euclid/
rotation.rs

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1// Copyright 2013 The Servo Project Developers. See the COPYRIGHT
2// file at the top-level directory of this distribution.
3//
4// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
5// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
6// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
7// option. This file may not be copied, modified, or distributed
8// except according to those terms.
9
10use crate::approxeq::ApproxEq;
11use crate::trig::Trig;
12use crate::{point2, point3, vec3, Angle, Point2D, Point3D, Vector2D, Vector3D};
13use crate::{Transform2D, Transform3D, UnknownUnit};
14
15use core::cmp::{Eq, PartialEq};
16use core::fmt;
17use core::hash::Hash;
18use core::marker::PhantomData;
19use core::ops::{Add, Mul, Neg, Sub};
20
21#[cfg(feature = "bytemuck")]
22use bytemuck::{Pod, Zeroable};
23use num_traits::real::Real;
24use num_traits::{NumCast, One, Zero};
25#[cfg(feature = "serde")]
26use serde::{Deserialize, Serialize};
27
28/// A transform that can represent rotations in 2d, represented as an angle in radians.
29#[repr(C)]
30#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
31#[cfg_attr(
32    feature = "serde",
33    serde(bound(
34        serialize = "T: serde::Serialize",
35        deserialize = "T: serde::Deserialize<'de>"
36    ))
37)]
38pub struct Rotation2D<T, Src, Dst> {
39    /// Angle in radians
40    pub angle: T,
41    #[doc(hidden)]
42    pub _unit: PhantomData<(Src, Dst)>,
43}
44
45impl<T: Copy, Src, Dst> Copy for Rotation2D<T, Src, Dst> {}
46
47impl<T: Clone, Src, Dst> Clone for Rotation2D<T, Src, Dst> {
48    fn clone(&self) -> Self {
49        Rotation2D {
50            angle: self.angle.clone(),
51            _unit: PhantomData,
52        }
53    }
54}
55
56impl<T, Src, Dst> Eq for Rotation2D<T, Src, Dst> where T: Eq {}
57
58impl<T, Src, Dst> PartialEq for Rotation2D<T, Src, Dst>
59where
60    T: PartialEq,
61{
62    fn eq(&self, other: &Self) -> bool {
63        self.angle == other.angle
64    }
65}
66
67impl<T, Src, Dst> Hash for Rotation2D<T, Src, Dst>
68where
69    T: Hash,
70{
71    fn hash<H: core::hash::Hasher>(&self, h: &mut H) {
72        self.angle.hash(h);
73    }
74}
75
76#[cfg(feature = "arbitrary")]
77impl<'a, T, Src, Dst> arbitrary::Arbitrary<'a> for Rotation2D<T, Src, Dst>
78where
79    T: arbitrary::Arbitrary<'a>,
80{
81    fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
82        Ok(Rotation2D::new(arbitrary::Arbitrary::arbitrary(u)?))
83    }
84}
85
86#[cfg(feature = "bytemuck")]
87unsafe impl<T: Zeroable, Src, Dst> Zeroable for Rotation2D<T, Src, Dst> {}
88
89#[cfg(feature = "bytemuck")]
90unsafe impl<T: Pod, Src: 'static, Dst: 'static> Pod for Rotation2D<T, Src, Dst> {}
91
92impl<T, Src, Dst> Rotation2D<T, Src, Dst> {
93    /// Creates a rotation from an angle in radians.
94    #[inline]
95    pub fn new(angle: Angle<T>) -> Self {
96        Rotation2D {
97            angle: angle.radians,
98            _unit: PhantomData,
99        }
100    }
101
102    /// Creates a rotation from an angle in radians.
103    pub fn radians(angle: T) -> Self {
104        Self::new(Angle::radians(angle))
105    }
106
107    /// Creates the identity rotation.
108    #[inline]
109    pub fn identity() -> Self
110    where
111        T: Zero,
112    {
113        Self::radians(T::zero())
114    }
115}
116
117impl<T: Copy, Src, Dst> Rotation2D<T, Src, Dst> {
118    /// Cast the unit, preserving the numeric value.
119    ///
120    /// # Example
121    ///
122    /// ```rust
123    /// # use euclid::Rotation2D;
124    /// enum Local {}
125    /// enum World {}
126    ///
127    /// enum Local2 {}
128    /// enum World2 {}
129    ///
130    /// let to_world: Rotation2D<_, Local, World> = Rotation2D::radians(42);
131    ///
132    /// assert_eq!(to_world.angle, to_world.cast_unit::<Local2, World2>().angle);
133    /// ```
134    #[inline]
135    pub fn cast_unit<Src2, Dst2>(&self) -> Rotation2D<T, Src2, Dst2> {
136        Rotation2D {
137            angle: self.angle,
138            _unit: PhantomData,
139        }
140    }
141
142    /// Drop the units, preserving only the numeric value.
