<span class="doccomment">/// 3. a 15° rotation around the _z_ axis</span>
<span class="doccomment">///</span>
<span class="doccomment">/// you can use the following code:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use cgmath::{Deg, Euler, Quaternion};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let rotation = Quaternion::from(Euler {</span>
<span class="doccomment">/// x: Deg(90.0),</span>
<span class="doccomment">/// y: Deg(45.0),</span>
<span class="doccomment">/// z: Deg(15.0),</span>
<span class="doccomment">/// });</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">///</span>
<span class="doccomment">/// [Euler angles]: https://en.wikipedia.org/wiki/Euler_angles</span>
<span class="doccomment">/// [gimbal lock]: https://en.wikipedia.org/wiki/Gimbal_lock#Gimbal_lock_in_applied_mathematics</span>
<span class="doccomment">/// [convert]: #defining-rotations-using-euler-angles</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">Copy</span>, <span class="ident">Clone</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
<span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"serde"</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="doccomment">/// The angle to apply around the _x_ axis. Also known at the _pitch_.</span>
<span class="kw">pub</span> <span class="ident">x</span>: <span class="ident">A</span>,
<span class="doccomment">/// The angle to apply around the _y_ axis. Also known at the _yaw_.</span>
<span class="kw">pub</span> <span class="ident">y</span>: <span class="ident">A</span>,
<span class="doccomment">/// The angle to apply around the _z_ axis. Also known at the _roll_.</span>
<span class="kw">pub</span> <span class="ident">z</span>: <span class="ident">A</span>,
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="doccomment">/// Construct a set of euler angles.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Arguments</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * `x` - The angle to apply around the _x_ axis. Also known at the _pitch_.</span>
<span class="doccomment">/// * `y` - The angle to apply around the _y_ axis. Also known at the _yaw_.</span>
<span class="doccomment">/// * `z` - The angle to apply around the _z_ axis. Also known at the _roll_.</span>
<span class="kw">pub</span> <span class="kw">const</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">x</span>: <span class="ident">A</span>, <span class="ident">y</span>: <span class="ident">A</span>, <span class="ident">z</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="ident">Euler</span> { <span class="ident">x</span>: <span class="ident">x</span>, <span class="ident">y</span>: <span class="ident">y</span>, <span class="ident">z</span>: <span class="ident">z</span> }
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">S</span>: <span class="ident">BaseFloat</span><span class="op">></span> <span class="ident">From</span><span class="op"><</span><span class="ident">Quaternion</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">Rad</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">src</span>: <span class="ident">Quaternion</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">Rad</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> {
<span class="kw">let</span> <span class="ident">sig</span>: <span class="ident">S</span> <span class="op">=</span> <span class="ident">cast</span>(<span class="number">0.499</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="ident">two</span>: <span class="ident">S</span> <span class="op">=</span> <span class="ident">cast</span>(<span class="number">2</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="ident">one</span>: <span class="ident">S</span> <span class="op">=</span> <span class="ident">cast</span>(<span class="number">1</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> (<span class="ident">qw</span>, <span class="ident">qx</span>, <span class="ident">qy</span>, <span class="ident">qz</span>) <span class="op">=</span> (<span class="ident">src</span>.<span class="ident">s</span>, <span class="ident">src</span>.<span class="ident">v</span>.<span class="ident">x</span>, <span class="ident">src</span>.<span class="ident">v</span>.<span class="ident">y</span>, <span class="ident">src</span>.<span class="ident">v</span>.<span class="ident">z</span>);
<span class="kw">let</span> (<span class="ident">sqw</span>, <span class="ident">sqx</span>, <span class="ident">sqy</span>, <span class="ident">sqz</span>) <span class="op">=</span> (<span class="ident">qw</span> <span class="op">*</span> <span class="ident">qw</span>, <span class="ident">qx</span> <span class="op">*</span> <span class="ident">qx</span>, <span class="ident">qy</span> <span class="op">*</span> <span class="ident">qy</span>, <span class="ident">qz</span> <span class="op">*</span> <span class="ident">qz</span>);
<span class="kw">let</span> <span class="ident">unit</span> <span class="op">=</span> <span class="ident">sqx</span> <span class="op">+</span> <span class="ident">sqz</span> <span class="op">+</span> <span class="ident">sqy</span> <span class="op">+</span> <span class="ident">sqw</span>;
<span class="kw">let</span> <span class="ident">test</span> <span class="op">=</span> <span class="ident">qx</span> <span class="op">*</span> <span class="ident">qz</span> <span class="op">+</span> <span class="ident">qy</span> <span class="op">*</span> <span class="ident">qw</span>;
<span class="comment">// We set x to zero and z to the value, but the other way would work too.</span>
<span class="kw">if</span> <span class="ident">test</span> <span class="op">></span> <span class="ident">sig</span> <span class="op">*</span> <span class="ident">unit</span> {
<span class="comment">// x + z = 2 * atan(x / w)</span>
<span class="ident">Euler</span> {
<span class="ident">x</span>: <span class="ident">Rad</span>::<span class="ident">zero</span>(),
<span class="ident">y</span>: <span class="ident">Rad</span>::<span class="ident">turn_div_4</span>(),
