905 lines
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905 lines
76 KiB
HTML
<!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/rotation.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>rotation.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>
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<span id="421">421</span>
|
||
<span id="422">422</span>
|
||
<span id="423">423</span>
|
||
<span id="424">424</span>
|
||
<span id="425">425</span>
|
||
<span id="426">426</span>
|
||
<span id="427">427</span>
|
||
<span id="428">428</span>
|
||
<span id="429">429</span>
|
||
<span id="430">430</span>
|
||
<span id="431">431</span>
|
||
<span id="432">432</span>
|
||
<span id="433">433</span>
|
||
<span id="434">434</span>
|
||
<span id="435">435</span>
|
||
<span id="436">436</span>
|
||
<span id="437">437</span>
|
||
<span id="438">438</span>
|
||
<span id="439">439</span>
|
||
<span id="440">440</span>
|
||
<span id="441">441</span>
|
||
<span id="442">442</span>
|
||
<span id="443">443</span>
|
||
<span id="444">444</span>
|
||
<span id="445">445</span>
|
||
<span id="446">446</span>
|
||
<span id="447">447</span>
|
||
<span id="448">448</span>
|
||
<span id="449">449</span>
|
||
<span id="450">450</span>
|
||
<span id="451">451</span>
|
||
</pre><div class="example-wrap"><pre class="rust ">
|
||
<span class="comment">// Copyright 2014 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">std</span>::<span class="ident">fmt</span>;
|
||
<span class="kw">use</span> <span class="ident">std</span>::<span class="ident">iter</span>;
|
||
<span class="kw">use</span> <span class="ident">std</span>::<span class="ident">ops</span>::<span class="kw-2">*</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">euler</span>::<span class="ident">Euler</span>;
|
||
<span class="kw">use</span> <span class="ident">matrix</span>::{<span class="ident">Matrix2</span>, <span class="ident">Matrix3</span>};
|
||
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">BaseFloat</span>;
|
||
<span class="kw">use</span> <span class="ident">point</span>::{<span class="ident">Point2</span>, <span class="ident">Point3</span>};
|
||
<span class="kw">use</span> <span class="ident">quaternion</span>::<span class="ident">Quaternion</span>;
|
||
<span class="kw">use</span> <span class="ident">vector</span>::{<span class="ident">Vector2</span>, <span class="ident">Vector3</span>};
|
||
|
||
<span class="doccomment">/// A trait for a generic rotation. A rotation is a transformation that</span>
|
||
<span class="doccomment">/// creates a circular motion, and preserves at least one point in the space.</span>
|
||
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">Rotation</span><span class="op"><</span><span class="ident">P</span>: <span class="ident">EuclideanSpace</span><span class="op">></span>: <span class="ident">Sized</span> <span class="op">+</span> <span class="ident">Copy</span> <span class="op">+</span> <span class="ident">One</span>
|
||
<span class="kw">where</span>
|
||
<span class="comment">// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092</span>
|
||
<span class="self">Self</span>: <span class="ident">approx</span>::<span class="ident">AbsDiffEq</span><span class="op"><</span><span class="ident">Epsilon</span> <span class="op">=</span> <span class="ident">P</span>::<span class="ident">Scalar</span><span class="op">></span>,
|
||
<span class="self">Self</span>: <span class="ident">approx</span>::<span class="ident">RelativeEq</span><span class="op"><</span><span class="ident">Epsilon</span> <span class="op">=</span> <span class="ident">P</span>::<span class="ident">Scalar</span><span class="op">></span>,
|
||
<span class="self">Self</span>: <span class="ident">approx</span>::<span class="ident">UlpsEq</span><span class="op"><</span><span class="ident">Epsilon</span> <span class="op">=</span> <span class="ident">P</span>::<span class="ident">Scalar</span><span class="op">></span>,
|
||
<span class="ident">P</span>::<span class="ident">Scalar</span>: <span class="ident">BaseFloat</span>,
|
||
<span class="self">Self</span>: <span class="ident">iter</span>::<span class="ident">Product</span><span class="op"><</span><span class="self">Self</span><span class="op">></span>,
|
||
{
|
||
<span class="doccomment">/// Create a rotation to a given direction with an 'up' vector.</span>
|
||
<span class="kw">fn</span> <span class="ident">look_at</span>(<span class="ident">dir</span>: <span class="ident">P</span>::<span class="ident">Diff</span>, <span class="ident">up</span>: <span class="ident">P</span>::<span class="ident">Diff</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
|
||
|
||
<span class="doccomment">/// Create a shortest rotation to transform vector 'a' into 'b'.</span>
|
||
<span class="doccomment">/// Both given vectors are assumed to have unit length.</span>
|
||
<span class="kw">fn</span> <span class="ident">between_vectors</span>(<span class="ident">a</span>: <span class="ident">P</span>::<span class="ident">Diff</span>, <span class="ident">b</span>: <span class="ident">P</span>::<span class="ident">Diff</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
