1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
#[cfg(feature = "arbitrary")]
use crate::base::storage::Owned;
#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};

use num::One;
#[cfg(feature = "rand-no-std")]
use rand::{
    distributions::{Distribution, Standard},
    Rng,
};

use simba::scalar::SupersetOf;
use simba::simd::SimdRealField;

use crate::base::allocator::Allocator;
use crate::base::dimension::{DimName, U2};
use crate::base::{DefaultAllocator, Vector2, Vector3};

use crate::{
    AbstractRotation, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Point,
    Point3, Rotation, Rotation3, Scalar, Translation, Translation2, Translation3, UnitComplex,
    UnitQuaternion,
};

impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D>,
{
    /// Creates a new identity isometry.
    ///
    /// # Example
    ///
    /// ```
    /// # use nalgebra::{Isometry2, Point2, Isometry3, Point3};
    ///
    /// let iso = Isometry2::identity();
    /// let pt = Point2::new(1.0, 2.0);
    /// assert_eq!(iso * pt, pt);
    ///
    /// let iso = Isometry3::identity();
    /// let pt = Point3::new(1.0, 2.0, 3.0);
    /// assert_eq!(iso * pt, pt);
    /// ```
    #[inline]
    pub fn identity() -> Self {
        Self::from_parts(Translation::identity(), R::identity())
    }

    /// The isometry that applies the rotation `r` with its axis passing through the point `p`.
    /// This effectively lets `p` invariant.
    ///
    /// # Example
    ///
    /// ```
    /// # #[macro_use] extern crate approx;
    /// # use std::f32;
    /// # use nalgebra::{Isometry2, Point2, UnitComplex};
    /// let rot = UnitComplex::new(f32::consts::PI);
    /// let pt = Point2::new(1.0, 0.0);
    /// let iso = Isometry2::rotation_wrt_point(rot, pt);
    ///
    /// assert_eq!(iso * pt, pt); // The rotation center is not affected.
    /// assert_relative_eq!(iso * Point2::new(1.0, 2.0), Point2::new(1.0, -2.0), epsilon = 1.0e-6);
    /// ```
    #[inline]
    pub fn rotation_wrt_point(r: R, p: Point<N, D>) -> Self {
        let shift = r.transform_vector(&-&p.coords);
        Self::from_parts(Translation::from(shift + p.coords), r)
    }
}

impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> One for Isometry<N, D, R>
where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D>,
{
    /// Creates a new identity isometry.
    #[inline]
    fn one() -> Self {
        Self::identity()
    }
}

#[cfg(feature = "rand-no-std")]
impl<N: crate::RealField, D: DimName, R> Distribution<Isometry<N, D, R>> for Standard
where
    R: AbstractRotation<N, D>,
    Standard: Distribution<N> + Distribution<R>,
    DefaultAllocator: Allocator<N, D>,
{
    #[inline]
    fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Isometry<N, D, R> {
        Isometry::from_parts(rng.gen(), rng.gen())
    }
}

#[cfg(feature = "arbitrary")]
impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
where
    N: SimdRealField + Arbitrary + Send,
    N::Element: SimdRealField,
    R: AbstractRotation<N, D> + Arbitrary + Send,
    Owned<N, D>: Send,
    DefaultAllocator: Allocator<N, D>,
{
    #[inline]
    fn arbitrary(rng: &mut Gen) -> Self {
        Self::from_parts(Arbitrary::arbitrary(rng), Arbitrary::arbitrary(rng))
    }
}

/*
 *
 * Constructors for various static dimensions.
 *
 */

/// # Construction from a 2D vector and/or a rotation angle
impl<N: SimdRealField> IsometryMatrix2<N>
where
    N::Element: SimdRealField,
{
    /// Creates a new 2D isometry from a translation and a rotation angle.
    ///
    /// Its rotational part is represented as a 2x2 rotation matrix.
    ///
    /// # Example
    ///
    /// ```
    /// # use std::f32;
    /// # use nalgebra::{Isometry2, Vector2, Point2};
    /// let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
    ///
    /// assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));
    /// ```
    #[inline]
    pub fn new(translation: Vector2<N>, angle: N) -> Self {
        Self::from_parts(
            Translation::from(translation),
            Rotation::<N, U2>::new(angle),
        )
    }

    /// Creates a new isometry from the given translation coordinates.
    #[inline]
    pub fn translation(x: N, y: N) -> Self {
        Self::new(Vector2::new(x, y), N::zero())
    }

    /// Creates a new isometry from the given rotation angle.
    #[inline]
    pub fn rotation(angle: N) -> Self {
        Self::new(Vector2::zeros(), angle)
    }

    /// Cast the components of `self` to another type.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::IsometryMatrix2;
    /// let iso = IsometryMatrix2::<f64>::identity();
    /// let iso2 = iso.cast::<f32>();
    /// assert_eq!(iso2, IsometryMatrix2::<f32>::identity());
    /// ```
    pub fn cast<To: Scalar>(self) -> IsometryMatrix2<To>
    where
        IsometryMatrix2<To>: SupersetOf<Self>,
    {
        crate::convert(self)
    }
}

impl<N: SimdRealField> Isometry2<N>
where
    N::Element: SimdRealField,
{
    /// Creates a new 2D isometry from a translation and a rotation angle.
    ///
    /// Its rotational part is represented as an unit complex number.
    ///
    /// # Example
    ///
    /// ```
    /// # use std::f32;
    /// # use nalgebra::{IsometryMatrix2, Point2, Vector2};
    /// let iso = IsometryMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
    ///
    /// assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));
    /// ```
    #[inline]
    pub fn new(translation: Vector2<N>, angle: N) -> Self {
        Self::from_parts(
            Translation::from(translation),
            UnitComplex::from_angle(angle),
        )
    }