143    ///
144    /// # Example
145    ///
146    /// ```rust
147    /// # use euclid::Rotation2D;
148    /// enum Local {}
149    /// enum World {}
150    ///
151    /// let to_world: Rotation2D<_, Local, World> = Rotation2D::radians(42);
152    ///
153    /// assert_eq!(to_world.angle, to_world.to_untyped().angle);
154    /// ```
155    #[inline]
156    pub fn to_untyped(&self) -> Rotation2D<T, UnknownUnit, UnknownUnit> {
157        self.cast_unit()
158    }
159
160    /// Tag a unitless value with units.
161    ///
162    /// # Example
163    ///
164    /// ```rust
165    /// # use euclid::Rotation2D;
166    /// use euclid::UnknownUnit;
167    /// enum Local {}
168    /// enum World {}
169    ///
170    /// let rot: Rotation2D<_, UnknownUnit, UnknownUnit> = Rotation2D::radians(42);
171    ///
172    /// assert_eq!(rot.angle, Rotation2D::<_, Local, World>::from_untyped(&rot).angle);
173    /// ```
174    #[inline]
175    pub fn from_untyped(r: &Rotation2D<T, UnknownUnit, UnknownUnit>) -> Self {
176        r.cast_unit()
177    }
178}
179
180impl<T, Src, Dst> Rotation2D<T, Src, Dst>
181where
182    T: Copy,
183{
184    /// Returns self.angle as a strongly typed `Angle<T>`.
185    pub fn get_angle(&self) -> Angle<T> {
186        Angle::radians(self.angle)
187    }
188}
189
190impl<T: Real, Src, Dst> Rotation2D<T, Src, Dst> {
191    /// Creates a 3d rotation (around the z axis) from this 2d rotation.
192    #[inline]
193    pub fn to_3d(&self) -> Rotation3D<T, Src, Dst> {
194        Rotation3D::around_z(self.get_angle())
195    }
196
197    /// Returns the inverse of this rotation.
198    #[inline]
199    pub fn inverse(&self) -> Rotation2D<T, Dst, Src> {
200        Rotation2D::radians(-self.angle)
201    }
202
203    /// Returns a rotation representing the other rotation followed by this rotation.
204    #[inline]
205    pub fn then<NewSrc>(&self, other: &Rotation2D<T, NewSrc, Src>) -> Rotation2D<T, NewSrc, Dst> {
206        Rotation2D::radians(self.angle + other.angle)
207    }
208
209    /// Returns the given 2d point transformed by this rotation.
210    ///
211    /// The input point must be use the unit Src, and the returned point has the unit Dst.
212    #[inline]
213    pub fn transform_point(&self, point: Point2D<T, Src>) -> Point2D<T, Dst> {
214        let (sin, cos) = Real::sin_cos(self.angle);
215        point2(point.x * cos - point.y * sin, point.y * cos + point.x * sin)
216    }
217
218    /// Returns the given 2d vector transformed by this rotation.
219    ///
220    /// The input point must be use the unit Src, and the returned point has the unit Dst.
221    #[inline]
222    pub fn transform_vector(&self, vector: Vector2D<T, Src>) -> Vector2D<T, Dst> {
223        self.transform_point(vector.to_point()).to_vector()
224    }
225}
226
227impl<T, Src, Dst> Rotation2D<T, Src, Dst>
228where
229    T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + Trig,
230{
231    /// Returns the matrix representation of this rotation.
232    #[inline]
233    pub fn to_transform(&self) -> Transform2D<T, Src, Dst> {
234        Transform2D::rotation(self.get_angle())
235    }
236}
237
238impl<T: fmt::Debug, Src, Dst> fmt::Debug for Rotation2D<T, Src, Dst> {
239    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
240        write!(f, "Rotation({:?} rad)", self.angle)
241    }
242}
243
244impl<T, Src, Dst> ApproxEq<T> for Rotation2D<T, Src, Dst>
245where
246    T: Copy + Neg<Output = T> + ApproxEq<T>,
247{
248    fn approx_epsilon() -> T {
249        T::approx_epsilon()
250    }
251
252    fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool {
253        self.angle.approx_eq_eps(&other.angle, eps)
254    }
255}
256
257/// A transform that can represent rotations in 3d, represented as a quaternion.
258///
259/// Most methods expect the quaternion to be normalized.
260/// When in doubt, use [`unit_quaternion`] instead of [`quaternion`] to create
261/// a rotation as the former will ensure that its result is normalized.
262///
263/// Some people use the `x, y, z, w` (or `w, x, y, z`) notations. The equivalence is
264/// as follows: `x -> i`, `y -> j`, `z -> k`, `w -> r`.
265/// The memory layout of this type corresponds to the `x, y, z, w` notation
266///
267/// [`quaternion`]: Self::quaternion
268/// [`unit_quaternion`]: Self::unit_quaternion
269#[repr(C)]
270#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
271#[cfg_attr(
272    feature = "serde",
273    serde(bound(
274        serialize = "T: serde::Serialize",
275        deserialize = "T: serde::Deserialize<'de>"
276    ))
277)]
278pub struct Rotation3D<T, Src, Dst> {
279    /// Component multiplied by the imaginary number `i`.