<span class="ident">z</span>: <span class="ident">Rad</span>::<span class="ident">atan2</span>(<span class="ident">qx</span>, <span class="ident">qw</span>) <span class="op">*</span> <span class="ident">two</span>,
}
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">test</span> <span class="op"><</span> <span class="op">-</span><span class="ident">sig</span> <span class="op">*</span> <span class="ident">unit</span> {
<span class="comment">// x - z = 2 * atan(x / w)</span>
<span class="ident">Euler</span> {
<span class="ident">x</span>: <span class="ident">Rad</span>::<span class="ident">zero</span>(),
<span class="ident">y</span>: <span class="op">-</span><span class="ident">Rad</span>::<span class="ident">turn_div_4</span>(),
<span class="ident">z</span>: <span class="op">-</span><span class="ident">Rad</span>::<span class="ident">atan2</span>(<span class="ident">qx</span>, <span class="ident">qw</span>) <span class="op">*</span> <span class="ident">two</span>,
}
} <span class="kw">else</span> {
<span class="comment">// Using the quat-to-matrix equation from either</span>
<span class="comment">// http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/index.htm</span>
<span class="comment">// or equation 15 on page 7 of</span>
<span class="comment">// http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf</span>
<span class="comment">// to fill in the equations on page A-2 of the NASA document gives the below.</span>
<span class="ident">Euler</span> {
<span class="ident">x</span>: <span class="ident">Rad</span>::<span class="ident">atan2</span>(<span class="ident">two</span> <span class="op">*</span> (<span class="op">-</span><span class="ident">qy</span> <span class="op">*</span> <span class="ident">qz</span> <span class="op">+</span> <span class="ident">qx</span> <span class="op">*</span> <span class="ident">qw</span>), <span class="ident">one</span> <span class="op">-</span> <span class="ident">two</span> <span class="op">*</span> (<span class="ident">sqx</span> <span class="op">+</span> <span class="ident">sqy</span>)),
<span class="ident">y</span>: <span class="ident">Rad</span>::<span class="ident">asin</span>(<span class="ident">two</span> <span class="op">*</span> (<span class="ident">qx</span> <span class="op">*</span> <span class="ident">qz</span> <span class="op">+</span> <span class="ident">qy</span> <span class="op">*</span> <span class="ident">qw</span>)),
<span class="ident">z</span>: <span class="ident">Rad</span>::<span class="ident">atan2</span>(<span class="ident">two</span> <span class="op">*</span> (<span class="op">-</span><span class="ident">qx</span> <span class="op">*</span> <span class="ident">qy</span> <span class="op">+</span> <span class="ident">qz</span> <span class="op">*</span> <span class="ident">qw</span>), <span class="ident">one</span> <span class="op">-</span> <span class="ident">two</span> <span class="op">*</span> (<span class="ident">sqy</span> <span class="op">+</span> <span class="ident">sqz</span>)),
}
}
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Angle</span><span class="op">></span> <span class="ident">approx</span>::<span class="ident">AbsDiffEq</span> <span class="kw">for</span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="kw">type</span> <span class="ident">Epsilon</span> <span class="op">=</span> <span class="ident">A</span>::<span class="ident">Epsilon</span>;
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">default_epsilon</span>() <span class="op">-</span><span class="op">></span> <span class="ident">A</span>::<span class="ident">Epsilon</span> {
<span class="ident">A</span>::<span class="ident">default_epsilon</span>()
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">abs_diff_eq</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="ident">epsilon</span>: <span class="ident">A</span>::<span class="ident">Epsilon</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="ident">A</span>::<span class="ident">abs_diff_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">x</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">x</span>, <span class="ident">epsilon</span>)
<span class="kw-2">&</span><span class="op">&</span> <span class="ident">A</span>::<span class="ident">abs_diff_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">y</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">y</span>, <span class="ident">epsilon</span>)
<span class="kw-2">&</span><span class="op">&</span> <span class="ident">A</span>::<span class="ident">abs_diff_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">z</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">z</span>, <span class="ident">epsilon</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Angle</span><span class="op">></span> <span class="ident">approx</span>::<span class="ident">RelativeEq</span> <span class="kw">for</span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">default_max_relative</span>() <span class="op">-</span><span class="op">></span> <span class="ident">A</span>::<span class="ident">Epsilon</span> {
<span class="ident">A</span>::<span class="ident">default_max_relative</span>()
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">relative_eq</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="ident">epsilon</span>: <span class="ident">A</span>::<span class="ident">Epsilon</span>, <span class="ident">max_relative</span>: <span class="ident">A</span>::<span class="ident">Epsilon</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="ident">A</span>::<span class="ident">relative_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">x</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">x</span>, <span class="ident">epsilon</span>, <span class="ident">max_relative</span>)
<span class="kw-2">&</span><span class="op">&</span> <span class="ident">A</span>::<span class="ident">relative_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">y</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">y</span>, <span class="ident">epsilon</span>, <span class="ident">max_relative</span>)