|
||
|
||
<span class="doccomment">/// Rotate a vector using this rotation.</span>
|
||
<span class="kw">fn</span> <span class="ident">rotate_vector</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">vec</span>: <span class="ident">P</span>::<span class="ident">Diff</span>) <span class="op">-</span><span class="op">></span> <span class="ident">P</span>::<span class="ident">Diff</span>;
|
||
|
||
<span class="doccomment">/// Rotate a point using this rotation, by converting it to its</span>
|
||
<span class="doccomment">/// representation as a vector.</span>
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">rotate_point</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">point</span>: <span class="ident">P</span>) <span class="op">-</span><span class="op">></span> <span class="ident">P</span> {
|
||
<span class="ident">P</span>::<span class="ident">from_vec</span>(<span class="self">self</span>.<span class="ident">rotate_vector</span>(<span class="ident">point</span>.<span class="ident">to_vec</span>()))
|
||
}
|
||
|
||
<span class="doccomment">/// Create a new rotation which "un-does" this rotation. That is,</span>
|
||
<span class="doccomment">/// `r * r.invert()` is the identity.</span>
|
||
<span class="kw">fn</span> <span class="ident">invert</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
|
||
}
|
||
|
||
<span class="doccomment">/// A two-dimensional rotation.</span>
|
||
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">Rotation2</span><span class="op"><</span><span class="ident">S</span>: <span class="ident">BaseFloat</span><span class="op">></span>
|
||
: <span class="ident">Rotation</span><span class="op"><</span><span class="ident">Point2</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">Into</span><span class="op"><</span><span class="ident">Matrix2</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">Into</span><span class="op"><</span><span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span><span class="op">></span> {
|
||
<span class="doccomment">/// Create a rotation by a given angle. Thus is a redundant case of both</span>
|
||
<span class="doccomment">/// from_axis_angle() and from_euler() for 2D space.</span>
|
||
<span class="kw">fn</span> <span class="ident">from_angle</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
|
||
}
|
||
|
||
<span class="doccomment">/// A three-dimensional rotation.</span>
|
||
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">Rotation3</span><span class="op"><</span><span class="ident">S</span>: <span class="ident">BaseFloat</span><span class="op">></span>
|
||
: <span class="ident">Rotation</span><span class="op"><</span><span class="ident">Point3</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">Into</span><span class="op"><</span><span class="ident">Matrix3</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">Into</span><span class="op"><</span><span class="ident">Basis3</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">Into</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="op">+</span> <span class="ident">From</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="op">></span>
|
||
{
|
||
<span class="doccomment">/// Create a rotation using an angle around a given axis.</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// The specified axis **must be normalized**, or it represents an invalid rotation.</span>
|
||
<span class="kw">fn</span> <span class="ident">from_axis_angle</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">axis</span>: <span class="ident">Vector3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>, <span class="ident">angle</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
|
||
|
||
<span class="doccomment">/// Create a rotation from an angle around the `x` axis (pitch).</span>
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">from_angle_x</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
|
||
<span class="ident">Rotation3</span>::<span class="ident">from_axis_angle</span>(<span class="ident">Vector3</span>::<span class="ident">unit_x</span>(), <span class="ident">theta</span>)
|
||
}
|
||
|
||
<span class="doccomment">/// Create a rotation from an angle around the `y` axis (yaw).</span>
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">from_angle_y</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
|
||
<span class="ident">Rotation3</span>::<span class="ident">from_axis_angle</span>(<span class="ident">Vector3</span>::<span class="ident">unit_y</span>(), <span class="ident">theta</span>)
|
||
}
|
||
|
||
<span class="doccomment">/// Create a rotation from an angle around the `z` axis (roll).</span>
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">from_angle_z</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
|
||
<span class="ident">Rotation3</span>::<span class="ident">from_axis_angle</span>(<span class="ident">Vector3</span>::<span class="ident">unit_z</span>(), <span class="ident">theta</span>)
|
||
}
|
||
}
|
||
|
||