280    pub i: T,
281    /// Component multiplied by the imaginary number `j`.
282    pub j: T,
283    /// Component multiplied by the imaginary number `k`.
284    pub k: T,
285    /// The real part.
286    pub r: T,
287    #[doc(hidden)]
288    pub _unit: PhantomData<(Src, Dst)>,
289}
290
291impl<T: Copy, Src, Dst> Copy for Rotation3D<T, Src, Dst> {}
292
293impl<T: Clone, Src, Dst> Clone for Rotation3D<T, Src, Dst> {
294    fn clone(&self) -> Self {
295        Rotation3D {
296            i: self.i.clone(),
297            j: self.j.clone(),
298            k: self.k.clone(),
299            r: self.r.clone(),
300            _unit: PhantomData,
301        }
302    }
303}
304
305impl<T, Src, Dst> Eq for Rotation3D<T, Src, Dst> where T: Eq {}
306
307impl<T, Src, Dst> PartialEq for Rotation3D<T, Src, Dst>
308where
309    T: PartialEq,
310{
311    fn eq(&self, other: &Self) -> bool {
312        self.i == other.i && self.j == other.j && self.k == other.k && self.r == other.r
313    }
314}
315
316impl<T, Src, Dst> Hash for Rotation3D<T, Src, Dst>
317where
318    T: Hash,
319{
320    fn hash<H: core::hash::Hasher>(&self, h: &mut H) {
321        self.i.hash(h);
322        self.j.hash(h);
323        self.k.hash(h);
324        self.r.hash(h);
325    }
326}
327
328/// Note: the quaternions produced by this implementation are not normalized
329/// (nor even necessarily finite). That is, this is not appropriate to use to
330/// choose an actual “arbitrary rotation”, at least not without postprocessing.
331#[cfg(feature = "arbitrary")]
332impl<'a, T, Src, Dst> arbitrary::Arbitrary<'a> for Rotation3D<T, Src, Dst>
333where
334    T: arbitrary::Arbitrary<'a>,
335{
336    fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
337        let (i, j, k, r) = arbitrary::Arbitrary::arbitrary(u)?;
338        Ok(Rotation3D::quaternion(i, j, k, r))
339    }
340}
341
342#[cfg(feature = "bytemuck")]
343unsafe impl<T: Zeroable, Src, Dst> Zeroable for Rotation3D<T, Src, Dst> {}
344
345#[cfg(feature = "bytemuck")]
346unsafe impl<T: Pod, Src: 'static, Dst: 'static> Pod for Rotation3D<T, Src, Dst> {}
347
348impl<T, Src, Dst> Rotation3D<T, Src, Dst> {
349    /// Creates a rotation around from a quaternion representation.
350    ///
351    /// The parameters are a, b, c and r compose the quaternion `a*i + b*j + c*k + r`
352    /// where `a`, `b` and `c` describe the vector part and the last parameter `r` is
353    /// the real part.
354    ///
355    /// The resulting quaternion is not necessarily normalized. See [`unit_quaternion`].
356    ///
357    /// [`unit_quaternion`]: Self::unit_quaternion
358    #[inline]
359    pub fn quaternion(a: T, b: T, c: T, r: T) -> Self {
360        Rotation3D {
361            i: a,
362            j: b,
363            k: c,
364            r,
365            _unit: PhantomData,
366        }
367    }
368
369    /// Creates the identity rotation.
370    #[inline]
371    pub fn identity() -> Self
372    where
373        T: Zero + One,
374    {
375        Self::quaternion(T::zero(), T::zero(), T::zero(), T::one())
376    }
377}
378
379impl<T, Src, Dst> Rotation3D<T, Src, Dst>
380where
381    T: Copy,
382{
383    /// Returns the vector part (i, j, k) of this quaternion.
384    #[inline]
385    pub fn vector_part(&self) -> Vector3D<T, UnknownUnit> {
386        vec3(self.i, self.j, self.k)
387    }
388
389    /// Cast the unit, preserving the numeric value.
390    ///
391    /// # Example
392    ///
393    /// ```rust
394    /// # use euclid::Rotation3D;
395    /// enum Local {}
396    /// enum World {}
397    ///
398    /// enum Local2 {}
399    /// enum World2 {}
400    ///
401    /// let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);
402    ///
403    /// assert_eq!(to_world.i, to_world.cast_unit::<Local2, World2>().i);
404    /// assert_eq!(to_world.j, to_world.cast_unit::<Local2, World2>().j);
405    /// assert_eq!(to_world.k, to_world.cast_unit::<Local2, World2>().k);
406    /// assert_eq!(to_world.r, to_world.cast_unit::<Local2, World2>().r);
407    /// ```
408    #[inline]
409    pub fn cast_unit<Src2, Dst2>(&self) -> Rotation3D<T, Src2, Dst2> {
410        Rotation3D {
411            i: self.i,
412            j: self.j,
413            k: self.k,
414            r: self.r,
415            _unit: PhantomData,
416        }
417    }
418
419    /// Drop the units, preserving only the numeric value.