<span class="kw-2">&</span><span class="op">&</span> <span class="ident">A</span>::<span class="ident">relative_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">z</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">z</span>, <span class="ident">epsilon</span>, <span class="ident">max_relative</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Angle</span><span class="op">></span> <span class="ident">approx</span>::<span class="ident">UlpsEq</span> <span class="kw">for</span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">default_max_ulps</span>() <span class="op">-</span><span class="op">></span> <span class="ident">u32</span> {
<span class="ident">A</span>::<span class="ident">default_max_ulps</span>()
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">ulps_eq</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="ident">epsilon</span>: <span class="ident">A</span>::<span class="ident">Epsilon</span>, <span class="ident">max_ulps</span>: <span class="ident">u32</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="ident">A</span>::<span class="ident">ulps_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">x</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">x</span>, <span class="ident">epsilon</span>, <span class="ident">max_ulps</span>)
<span class="kw-2">&</span><span class="op">&</span> <span class="ident">A</span>::<span class="ident">ulps_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">y</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">y</span>, <span class="ident">epsilon</span>, <span class="ident">max_ulps</span>)
<span class="kw-2">&</span><span class="op">&</span> <span class="ident">A</span>::<span class="ident">ulps_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">z</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">z</span>, <span class="ident">epsilon</span>, <span class="ident">max_ulps</span>)
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Standard</span>
<span class="kw">where</span> <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">A</span><span class="op">></span>,
<span class="ident">A</span>: <span class="ident">Angle</span> {
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</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="op">></span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="ident">Euler</span> {
<span class="ident">x</span>: <span class="ident">rng</span>.<span class="ident">gen</span>(),
<span class="ident">y</span>: <span class="ident">rng</span>.<span class="ident">gen</span>(),
<span class="ident">z</span>: <span class="ident">rng</span>.<span class="ident">gen</span>(),
}
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"mint"</span>)]</span>
<span class="kw">type</span> <span class="ident">MintEuler</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> <span class="op">=</span> <span class="ident">mint</span>::<span class="ident">EulerAngles</span><span class="op"><</span><span class="ident">S</span>, <span class="ident">mint</span>::<span class="ident">IntraXYZ</span><span class="op">></span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"mint"</span>)]</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">S</span>, <span class="ident">A</span>: <span class="ident">Angle</span> <span class="op">+</span> <span class="ident">From</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> <span class="ident">From</span><span class="op"><</span><span class="ident">MintEuler</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">mint</span>: <span class="ident">MintEuler</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="ident">Euler</span> {
<span class="ident">x</span>: <span class="ident">mint</span>.<span class="ident">a</span>.<span class="ident">into</span>(),
<span class="ident">y</span>: <span class="ident">mint</span>.<span class="ident">b</span>.<span class="ident">into</span>(),
<span class="ident">z</span>: <span class="ident">mint</span>.<span class="ident">c</span>.<span class="ident">into</span>(),
}
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"mint"</span>)]</span>
<span class="kw">impl</span><span class="op"><</span><span class="ident">S</span>: <span class="ident">Clone</span>, <span class="ident">A</span>: <span class="ident">Angle</span> <span class="op">+</span> <span class="ident">Into</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> <span class="ident">Into</span><span class="op"><</span><span class="ident">MintEuler</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> <span class="kw">for</span> <span class="ident">Euler</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="kw">fn</span> <span class="ident">into</span>(<span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">MintEuler</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
<span class="ident">MintEuler</span>::<span class="ident">from</span>([<span class="self">self</span>.<span class="ident">x</span>.<span class="ident">into</span>(), <span class="self">self</span>.<span class="ident">y</span>.<span class="ident">into</span>(), <span class="self">self</span>.<span class="ident">z</span>.<span class="ident">into</span>()])
}
}
</pre></div>
</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><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd>↑</kbd></dt><dd>Move up in search results</dd><dt><kbd>↓</kbd></dt><dd>Move down in search results</dd><dt><kbd>↹</kbd></dt><dd>Switch tab</dd><dt><kbd>⏎</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse 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><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "cgmath";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script src="../../source-script.js"></script><script src="../../source-files.js"></script><script defer src="../../search-index.js"></script></body></html>