<span class="doccomment">/// A two-dimensional rotation matrix.</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// The matrix is guaranteed to be orthogonal, so some operations can be</span>
|
||
<span class="doccomment">/// implemented more efficiently than the implementations for `math::Matrix2`. To</span>
|
||
<span class="doccomment">/// enforce orthogonality at the type level the operations have been restricted</span>
|
||
<span class="doccomment">/// to a subset of those implemented on `Matrix2`.</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// ## Example</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// Suppose we want to rotate a vector that lies in the x-y plane by some</span>
|
||
<span class="doccomment">/// angle. We can accomplish this quite easily with a two-dimensional rotation</span>
|
||
<span class="doccomment">/// matrix:</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// ```no_run</span>
|
||
<span class="doccomment">/// use cgmath::Rad;</span>
|
||
<span class="doccomment">/// use cgmath::Vector2;</span>
|
||
<span class="doccomment">/// use cgmath::{Matrix, Matrix2};</span>
|
||
<span class="doccomment">/// use cgmath::{Rotation, Rotation2, Basis2};</span>
|
||
<span class="doccomment">/// use cgmath::UlpsEq;</span>
|
||
<span class="doccomment">/// use std::f64;</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// // For simplicity, we will rotate the unit x vector to the unit y vector --</span>
|
||
<span class="doccomment">/// // so the angle is 90 degrees, or π/2.</span>
|
||
<span class="doccomment">/// let unit_x: Vector2<f64> = Vector2::unit_x();</span>
|
||
<span class="doccomment">/// let rot: Basis2<f64> = Rotation2::from_angle(Rad(0.5f64 * f64::consts::PI));</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// // Rotate the vector using the two-dimensional rotation matrix:</span>
|
||
<span class="doccomment">/// let unit_y = rot.rotate_vector(unit_x);</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// // Since sin(π/2) may not be exactly zero due to rounding errors, we can</span>
|
||
<span class="doccomment">/// // use approx's assert_ulps_eq!() feature to show that it is close enough.</span>
|
||
<span class="doccomment">/// // assert_ulps_eq!(&unit_y, &Vector2::unit_y()); // TODO: Figure out how to use this</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// // This is exactly equivalent to using the raw matrix itself:</span>
|
||
<span class="doccomment">/// let unit_y2: Matrix2<_> = rot.into();</span>
|
||
<span class="doccomment">/// let unit_y2 = unit_y2 * unit_x;</span>
|
||
<span class="doccomment">/// assert_eq!(unit_y2, unit_y);</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// // Note that we can also concatenate rotations:</span>
|
||
<span class="doccomment">/// let rot_half: Basis2<f64> = Rotation2::from_angle(Rad(0.25f64 * f64::consts::PI));</span>
|
||
<span class="doccomment">/// let unit_y3 = (rot_half * rot_half).rotate_vector(unit_x);</span>
|
||
<span class="doccomment">/// // assert_ulps_eq!(&unit_y3, &unit_y2); // TODO: Figure out how to use this</span>
|
||
<span class="doccomment">/// ```</span>
|
||
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">PartialEq</span>, <span class="ident">Copy</span>, <span class="ident">Clone</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix2</span><span class="op"><</span><span class="ident">S</span><span class="op">></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">AsRef</span><span class="op"><</span><span class="ident">Matrix2</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">as_ref</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="kw-2">&</span><span class="ident">Matrix2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</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">Basis2</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">Matrix2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">b</span>: <span class="ident">Basis2</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">Matrix2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">b</span>.<span class="ident">mat</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">iter</span>::<span class="ident">Product</span><span class="op"><</span><span class="ident">Basis2</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">product</span><span class="op"><</span><span class="ident">I</span>: <span class="ident">Iterator</span><span class="op"><</span><span class="ident">Item</span> <span class="op">=</span> <span class="ident">Basis2</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">iter</span>: <span class="ident">I</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">iter</span>.<span class="ident">fold</span>(<span class="ident">Basis2</span>::<span class="ident">one</span>(), <span class="ident">Mul</span>::<span class="ident">mul</span>)
|
||
}
|
||
}
|
||
|
||