420    ///
421    /// # Example
422    ///
423    /// ```rust
424    /// # use euclid::Rotation3D;
425    /// enum Local {}
426    /// enum World {}
427    ///
428    /// let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);
429    ///
430    /// assert_eq!(to_world.i, to_world.to_untyped().i);
431    /// assert_eq!(to_world.j, to_world.to_untyped().j);
432    /// assert_eq!(to_world.k, to_world.to_untyped().k);
433    /// assert_eq!(to_world.r, to_world.to_untyped().r);
434    /// ```
435    #[inline]
436    pub fn to_untyped(&self) -> Rotation3D<T, UnknownUnit, UnknownUnit> {
437        self.cast_unit()
438    }
439
440    /// Tag a unitless value with units.
441    ///
442    /// # Example
443    ///
444    /// ```rust
445    /// # use euclid::Rotation3D;
446    /// use euclid::UnknownUnit;
447    /// enum Local {}
448    /// enum World {}
449    ///
450    /// let rot: Rotation3D<_, UnknownUnit, UnknownUnit> = Rotation3D::quaternion(1, 2, 3, 4);
451    ///
452    /// assert_eq!(rot.i, Rotation3D::<_, Local, World>::from_untyped(&rot).i);
453    /// assert_eq!(rot.j, Rotation3D::<_, Local, World>::from_untyped(&rot).j);
454    /// assert_eq!(rot.k, Rotation3D::<_, Local, World>::from_untyped(&rot).k);
455    /// assert_eq!(rot.r, Rotation3D::<_, Local, World>::from_untyped(&rot).r);
456    /// ```
457    #[inline]
458    pub fn from_untyped(r: &Rotation3D<T, UnknownUnit, UnknownUnit>) -> Self {
459        r.cast_unit()
460    }
461}
462
463impl<T, Src, Dst> Rotation3D<T, Src, Dst>
464where
465    T: Real,
466{
467    /// Creates a rotation around from a quaternion representation and normalizes it.
468    ///
469    /// The parameters are a, b, c and r compose the quaternion `a*i + b*j + c*k + r`
470    /// before normalization, where `a`, `b` and `c` describe the vector part and the
471    /// last parameter `r` is the real part.
472    #[inline]
473    pub fn unit_quaternion(i: T, j: T, k: T, r: T) -> Self {
474        Self::quaternion(i, j, k, r).normalize()
475    }
476
477    /// Creates a rotation around a given axis.
478    pub fn around_axis(axis: Vector3D<T, Src>, angle: Angle<T>) -> Self {
479        let axis = axis.normalize();
480        let two = T::one() + T::one();
481        let (sin, cos) = Angle::sin_cos(angle / two);
482        Self::quaternion(axis.x * sin, axis.y * sin, axis.z * sin, cos)
483    }
484
485    /// Creates a rotation around the x axis.
486    pub fn around_x(angle: Angle<T>) -> Self {
487        let zero = Zero::zero();
488        let two = T::one() + T::one();
489        let (sin, cos) = Angle::sin_cos(angle / two);
490        Self::quaternion(sin, zero, zero, cos)
491    }
492
493    /// Creates a rotation around the y axis.
494    pub fn around_y(angle: Angle<T>) -> Self {
495        let zero = Zero::zero();
496        let two = T::one() + T::one();
497        let (sin, cos) = Angle::sin_cos(angle / two);
498        Self::quaternion(zero, sin, zero, cos)
499    }
500
501    /// Creates a rotation around the z axis.
502    pub fn around_z(angle: Angle<T>) -> Self {
503        let zero = Zero::zero();
504        let two = T::one() + T::one();
505        let (sin, cos) = Angle::sin_cos(angle / two);
506        Self::quaternion(zero, zero, sin, cos)
507    }
508
509    /// Creates a rotation from Euler angles.
510    ///
511    /// The rotations are applied in roll then pitch then yaw order.
512    ///
513    ///  - Roll (also called bank) is a rotation around the x axis.
514    ///  - Pitch (also called bearing) is a rotation around the y axis.
515    ///  - Yaw (also called heading) is a rotation around the z axis.
516    pub fn euler(roll: Angle<T>, pitch: Angle<T>, yaw: Angle<T>) -> Self {
517        let half = T::one() / (T::one() + T::one());
518
519        let (sy, cy) = Real::sin_cos(half * yaw.get());
520        let (sp, cp) = Real::sin_cos(half * pitch.get());
521        let (sr, cr) = Real::sin_cos(half * roll.get());
522
523        Self::quaternion(
524            cy * sr * cp - sy * cr * sp,
525            cy * cr * sp + sy * sr * cp,
526            sy * cr * cp - cy * sr * sp,
527            cy * cr * cp + sy * sr * sp,
528        )
529    }
530
531    /// Returns the inverse of this rotation.
532    #[inline]
533    pub fn inverse(&self) -> Rotation3D<T, Dst, Src> {
534        Rotation3D::quaternion(-self.i, -self.j, -self.k, self.r)
535    }
536
537    /// Computes the norm of this quaternion.
