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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> 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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> </pre><div class="example-wrap"><pre class="rust "> <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="kw">crate</span>::<span class="ident">base</span>::<span class="ident">storage</span>::<span class="ident">Owned</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="kw">use</span> <span class="ident">num</span>::<span class="ident">One</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">alga</span>::<span class="ident">general</span>::<span class="ident">RealField</span>; <span class="kw">use</span> <span class="ident">alga</span>::<span class="ident">linear</span>::<span class="ident">Rotation</span> <span class="kw">as</span> <span class="ident">AlgaRotation</span>; <span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::<span class="ident">allocator</span>::<span class="ident">Allocator</span>; <span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::<span class="ident">dimension</span>::{<span class="ident">DimName</span>, <span class="ident">U2</span>, <span class="ident">U3</span>}; <span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::{<span class="ident">DefaultAllocator</span>, <span class="ident">Vector2</span>, <span class="ident">Vector3</span>}; <span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">geometry</span>::{ <span class="ident">Isometry</span>, <span class="ident">Point</span>, <span class="ident">Point3</span>, <span class="ident">Rotation</span>, <span class="ident">Rotation2</span>, <span class="ident">Rotation3</span>, <span class="ident">Translation</span>, <span class="ident">UnitComplex</span>, <span class="ident">UnitQuaternion</span>, <span class="ident">Translation2</span>, <span class="ident">Translation3</span> }; <span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">RealField</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span>: <span class="ident">AlgaRotation</span><span class="op"><</span><span class="ident">Point</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span><span class="op">></span><span class="op">></span> <span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">></span> <span class="kw">where</span> <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span> { <span class="doccomment">/// Creates a new identity isometry.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # use nalgebra::{Isometry2, Point2, Isometry3, Point3};</span> <span class="doccomment">///</span> <span class="doccomment">/// let iso = Isometry2::identity();</span> <span class="doccomment">/// let pt = Point2::new(1.0, 2.0);</span> <span class="doccomment">/// assert_eq!(iso * pt, pt);</span> <span class="doccomment">///</span> <span class="doccomment">/// let iso = Isometry3::identity();</span> <span class="doccomment">/// let pt = Point3::new(1.0, 2.0, 3.0);</span> <span class="doccomment">/// assert_eq!(iso * pt, pt);</span> <span class="doccomment">/// ```</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">identity</span>() <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">identity</span>(), <span class="ident">R</span>::<span class="ident">identity</span>()) } <span class="doccomment">/// The isometry that applies the rotation `r` with its axis passing through the point `p`.</span> <span class="doccomment">/// This effectively lets `p` invariant.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # #[macro_use] extern crate approx;</span> <span class="doccomment">/// # use std::f32;</span> <span class="doccomment">/// # use nalgebra::{Isometry2, Point2, UnitComplex};</span> <span class="doccomment">/// let rot = UnitComplex::new(f32::consts::PI);</span> <span class="doccomment">/// let pt = Point2::new(1.0, 0.0);</span> <span class="doccomment">/// let iso = Isometry2::rotation_wrt_point(rot, pt);</span> <span class="doccomment">///</span> <span class="doccomment">/// assert_eq!(iso * pt, pt); // The rotation center is not affected.</span> <span class="doccomment">/// assert_relative_eq!(iso * Point2::new(1.0, 2.0), Point2::new(1.0, -2.0), epsilon = 1.0e-6);</span> <span class="doccomment">/// ```</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation_wrt_point</span>(<span class="ident">r</span>: <span class="ident">R</span>, <span class="ident">p</span>: <span class="ident">Point</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="kw">let</span> <span class="ident">shift</span> <span class="op">=</span> <span class="ident">r</span>.<span class="ident">transform_vector</span>(<span class="kw-2">&</span><span class="op">-</span><span class="kw-2">&</span><span class="ident">p</span>.<span class="ident">coords</span>); <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">shift</span> <span class="op">+</span> <span class="ident">p</span>.<span class="ident">coords</span>), <span class="ident">r</span>) } } <span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">RealField</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span>: <span class="ident">AlgaRotation</span><span class="op"><</span><span class="ident">Point</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span><span class="op">></span><span class="op">></span> <span class="ident">One</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">></span> <span class="kw">where</span> <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span> { <span class="doccomment">/// Creates a new identity isometry.</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="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">identity</span>() } } <span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">RealField</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span><span class="op">></span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</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">R</span>: <span class="ident">AlgaRotation</span><span class="op"><</span><span class="ident">Point</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span><span class="op">></span>, <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">N</span><span class="op">></span> <span class="op">+</span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">R</span><span class="op">></span>, <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span>, { <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">G</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="lifetime">'a</span> <span class="kw-2">mut</span> <span class="ident">G</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">></span> { <span class="ident">Isometry</span>::<span class="ident">from_parts</span>(<span class="ident">rng</span>.