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">S</span>: <span class="lifetime">'a</span> <span class="op">+</span> <span class="ident">BaseFloat</span><span class="op">></span> <span class="ident">iter</span>::<span class="ident">Product</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Basis2</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">product</span><span class="op"><</span><span class="ident">I</span>: <span class="ident">Iterator</span><span class="op"><</span><span class="ident">Item</span> <span class="op">=</span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Basis2</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">iter</span>: <span class="ident">I</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">iter</span>.<span class="ident">fold</span>(<span class="ident">Basis2</span>::<span class="ident">one</span>(), <span class="ident">Mul</span>::<span class="ident">mul</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">Rotation</span><span class="op"><</span><span class="ident">Point2</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">look_at</span>(<span class="ident">dir</span>: <span class="ident">Vector2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>, <span class="ident">up</span>: <span class="ident">Vector2</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis2</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix2</span>::<span class="ident">look_at</span>(<span class="ident">dir</span>, <span class="ident">up</span>),
|
||
}
|
||
}
|
||
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">between_vectors</span>(<span class="ident">a</span>: <span class="ident">Vector2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>, <span class="ident">b</span>: <span class="ident">Vector2</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Rotation2</span>::<span class="ident">from_angle</span>(<span class="ident">Rad</span>::<span class="ident">acos</span>(<span class="ident">a</span>.<span class="ident">dot</span>(<span class="ident">b</span>)))
|
||
}
|
||
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">rotate_vector</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">vec</span>: <span class="ident">Vector2</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">Vector2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="self">self</span>.<span class="ident">mat</span> <span class="op">*</span> <span class="ident">vec</span>
|
||
}
|
||
|
||
<span class="comment">// TODO: we know the matrix is orthogonal, so this could be re-written</span>
|
||
<span class="comment">// to be faster</span>
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">invert</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis2</span> {
|
||
<span class="ident">mat</span>: <span class="self">self</span>.<span class="ident">mat</span>.<span class="ident">invert</span>().<span class="ident">unwrap</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">One</span> <span class="kw">for</span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">one</span>() <span class="op">-</span><span class="op">></span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis2</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix2</span>::<span class="ident">one</span>(),
|
||
}
|
||
}
|
||
}
|
||
|
||
<span class="macro">impl_operator</span><span class="macro">!</span>(<span class="op"><</span><span class="ident">S</span>: <span class="ident">BaseFloat</span><span class="op">></span> <span class="ident">Mul</span><span class="op"><</span><span class="ident">Basis2</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">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">fn</span> <span class="ident">mul</span>(<span class="ident">lhs</span>, <span class="ident">rhs</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> { <span class="ident">Basis2</span> { <span class="ident">mat</span>: <span class="ident">lhs</span>.<span class="ident">mat</span> <span class="op">*</span> <span class="ident">rhs</span>.<span class="ident">mat</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">approx</span>::<span class="ident">AbsDiffEq</span> <span class="kw">for</span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">type</span> <span class="ident">Epsilon</span> <span class="op">=</span> <span class="ident">S</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">S</span>::<span class="ident">Epsilon</span> {
|
||
<span class="ident">S</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">S</span>::<span class="ident">Epsilon</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
|
||
<span class="ident">Matrix2</span>::<span class="ident">abs_diff_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">mat</span>, <span class="ident">epsilon</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">approx</span>::<span class="ident">RelativeEq</span> <span class="kw">for</span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</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">S</span>::<span class="ident">Epsilon</span> {
|
||
<span class="ident">S</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">S</span>::<span class="ident">Epsilon</span>, <span class="ident">max_relative</span>: <span class="ident">S</span>::<span class="ident">Epsilon</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
|
||