538    #[inline]
539    pub fn norm(&self) -> T {
540        self.square_norm().sqrt()
541    }
542
543    /// Computes the squared norm of this quaternion.
544    #[inline]
545    pub fn square_norm(&self) -> T {
546        self.i * self.i + self.j * self.j + self.k * self.k + self.r * self.r
547    }
548
549    /// Returns a [unit quaternion] from this one.
550    ///
551    /// [unit quaternion]: https://en.wikipedia.org/wiki/Quaternion#Unit_quaternion
552    #[inline]
553    pub fn normalize(&self) -> Self {
554        self.mul(T::one() / self.norm())
555    }
556
557    /// Returns `true` if [norm] of this quaternion is (approximately) one.
558    ///
559    /// [norm]: Self::norm
560    #[inline]
561    pub fn is_normalized(&self) -> bool
562    where
563        T: ApproxEq<T>,
564    {
565        let eps = NumCast::from(1.0e-5).unwrap();
566        self.square_norm().approx_eq_eps(&T::one(), &eps)
567    }
568
569    /// Spherical linear interpolation between this rotation and another rotation.
570    ///
571    /// `t` is expected to be between zero and one.
572    pub fn slerp(&self, other: &Self, t: T) -> Self
573    where
574        T: ApproxEq<T>,
575    {
576        debug_assert!(self.is_normalized());
577        debug_assert!(other.is_normalized());
578
579        let r1 = *self;
580        let mut r2 = *other;
581
582        let mut dot = r1.i * r2.i + r1.j * r2.j + r1.k * r2.k + r1.r * r2.r;
583
584        let one = T::one();
585
586        if dot.approx_eq(&T::one()) {
587            // If the inputs are too close, linearly interpolate to avoid precision issues.
588            return r1.lerp(&r2, t);
589        }
590
591        // If the dot product is negative, the quaternions
592        // have opposite handed-ness and slerp won't take
593        // the shorter path. Fix by reversing one quaternion.
594        if dot < T::zero() {
595            r2 = r2.mul(-T::one());
596            dot = -dot;
597        }
598
599        // For robustness, stay within the domain of acos.
600        dot = Real::min(dot, one);
601
602        // Angle between r1 and the result.
603        let theta = Real::acos(dot) * t;
604
605        // r1 and r3 form an orthonormal basis.
606        let r3 = r2.sub(r1.mul(dot)).normalize();
607        let (sin, cos) = Real::sin_cos(theta);
608        r1.mul(cos).add(r3.mul(sin))
609    }
610
611    /// Basic Linear interpolation between this rotation and another rotation.
612    #[inline]
613    pub fn lerp(&self, other: &Self, t: T) -> Self {
614        let one_t = T::one() - t;
615        self.mul(one_t).add(other.mul(t)).normalize()
616    }
617
618    /// Returns the given 3d point transformed by this rotation.
619    ///
620    /// The input point must be use the unit Src, and the returned point has the unit Dst.
621    pub fn transform_point3d(&self, point: Point3D<T, Src>) -> Point3D<T, Dst>
622    where
623        T: ApproxEq<T>,
624    {
625        debug_assert!(self.is_normalized());
626
627        let two = T::one() + T::one();
628        let cross = self.vector_part().cross(point.to_vector().to_untyped()) * two;
629
630        point3(
631            point.x + self.r * cross.x + self.j * cross.z - self.k * cross.y,
632            point.y + self.r * cross.y + self.k * cross.x - self.i * cross.z,
633            point.z + self.r * cross.z + self.i * cross.y - self.j * cross.x,
634        )
635    }
636
637    /// Returns the given 2d point transformed by this rotation then projected on the xy plane.
638    ///
639    /// The input point must be use the unit Src, and the returned point has the unit Dst.
640    #[inline]
641    pub fn transform_point2d(&self, point: Point2D<T, Src>) -> Point2D<T, Dst>
642    where
643        T: ApproxEq<T>,
644    {
645        self.transform_point3d(point.to_3d()).xy()
646    }
647
648    /// Returns the given 3d vector transformed by this rotation.
649    ///
650    /// The input vector must be use the unit Src, and the returned point has the unit Dst.
651    #[inline]
652    pub fn transform_vector3d(&self, vector: Vector3D<T, Src>) -> Vector3D<T, Dst>
653    where
654        T: ApproxEq<T>,
655    {
656        self.transform_point3d(vector.to_point()).to_vector()
657    }
658
659    /// Returns the given 2d vector transformed by this rotation then projected on the xy plane.
660    ///
661    /// The input vector must be use the unit Src, and the returned point has the unit Dst.
662    #[inline]
663    pub fn transform_vector2d(&self, vector: Vector2D<T, Src>) -> Vector2D<T, Dst>
664    where
665        T: ApproxEq<T>,
666    {
667        self.transform_vector3d(vector.to_3d()).xy()
668    }
669
670    /// Returns the matrix representation of this rotation.