<span class="ident">gen</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">"arbitrary"</span>)]</span> <span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span><span class="op">></span> <span class="ident">Arbitrary</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">></span> <span class="kw">where</span> <span class="ident">N</span>: <span class="ident">RealField</span> <span class="op">+</span> <span class="ident">Arbitrary</span> <span class="op">+</span> <span class="ident">Send</span>, <span class="ident">R</span>: <span class="ident">AlgaRotation</span><span class="op"><</span><span class="ident">Point</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span><span class="op">></span> <span class="op">+</span> <span class="ident">Arbitrary</span> <span class="op">+</span> <span class="ident">Send</span>, <span class="ident">Owned</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span>: <span class="ident">Send</span>, <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">></span>, { <span class="attribute">#[<span class="ident">inline</span>]</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">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">G</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Arbitrary</span>::<span class="ident">arbitrary</span>(<span class="ident">rng</span>), <span class="ident">Arbitrary</span>::<span class="ident">arbitrary</span>(<span class="ident">rng</span>)) } } <span class="comment">/* * * Constructors for various static dimensions. * */</span> <span class="comment">// 2D rotation.</span> <span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">RealField</span><span class="op">></span> <span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">U2</span>, <span class="ident">Rotation2</span><span class="op"><</span><span class="ident">N</span><span class="op">></span><span class="op">></span> { <span class="doccomment">/// Creates a new 2D isometry from a translation and a rotation angle.</span> <span class="doccomment">///</span> <span class="doccomment">/// Its rotational part is represented as a 2x2 rotation matrix.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # use std::f32;</span> <span class="doccomment">/// # use nalgebra::{Isometry2, Vector2, Point2};</span> <span class="doccomment">/// let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);</span> <span class="doccomment">///</span> <span class="doccomment">/// assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));</span> <span class="doccomment">/// ```</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">translation</span>: <span class="ident">Vector2</span><span class="op"><</span><span class="ident">N</span><span class="op">></span>, <span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>( <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">translation</span>), <span class="ident">Rotation</span>::<span class="op"><</span><span class="ident">N</span>, <span class="ident">U2</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">angle</span>), ) } <span class="doccomment">/// Creates a new isometry from the given translation coordinates.</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">translation</span>(<span class="ident">x</span>: <span class="ident">N</span>, <span class="ident">y</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector2</span>::<span class="ident">new</span>(<span class="ident">x</span>, <span class="ident">y</span>), <span class="ident">N</span>::<span class="ident">zero</span>()) } <span class="doccomment">/// Creates a new isometry from the given rotation angle.</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation</span>(<span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector2</span>::<span class="ident">zeros</span>(), <span class="ident">angle</span>) } } <span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">RealField</span><span class="op">></span> <span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">U2</span>, <span class="ident">UnitComplex</span><span class="op"><</span><span class="ident">N</span><span class="op">></span><span class="op">></span> { <span class="doccomment">/// Creates a new 2D isometry from a translation and a rotation angle.</span> <span class="doccomment">///</span> <span class="doccomment">/// Its rotational part is represented as an unit complex number.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # use std::f32;</span> <span class="doccomment">/// # use nalgebra::{IsometryMatrix2, Point2, Vector2};</span> <span class="doccomment">/// let iso = IsometryMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);</span> <span class="doccomment">///</span> <span class="doccomment">/// assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));</span> <span class="doccomment">/// ```</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">translation</span>: <span class="ident">Vector2</span><span class="op"><</span><span class="ident">N</span><span class="op">></span>, <span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>( <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">translation</span>), <span class="ident">UnitComplex</span>::<span class="ident">from_angle</span>(<span class="ident">angle</span>), ) } <span class="doccomment">/// Creates a new isometry from the given translation coordinates.</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">translation</span>(<span class="ident">x</span>: <span class="ident">N</span>, <span class="ident">y</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation2</span>::<span class="ident">new</span>(<span class="ident">x</span>, <span class="ident">y</span>), <span class="ident">UnitComplex</span>::<span class="ident">identity</span>()) } <span class="doccomment">/// Creates a new isometry from the given rotation angle.</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation</span>(<span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector2</span>::<span class="ident">zeros</span>(), <span class="ident">angle</span>) } } <span class="comment">// 3D rotation.