<span class="ident">Matrix2</span>::<span class="ident">relative_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">mat</span>, <span class="ident">epsilon</span>, <span class="ident">max_relative</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">approx</span>::<span class="ident">UlpsEq</span> <span class="kw">for</span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</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">S</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">S</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">Matrix2</span>::<span class="ident">ulps_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">mat</span>, <span class="ident">epsilon</span>, <span class="ident">max_ulps</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">Rotation2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">fn</span> <span class="ident">from_angle</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis2</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix2</span>::<span class="ident">from_angle</span>(<span class="ident">theta</span>),
|
||
}
|
||
}
|
||
}
|
||
|
||
<span class="kw">impl</span><span class="op"><</span><span class="ident">S</span>: <span class="ident">fmt</span>::<span class="ident">Debug</span><span class="op">></span> <span class="ident">fmt</span>::<span class="ident">Debug</span> <span class="kw">for</span> <span class="ident">Basis2</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt</span>::<span class="ident">Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt</span>::<span class="prelude-ty">Result</span> {
|
||
<span class="macro">try</span><span class="macro">!</span>(<span class="macro">write</span><span class="macro">!</span>(<span class="ident">f</span>, <span class="string">"Basis2 "</span>));
|
||
<span class="op"><</span>[[<span class="ident">S</span>; <span class="number">2</span>]; <span class="number">2</span>] <span class="kw">as</span> <span class="ident">fmt</span>::<span class="ident">Debug</span><span class="op">></span>::<span class="ident">fmt</span>(<span class="self">self</span>.<span class="ident">mat</span>.<span class="ident">as_ref</span>(), <span class="ident">f</span>)
|
||
}
|
||
}
|
||
|
||
<span class="doccomment">/// A three-dimensional rotation matrix.</span>
|
||
<span class="doccomment">///</span>
|
||
<span class="doccomment">/// The matrix is guaranteed to be orthogonal, so some operations, specifically</span>
|
||
<span class="doccomment">/// inversion, can be implemented more efficiently than the implementations for</span>
|
||
<span class="doccomment">/// `math::Matrix3`. To ensure orthogonality is maintained, the operations have</span>
|
||
<span class="doccomment">/// been restricted to a subset of those implemented on `Matrix3`.</span>
|
||
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">PartialEq</span>, <span class="ident">Copy</span>, <span class="ident">Clone</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span><span class="op"><</span><span class="ident">S</span><span class="op">></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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="doccomment">/// Create a new rotation matrix from a quaternion.</span>
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_quaternion</span>(<span class="ident">quaternion</span>: <span class="kw-2">&</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">quaternion</span>.<span class="ident">clone</span>().<span class="ident">into</span>(),
|
||
}
|
||
}
|
||
}
|
||
|
||
<span class="kw">impl</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> <span class="ident">AsRef</span><span class="op"><</span><span class="ident">Matrix3</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">as_ref</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="kw-2">&</span><span class="ident">Matrix3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</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">Basis3</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">Matrix3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">b</span>: <span class="ident">Basis3</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">Matrix3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">b</span>.<span class="ident">mat</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">Basis3</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">Quaternion</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">b</span>: <span class="ident">Basis3</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">Quaternion</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">b</span>.<span class="ident">mat</span>.<span class="ident">into</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">iter</span>::<span class="ident">Product</span><span class="op"><</span><span class="ident">Basis3</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">product</span><span class="op"><</span><span class="ident">I</span>: <span class="ident">Iterator</span><span class="op"><</span><span class="ident">Item</span> <span class="op">=</span> <span class="ident">Basis3</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">iter</span>: <span class="ident">I</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">iter</span>.<span class="ident">fold</span>(<span class="ident">Basis3</span>::<span class="ident">one</span>(), <span class="ident">Mul</span>::<span class="ident">mul</span>)