671    #[inline]
672    #[rustfmt::skip]
673    pub fn to_transform(&self) -> Transform3D<T, Src, Dst>
674    where
675        T: ApproxEq<T>,
676    {
677        debug_assert!(self.is_normalized());
678
679        let i2 = self.i + self.i;
680        let j2 = self.j + self.j;
681        let k2 = self.k + self.k;
682        let ii = self.i * i2;
683        let ij = self.i * j2;
684        let ik = self.i * k2;
685        let jj = self.j * j2;
686        let jk = self.j * k2;
687        let kk = self.k * k2;
688        let ri = self.r * i2;
689        let rj = self.r * j2;
690        let rk = self.r * k2;
691
692        let one = T::one();
693        let zero = T::zero();
694
695        let m11 = one - (jj + kk);
696        let m12 = ij + rk;
697        let m13 = ik - rj;
698
699        let m21 = ij - rk;
700        let m22 = one - (ii + kk);
701        let m23 = jk + ri;
702
703        let m31 = ik + rj;
704        let m32 = jk - ri;
705        let m33 = one - (ii + jj);
706
707        Transform3D::new(
708            m11, m12, m13, zero,
709            m21, m22, m23, zero,
710            m31, m32, m33, zero,
711            zero, zero, zero, one,
712        )
713    }
714
715    /// Returns a rotation representing this rotation followed by the other rotation.
716    #[inline]
717    pub fn then<NewDst>(&self, other: &Rotation3D<T, Dst, NewDst>) -> Rotation3D<T, Src, NewDst>
718    where
719        T: ApproxEq<T>,
720    {
721        debug_assert!(self.is_normalized());
722        Rotation3D::quaternion(
723            other.i * self.r + other.r * self.i + other.j * self.k - other.k * self.j,
724            other.j * self.r + other.r * self.j + other.k * self.i - other.i * self.k,
725            other.k * self.r + other.r * self.k + other.i * self.j - other.j * self.i,
726            other.r * self.r - other.i * self.i - other.j * self.j - other.k * self.k,
727        )
728    }
729
730    // add, sub and mul are used internally for intermediate computation but aren't public
731    // because they don't carry real semantic meanings (I think?).
732
733    #[inline]
734    fn add(&self, other: Self) -> Self {
735        Self::quaternion(
736            self.i + other.i,
737            self.j + other.j,
738            self.k + other.k,
739            self.r + other.r,
740        )
741    }
742
743    #[inline]
744    fn sub(&self, other: Self) -> Self {
745        Self::quaternion(
746            self.i - other.i,
747            self.j - other.j,
748            self.k - other.k,
749            self.r - other.r,
750        )
751    }
752
753    #[inline]
754    fn mul(&self, factor: T) -> Self {
755        Self::quaternion(
756            self.i * factor,
757            self.j * factor,
758            self.k * factor,
759            self.r * factor,
760        )
761    }
762}
763
764impl<T: fmt::Debug, Src, Dst> fmt::Debug for Rotation3D<T, Src, Dst> {
765    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
766        write!(
767            f,
768            "Quat({:?}*i + {:?}*j + {:?}*k + {:?})",
769            self.i, self.j, self.k, self.r
770        )
771    }
772}
773
774impl<T, Src, Dst> ApproxEq<T> for Rotation3D<T, Src, Dst>
775where
776    T: Copy + Neg<Output = T> + ApproxEq<T>,
777{
778    fn approx_epsilon() -> T {
779        T::approx_epsilon()
780    }
781
782    fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool {
783        (self.i.approx_eq_eps(&other.i, eps)
784            && self.j.approx_eq_eps(&other.j, eps)
785            && self.k.approx_eq_eps(&other.k, eps)
786            && self.r.approx_eq_eps(&other.r, eps))
787            || (self.i.approx_eq_eps(&-other.i, eps)
788                && self.j.approx_eq_eps(&-other.j, eps)
789                && self.k.approx_eq_eps(&-other.k, eps)
790                && self.r.approx_eq_eps(&-other.r, eps))
791    }
792}
793
794#[test]
795fn simple_rotation_2d() {
796    use crate::default::Rotation2D;
797    use core::f32::consts::{FRAC_PI_2, PI};
798
799    let ri = Rotation2D::identity();
800    let r90 = Rotation2D::radians(FRAC_PI_2);
801    let rm90 = Rotation2D::radians(-FRAC_PI_2);
802    let r180 = Rotation2D::radians(PI);
803
804    assert!(ri
805        .transform_point(point2(1.0, 2.0))
806        .approx_eq(&point2(1.0, 2.0)));