</span> <span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">isometry_construction_impl</span>( (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>: <span class="ident">ident</span> <span class="op"><</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotParams</span>: <span class="ident">ident</span>),<span class="kw-2">*</span><span class="op">></span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RRDim</span>: <span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RCDim</span>: <span class="ident">ty</span>) <span class="op">=</span><span class="op">></span> { <span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">RealField</span><span class="op">></span> <span class="ident">Isometry</span><span class="op"><</span><span class="ident">N</span>, <span class="ident">U3</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span><span class="op"><</span>$(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotParams</span>),<span class="kw-2">*</span><span class="op">></span><span class="op">></span> { <span class="doccomment">/// Creates a new isometry from a translation and a rotation axis-angle.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # #[macro_use] extern crate approx;</span> <span class="doccomment">/// # use std::f32;</span> <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span> <span class="doccomment">/// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;</span> <span class="doccomment">/// let translation = Vector3::new(1.0, 2.0, 3.0);</span> <span class="doccomment">/// // Point and vector being transformed in the tests.</span> <span class="doccomment">/// let pt = Point3::new(4.0, 5.0, 6.0);</span> <span class="doccomment">/// let vec = Vector3::new(4.0, 5.0, 6.0);</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span> <span class="doccomment">/// let iso = Isometry3::new(translation, axisangle);</span> <span class="doccomment">/// assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);</span> <span class="doccomment">/// assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).</span> <span class="doccomment">/// let iso = IsometryMatrix3::new(translation, axisangle);</span> <span class="doccomment">/// assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);</span> <span class="doccomment">/// assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);</span> <span class="doccomment">/// ```</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">translation</span>: <span class="ident">Vector3</span><span class="op"><</span><span class="ident">N</span><span class="op">></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="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>( <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">translation</span>), <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="op"><</span>$(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotParams</span>),<span class="kw-2">*</span><span class="op">></span>::<span class="ident">from_scaled_axis</span>(<span class="ident">axisangle</span>)) } <span class="doccomment">/// Creates a new isometry from the given translation coordinates.</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">translation</span>(<span class="ident">x</span>: <span class="ident">N</span>, <span class="ident">y</span>: <span class="ident">N</span>, <span class="ident">z</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation3</span>::<span class="ident">new</span>(<span class="ident">x</span>, <span class="ident">y</span>, <span class="ident">z</span>), <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">identity</span>()) } <span class="doccomment">/// Creates a new isometry from the given rotation angle.</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation</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="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector3</span>::<span class="ident">zeros</span>(), <span class="ident">axisangle</span>) } <span class="doccomment">/// Creates an isometry that corresponds to the local frame of an observer standing at the</span> <span class="doccomment">/// point `eye` and looking toward `target`.</span> <span class="doccomment">///</span> <span class="doccomment">/// It maps the `z` axis to the view direction `target - eye`and the origin to the `eye`.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Arguments</span> <span class="doccomment">/// * eye - The observer position.</span> <span class="doccomment">/// * target - The target position.</span> <span class="doccomment">/// * up - Vertical direction. The only requirement of this parameter is to not be collinear</span> <span class="doccomment">/// to `eye - at`. Non-collinearity is not checked.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # #[macro_use] extern crate approx;</span> <span class="doccomment">/// # use std::f32;</span> <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span> <span class="doccomment">/// let eye = Point3::new(1.0, 2.0, 3.0);</span> <span class="doccomment">/// let target = Point3::new(2.0, 2.0, 3.0);</span> <span class="doccomment">/// let up = Vector3::y();</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span> <span class="doccomment">/// let iso = Isometry3::face_towards(&eye, &target, &up);</span> <span class="doccomment">/// assert_eq!(iso * Point3::origin(), eye);</span> <span class="doccomment">/// assert_relative_eq!(iso * Vector3::z(), Vector3::x());</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).</span> <span class="doccomment">/// let iso = IsometryMatrix3::face_towards(&eye, &target, &up);</span> <span class="doccomment">/// assert_eq!(iso * Point3::origin(), eye);</span> <span class="doccomment">/// assert_relative_eq!(iso * Vector3::z(), Vector3::x());</span> <span class="doccomment">/// ```</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">face_towards</span>(<span class="ident">eye</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="ident">target</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="ident">up</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="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">from_parts</span>( <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">eye</span>.<span class="ident">coords</span>.<span class="ident">clone</span>()), <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">face_towards</span>(<span class="kw-2">&</span>(<span class="ident">target</span> <span class="op">-</span> <span class="ident">eye</span>), <span class="ident">up</span>)) } <span class="doccomment">/// Deprecated: Use [Isometry::face_towards] instead.</span> <span class="attribute">#[<span class="ident">deprecated</span>(<span class="ident">note</span><span class="op">=</span><span class="string">"renamed to `face_towards`"</span>)]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new_observer_frame</span>(<span class="ident">eye</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="ident">target</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="ident">up</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="op">></span> <span class="self">Self</span> { <span class="self">Self</span>::<span class="ident">face_towards</span>(<span class="ident">eye</span>, <span class="ident">target</span>, <span class="ident">up</span>) } <span class="doccomment">/// Builds a right-handed look-at view matrix.