|
||
}
|
||
}
|
||
|
||
<span class="kw">impl</span><span class="op"><</span><span class="lifetime">'a</span>, <span class="ident">S</span>: <span class="lifetime">'a</span> <span class="op">+</span> <span class="ident">BaseFloat</span><span class="op">></span> <span class="ident">iter</span>::<span class="ident">Product</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Basis3</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">product</span><span class="op"><</span><span class="ident">I</span>: <span class="ident">Iterator</span><span class="op"><</span><span class="ident">Item</span> <span class="op">=</span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">Basis3</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">iter</span>: <span class="ident">I</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">iter</span>.<span class="ident">fold</span>(<span class="ident">Basis3</span>::<span class="ident">one</span>(), <span class="ident">Mul</span>::<span class="ident">mul</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">Rotation</span><span class="op"><</span><span class="ident">Point3</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">look_at</span>(<span class="ident">dir</span>: <span class="ident">Vector3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>, <span class="ident">up</span>: <span class="ident">Vector3</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span>::<span class="ident">look_at</span>(<span class="ident">dir</span>, <span class="ident">up</span>),
|
||
}
|
||
}
|
||
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">between_vectors</span>(<span class="ident">a</span>: <span class="ident">Vector3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>, <span class="ident">b</span>: <span class="ident">Vector3</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">let</span> <span class="ident">q</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="ident">Rotation</span>::<span class="ident">between_vectors</span>(<span class="ident">a</span>, <span class="ident">b</span>);
|
||
<span class="ident">q</span>.<span class="ident">into</span>()
|
||
}
|
||
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">rotate_vector</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">vec</span>: <span class="ident">Vector3</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">Vector3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="self">self</span>.<span class="ident">mat</span> <span class="op">*</span> <span class="ident">vec</span>
|
||
}
|
||
|
||
<span class="comment">// TODO: we know the matrix is orthogonal, so this could be re-written</span>
|
||
<span class="comment">// to be faster</span>
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">invert</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="self">self</span>.<span class="ident">mat</span>.<span class="ident">invert</span>().<span class="ident">unwrap</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">One</span> <span class="kw">for</span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="attribute">#[<span class="ident">inline</span>]</span>
|
||
<span class="kw">fn</span> <span class="ident">one</span>() <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span>::<span class="ident">one</span>(),
|
||
}
|
||
}
|
||
}
|
||
|
||
<span class="macro">impl_operator</span><span class="macro">!</span>(<span class="op"><</span><span class="ident">S</span>: <span class="ident">BaseFloat</span><span class="op">></span> <span class="ident">Mul</span><span class="op"><</span><span class="ident">Basis3</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">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">fn</span> <span class="ident">mul</span>(<span class="ident">lhs</span>, <span class="ident">rhs</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> { <span class="ident">Basis3</span> { <span class="ident">mat</span>: <span class="ident">lhs</span>.<span class="ident">mat</span> <span class="op">*</span> <span class="ident">rhs</span>.<span class="ident">mat</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">approx</span>::<span class="ident">AbsDiffEq</span> <span class="kw">for</span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">type</span> <span class="ident">Epsilon</span> <span class="op">=</span> <span class="ident">S</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">S</span>::<span class="ident">Epsilon</span> {
|
||
<span class="ident">S</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">S</span>::<span class="ident">Epsilon</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
|
||
<span class="ident">Matrix3</span>::<span class="ident">abs_diff_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">mat</span>, <span class="ident">epsilon</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">approx</span>::<span class="ident">RelativeEq</span> <span class="kw">for</span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</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">S</span>::<span class="ident">Epsilon</span> {