807    assert!(r90
808        .transform_point(point2(1.0, 2.0))
809        .approx_eq(&point2(-2.0, 1.0)));
810    assert!(rm90
811        .transform_point(point2(1.0, 2.0))
812        .approx_eq(&point2(2.0, -1.0)));
813    assert!(r180
814        .transform_point(point2(1.0, 2.0))
815        .approx_eq(&point2(-1.0, -2.0)));
816
817    assert!(r90
818        .inverse()
819        .inverse()
820        .transform_point(point2(1.0, 2.0))
821        .approx_eq(&r90.transform_point(point2(1.0, 2.0))));
822}
823
824#[test]
825fn simple_rotation_3d_in_2d() {
826    use crate::default::Rotation3D;
827    use core::f32::consts::{FRAC_PI_2, PI};
828
829    let ri = Rotation3D::identity();
830    let r90 = Rotation3D::around_z(Angle::radians(FRAC_PI_2));
831    let rm90 = Rotation3D::around_z(Angle::radians(-FRAC_PI_2));
832    let r180 = Rotation3D::around_z(Angle::radians(PI));
833
834    assert!(ri
835        .transform_point2d(point2(1.0, 2.0))
836        .approx_eq(&point2(1.0, 2.0)));
837    assert!(r90
838        .transform_point2d(point2(1.0, 2.0))
839        .approx_eq(&point2(-2.0, 1.0)));
840    assert!(rm90
841        .transform_point2d(point2(1.0, 2.0))
842        .approx_eq(&point2(2.0, -1.0)));
843    assert!(r180
844        .transform_point2d(point2(1.0, 2.0))
845        .approx_eq(&point2(-1.0, -2.0)));
846
847    assert!(r90
848        .inverse()
849        .inverse()
850        .transform_point2d(point2(1.0, 2.0))
851        .approx_eq(&r90.transform_point2d(point2(1.0, 2.0))));
852}
853
854#[test]
855fn pre_post() {
856    use crate::default::Rotation3D;
857    use core::f32::consts::FRAC_PI_2;
858
859    let r1 = Rotation3D::around_x(Angle::radians(FRAC_PI_2));
860    let r2 = Rotation3D::around_y(Angle::radians(FRAC_PI_2));
861    let r3 = Rotation3D::around_z(Angle::radians(FRAC_PI_2));
862
863    let t1 = r1.to_transform();
864    let t2 = r2.to_transform();
865    let t3 = r3.to_transform();
866
867    let p = point3(1.0, 2.0, 3.0);
868
869    // Check that the order of transformations is correct (corresponds to what
870    // we do in Transform3D).
871    let p1 = r1.then(&r2).then(&r3).transform_point3d(p);
872    let p2 = t1.then(&t2).then(&t3).transform_point3d(p);
873
874    assert!(p1.approx_eq(&p2.unwrap()));
875
876    // Check that changing the order indeed matters.
877    let p3 = t3.then(&t1).then(&t2).transform_point3d(p);
878    assert!(!p1.approx_eq(&p3.unwrap()));
879}
880
881#[test]
882fn to_transform3d() {
883    use crate::default::Rotation3D;
884
885    use core::f32::consts::{FRAC_PI_2, PI};
886    let rotations = [
887        Rotation3D::identity(),
888        Rotation3D::around_x(Angle::radians(FRAC_PI_2)),
889        Rotation3D::around_x(Angle::radians(-FRAC_PI_2)),
890        Rotation3D::around_x(Angle::radians(PI)),
891        Rotation3D::around_y(Angle::radians(FRAC_PI_2)),
892        Rotation3D::around_y(Angle::radians(-FRAC_PI_2)),
893        Rotation3D::around_y(Angle::radians(PI)),
894        Rotation3D::around_z(Angle::radians(FRAC_PI_2)),
895        Rotation3D::around_z(Angle::radians(-FRAC_PI_2)),
896        Rotation3D::around_z(Angle::radians(PI)),
897    ];
898
899    let points = [
900        point3(0.0, 0.0, 0.0),
901        point3(1.0, 2.0, 3.0),
902        point3(-5.0, 3.0, -1.0),
903        point3(-0.5, -1.0, 1.5),
904    ];
905
906    for rotation in &rotations {
907        for &point in &points {
908            let p1 = rotation.transform_point3d(point);
909            let p2 = rotation.to_transform().transform_point3d(point);
910            assert!(p1.approx_eq(&p2.unwrap()));
911        }
912    }
913}
914
915#[test]
916fn slerp() {
917    use crate::default::Rotation3D;
918
919    let q1 = Rotation3D::quaternion(1.0, 0.0, 0.0, 0.0);
920    let q2 = Rotation3D::quaternion(0.0, 1.0, 0.0, 0.0);
921    let q3 = Rotation3D::quaternion(0.0, 0.0, -1.0, 0.0);
922
923    // The values below can be obtained with a python program:
924    // import numpy
925    // import quaternion
926    // q1 = numpy.quaternion(1, 0, 0, 0)
927    // q2 = numpy.quaternion(0, 1, 0, 0)
928    // quaternion.slerp_evaluate(q1, q2, 0.2)
929
930    assert!(q1.slerp(&q2, 0.0).approx_eq(&q1));
931    assert!(q1.slerp(&q2, 0.2).approx_eq(&Rotation3D::quaternion(