</span> <span class="doccomment">///</span> <span class="doccomment">/// It maps the view direction `target - eye` to the **negative** `z` axis to and the `eye` to the origin.</span> <span class="doccomment">/// This conforms to the common notion of right handed camera look-at **view matrix** from</span> <span class="doccomment">/// the computer graphics community, i.e. the camera is assumed to look toward its local `-z` axis.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Arguments</span> <span class="doccomment">/// * eye - The eye position.</span> <span class="doccomment">/// * target - The target position.</span> <span class="doccomment">/// * up - A vector approximately aligned with required the vertical axis. The only</span> <span class="doccomment">/// requirement of this parameter is to not be collinear to `target - eye`.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # #[macro_use] extern crate approx;</span> <span class="doccomment">/// # use std::f32;</span> <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span> <span class="doccomment">/// let eye = Point3::new(1.0, 2.0, 3.0);</span> <span class="doccomment">/// let target = Point3::new(2.0, 2.0, 3.0);</span> <span class="doccomment">/// let up = Vector3::y();</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span> <span class="doccomment">/// let iso = Isometry3::look_at_rh(&eye, &target, &up);</span> <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span> <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z());</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).</span> <span class="doccomment">/// let iso = IsometryMatrix3::look_at_rh(&eye, &target, &up);</span> <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span> <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z());</span> <span class="doccomment">/// ```</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">look_at_rh</span>(<span class="ident">eye</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="ident">target</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="ident">up</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="op">></span> <span class="self">Self</span> { <span class="kw">let</span> <span class="ident">rotation</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">look_at_rh</span>(<span class="kw-2">&</span>(<span class="ident">target</span> <span class="op">-</span> <span class="ident">eye</span>), <span class="ident">up</span>); <span class="kw">let</span> <span class="ident">trans</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">rotation</span> <span class="op">*</span> (<span class="op">-</span><span class="ident">eye</span>); <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">trans</span>.<span class="ident">coords</span>), <span class="ident">rotation</span>) } <span class="doccomment">/// Builds a left-handed look-at view matrix.</span> <span class="doccomment">///</span> <span class="doccomment">/// It maps the view direction `target - eye` to the **positive** `z` axis and the `eye` to the origin.</span> <span class="doccomment">/// This conforms to the common notion of right handed camera look-at **view matrix** from</span> <span class="doccomment">/// the computer graphics community, i.e. the camera is assumed to look toward its local `z` axis.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Arguments</span> <span class="doccomment">/// * eye - The eye position.</span> <span class="doccomment">/// * target - The target position.</span> <span class="doccomment">/// * up - A vector approximately aligned with required the vertical axis. The only</span> <span class="doccomment">/// requirement of this parameter is to not be collinear to `target - eye`.</span> <span class="doccomment">///</span> <span class="doccomment">/// # Example</span> <span class="doccomment">///</span> <span class="doccomment">/// ```</span> <span class="doccomment">/// # #[macro_use] extern crate approx;</span> <span class="doccomment">/// # use std::f32;</span> <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span> <span class="doccomment">/// let eye = Point3::new(1.0, 2.0, 3.0);</span> <span class="doccomment">/// let target = Point3::new(2.0, 2.0, 3.0);</span> <span class="doccomment">/// let up = Vector3::y();</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span> <span class="doccomment">/// let iso = Isometry3::look_at_lh(&eye, &target, &up);</span> <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span> <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), Vector3::z());</span> <span class="doccomment">///</span> <span class="doccomment">/// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).</span> <span class="doccomment">/// let iso = IsometryMatrix3::look_at_lh(&eye, &target, &up);</span> <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span> <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), Vector3::z());</span> <span class="doccomment">/// ```</span> <span class="attribute">#[<span class="ident">inline</span>]</span> <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">look_at_lh</span>(<span class="ident">eye</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="ident">target</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="ident">up</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="op">></span> <span class="self">Self</span> { <span class="kw">let</span> <span class="ident">rotation</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">look_at_lh</span>(<span class="kw-2">&</span>(<span class="ident">target</span> <span class="op">-</span> <span class="ident">eye</span>), <span class="ident">up</span>); <span class="kw">let</span> <span class="ident">trans</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">rotation</span> <span class="op">*</span> (<span class="op">-</span><span class="ident">eye</span>); <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">trans</span>.<span class="ident">coords</span>), <span class="ident">rotation</span>) } } } ); <span class="macro">isometry_construction_impl</span><span class="macro">!</span>(<span class="ident">Rotation3</span><span class="op"><</span><span class="ident">N</span><span class="op">></span>, <span class="ident">U3</span>, <span class="ident">U3</span>); <span class="macro">isometry_construction_impl</span><span class="macro">!</span>(<span class="ident">UnitQuaternion</span><span class="op"><</span><span class="ident">N</span><span class="op">></span>, <span class="ident">U4</span>, <span class="ident">U1</span>); 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