|
||
<span class="ident">S</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">S</span>::<span class="ident">Epsilon</span>, <span class="ident">max_relative</span>: <span class="ident">S</span>::<span class="ident">Epsilon</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
|
||
<span class="ident">Matrix3</span>::<span class="ident">relative_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">mat</span>, <span class="ident">epsilon</span>, <span class="ident">max_relative</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">approx</span>::<span class="ident">UlpsEq</span> <span class="kw">for</span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</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">S</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">S</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">Matrix3</span>::<span class="ident">ulps_eq</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">mat</span>, <span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">mat</span>, <span class="ident">epsilon</span>, <span class="ident">max_ulps</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">Rotation3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">fn</span> <span class="ident">from_axis_angle</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">axis</span>: <span class="ident">Vector3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span>, <span class="ident">angle</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span>::<span class="ident">from_axis_angle</span>(<span class="ident">axis</span>, <span class="ident">angle</span>),
|
||
}
|
||
}
|
||
|
||
<span class="kw">fn</span> <span class="ident">from_angle_x</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span>::<span class="ident">from_angle_x</span>(<span class="ident">theta</span>),
|
||
}
|
||
}
|
||
|
||
<span class="kw">fn</span> <span class="ident">from_angle_y</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span>::<span class="ident">from_angle_y</span>(<span class="ident">theta</span>),
|
||
}
|
||
}
|
||
|
||
<span class="kw">fn</span> <span class="ident">from_angle_z</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Into</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="op">></span>(<span class="ident">theta</span>: <span class="ident">A</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span>::<span class="ident">from_angle_z</span>(<span class="ident">theta</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">From</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">Basis3</span><span class="op"><</span><span class="ident">A</span>::<span class="ident">Unitless</span><span class="op">></span>
|
||
<span class="kw">where</span>
|
||
<span class="ident">A</span>: <span class="ident">Into</span><span class="op"><</span><span class="ident">Rad</span><span class="op"><</span><span class="op"><</span><span class="ident">A</span> <span class="kw">as</span> <span class="ident">Angle</span><span class="op">></span>::<span class="ident">Unitless</span><span class="op">></span><span class="op">></span>,
|
||
{
|
||
<span class="doccomment">/// Create a three-dimensional rotation matrix from a set of euler angles.</span>
|
||
<span class="kw">fn</span> <span class="ident">from</span>(<span class="ident">src</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="op">></span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">A</span>::<span class="ident">Unitless</span><span class="op">></span> {
|
||
<span class="ident">Basis3</span> {
|
||
<span class="ident">mat</span>: <span class="ident">Matrix3</span>::<span class="ident">from</span>(<span class="ident">src</span>),
|
||
}
|
||
}
|
||
}
|
||
|
||
<span class="kw">impl</span><span class="op"><</span><span class="ident">S</span>: <span class="ident">fmt</span>::<span class="ident">Debug</span><span class="op">></span> <span class="ident">fmt</span>::<span class="ident">Debug</span> <span class="kw">for</span> <span class="ident">Basis3</span><span class="op"><</span><span class="ident">S</span><span class="op">></span> {
|
||
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt</span>::<span class="ident">Formatter</span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt</span>::<span class="prelude-ty">Result</span> {
|
||
<span class="macro">try</span><span class="macro">!</span>(<span class="macro">write</span><span class="macro">!</span>(<span class="ident">f</span>, <span class="string">"Basis3 "</span>));
|
||
<span class="op"><</span>[[<span class="ident">S</span>; <span class="number">3</span>]; <span class="number">3</span>] <span class="kw">as</span> <span class="ident">fmt</span>::<span class="ident">Debug</span><span class="op">></span>::<span class="ident">fmt</span>(<span class="self">self</span>.<span class="ident">mat</span>.<span class="ident">as_ref</span>(), <span class="ident">f</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> |