932        0.951056516295154,
933        0.309016994374947,
934        0.0,
935        0.0
936    )));
937    assert!(q1.slerp(&q2, 0.4).approx_eq(&Rotation3D::quaternion(
938        0.809016994374947,
939        0.587785252292473,
940        0.0,
941        0.0
942    )));
943    assert!(q1.slerp(&q2, 0.6).approx_eq(&Rotation3D::quaternion(
944        0.587785252292473,
945        0.809016994374947,
946        0.0,
947        0.0
948    )));
949    assert!(q1.slerp(&q2, 0.8).approx_eq(&Rotation3D::quaternion(
950        0.309016994374947,
951        0.951056516295154,
952        0.0,
953        0.0
954    )));
955    assert!(q1.slerp(&q2, 1.0).approx_eq(&q2));
956
957    assert!(q1.slerp(&q3, 0.0).approx_eq(&q1));
958    assert!(q1.slerp(&q3, 0.2).approx_eq(&Rotation3D::quaternion(
959        0.951056516295154,
960        0.0,
961        -0.309016994374947,
962        0.0
963    )));
964    assert!(q1.slerp(&q3, 0.4).approx_eq(&Rotation3D::quaternion(
965        0.809016994374947,
966        0.0,
967        -0.587785252292473,
968        0.0
969    )));
970    assert!(q1.slerp(&q3, 0.6).approx_eq(&Rotation3D::quaternion(
971        0.587785252292473,
972        0.0,
973        -0.809016994374947,
974        0.0
975    )));
976    assert!(q1.slerp(&q3, 0.8).approx_eq(&Rotation3D::quaternion(
977        0.309016994374947,
978        0.0,
979        -0.951056516295154,
980        0.0
981    )));
982    assert!(q1.slerp(&q3, 1.0).approx_eq(&q3));
983}
984
985#[test]
986fn around_axis() {
987    use crate::default::Rotation3D;
988    use core::f32::consts::{FRAC_PI_2, PI};
989
990    // Two sort of trivial cases:
991    let r1 = Rotation3D::around_axis(vec3(1.0, 1.0, 0.0), Angle::radians(PI));
992    let r2 = Rotation3D::around_axis(vec3(1.0, 1.0, 0.0), Angle::radians(FRAC_PI_2));
993    assert!(r1
994        .transform_point3d(point3(1.0, 2.0, 0.0))
995        .approx_eq(&point3(2.0, 1.0, 0.0)));
996    assert!(r2
997        .transform_point3d(point3(1.0, 0.0, 0.0))
998        .approx_eq(&point3(0.5, 0.5, -0.5.sqrt())));
999
1000    // A more arbitrary test (made up with numpy):
1001    let r3 = Rotation3D::around_axis(vec3(0.5, 1.0, 2.0), Angle::radians(2.291288));
1002    assert!(r3
1003        .transform_point3d(point3(1.0, 0.0, 0.0))
1004        .approx_eq(&point3(-0.58071821, 0.81401868, -0.01182979)));
1005}
1006
1007#[test]
1008fn from_euler() {
1009    use crate::default::Rotation3D;
1010    use core::f32::consts::FRAC_PI_2;
1011
1012    // First test simple separate yaw pitch and roll rotations, because it is easy to come
1013    // up with the corresponding quaternion.
1014    // Since several quaternions can represent the same transformation we compare the result
1015    // of transforming a point rather than the values of each quaternions.
1016    let p = point3(1.0, 2.0, 3.0);
1017
1018    let angle = Angle::radians(FRAC_PI_2);
1019    let zero = Angle::radians(0.0);
1020
1021    // roll
1022    let roll_re = Rotation3D::euler(angle, zero, zero);
1023    let roll_rq = Rotation3D::around_x(angle);
1024    let roll_pe = roll_re.transform_point3d(p);
1025    let roll_pq = roll_rq.transform_point3d(p);
1026
1027    // pitch
1028    let pitch_re = Rotation3D::euler(zero, angle, zero);
1029    let pitch_rq = Rotation3D::around_y(angle);
1030    let pitch_pe = pitch_re.transform_point3d(p);
1031    let pitch_pq = pitch_rq.transform_point3d(p);
1032
1033    // yaw
1034    let yaw_re = Rotation3D::euler(zero, zero, angle);
1035    let yaw_rq = Rotation3D::around_z(angle);
1036    let yaw_pe = yaw_re.transform_point3d(p);
1037    let yaw_pq = yaw_rq.transform_point3d(p);
1038
1039    assert!(roll_pe.approx_eq(&roll_pq));
1040    assert!(pitch_pe.approx_eq(&pitch_pq));
1041    assert!(yaw_pe.approx_eq(&yaw_pq));
1042
1043    // Now check that the yaw pitch and roll transformations when combined are applied in
1044    // the proper order: roll -> pitch -> yaw.
1045    let ypr_e = Rotation3D::euler(angle, angle, angle);
1046    let ypr_q = roll_rq.then(&pitch_rq).then(&yaw_rq);
1047    let ypr_pe = ypr_e.transform_point3d(p);
1048    let ypr_pq = ypr_q.transform_point3d(p);
1049
1050    assert!(ypr_pe.approx_eq(&ypr_pq));
1051}
euclid/rotation.rs

euclid/
rotation.rs