    /// Creates a new isometry from the given translation coordinates.
    #[inline]
    pub fn translation(x: N, y: N) -> Self {
        Self::from_parts(Translation2::new(x, y), UnitComplex::identity())
    }

    /// Creates a new isometry from the given rotation angle.
    #[inline]
    pub fn rotation(angle: N) -> Self {
        Self::new(Vector2::zeros(), angle)
    }

    /// Cast the components of `self` to another type.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::Isometry2;
    /// let iso = Isometry2::<f64>::identity();
    /// let iso2 = iso.cast::<f32>();
    /// assert_eq!(iso2, Isometry2::<f32>::identity());
    /// ```
    pub fn cast<To: Scalar>(self) -> Isometry2<To>
    where
        Isometry2<To>: SupersetOf<Self>,
    {
        crate::convert(self)
    }
}

// 3D rotation.
macro_rules! basic_isometry_construction_impl(
    ($RotId: ident < $($RotParams: ident),*>) => {
        /// Creates a new isometry from a translation and a rotation axis-angle.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
        /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
        /// let translation = Vector3::new(1.0, 2.0, 3.0);
        /// // Point and vector being transformed in the tests.
        /// let pt = Point3::new(4.0, 5.0, 6.0);
        /// let vec = Vector3::new(4.0, 5.0, 6.0);
        ///
        /// // Isometry with its rotation part represented as a UnitQuaternion
        /// let iso = Isometry3::new(translation, axisangle);
        /// assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
        /// assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
        ///
        /// // Isometry with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
        /// let iso = IsometryMatrix3::new(translation, axisangle);
        /// assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
        /// assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
        /// ```
        #[inline]
        pub fn new(translation: Vector3<N>, axisangle: Vector3<N>) -> Self {
            Self::from_parts(
                Translation::from(translation),
                $RotId::<$($RotParams),*>::from_scaled_axis(axisangle))
        }

        /// Creates a new isometry from the given translation coordinates.
        #[inline]
        pub fn translation(x: N, y: N, z: N) -> Self {
            Self::from_parts(Translation3::new(x, y, z), $RotId::identity())
        }

        /// Creates a new isometry from the given rotation angle.
        #[inline]
        pub fn rotation(axisangle: Vector3<N>) -> Self {
            Self::new(Vector3::zeros(), axisangle)
        }
    }
);

macro_rules! look_at_isometry_construction_impl(
    ($RotId: ident < $($RotParams: ident),*>) => {
        /// Creates an isometry that corresponds to the local frame of an observer standing at the
        /// point `eye` and looking toward `target`.
        ///
        /// It maps the `z` axis to the view direction `target - eye`and the origin to the `eye`.
        ///
        /// # Arguments
        ///   * eye - The observer position.
        ///   * target - The target position.
        ///   * up - Vertical direction. The only requirement of this parameter is to not be collinear
        ///   to `eye - at`. Non-collinearity is not checked.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
        /// let eye = Point3::new(1.0, 2.0, 3.0);
        /// let target = Point3::new(2.0, 2.0, 3.0);
        /// let up = Vector3::y();
        ///
        /// // Isometry with its rotation part represented as a UnitQuaternion
        /// let iso = Isometry3::face_towards(&eye, &target, &up);
        /// assert_eq!(iso * Point3::origin(), eye);
        /// assert_relative_eq!(iso * Vector3::z(), Vector3::x());
        ///
        /// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
        /// let iso = IsometryMatrix3::face_towards(&eye, &target, &up);
        /// assert_eq!(iso * Point3::origin(), eye);
        /// assert_relative_eq!(iso * Vector3::z(), Vector3::x());
        /// ```
        #[inline]
        pub fn face_towards(eye:    &Point3<N>,
                            target: &Point3<N>,
                            up:     &Vector3<N>)
                            -> Self {
            Self::from_parts(
                Translation::from(eye.coords.clone()),
                $RotId::face_towards(&(target - eye), up))
        }

        /// Deprecated: Use [Isometry::face_towards] instead.
        #[deprecated(note="renamed to `face_towards`")]
        pub fn new_observer_frame(eye:    &Point3<N>,
                                  target: &Point3<N>,
                                  up:     &Vector3<N>)
                                  -> Self {
            Self::face_towards(eye, target, up)
        }

        /// Builds a right-handed look-at view matrix.
        ///
        /// It maps the view direction `target - eye` to the **negative** `z` axis to and the `eye` to the origin.
        /// This conforms to the common notion of right handed camera look-at **view matrix** from
        /// the computer graphics community, i.e. the camera is assumed to look toward its local `-z` axis.
        ///
        /// # Arguments
        ///   * eye - The eye position.
        ///   * target - The target position.
        ///   * up - A vector approximately aligned with required the vertical axis. The only
        ///   requirement of this parameter is to not be collinear to `target - eye`.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
        /// let eye = Point3::new(1.0, 2.0, 3.0);
        /// let target = Point3::new(2.0, 2.0, 3.0);
        /// let up = Vector3::y();
        ///
        /// // Isometry with its rotation part represented as a UnitQuaternion
        /// let iso = Isometry3::look_at_rh(&eye, &target, &up);
        /// assert_eq!(iso * eye, Point3::origin());
        /// assert_relative_eq!(iso * Vector3::x(), -Vector3::z());
        ///
        /// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
        /// let iso = IsometryMatrix3::look_at_rh(&eye, &target, &up);
        /// assert_eq!(iso * eye, Point3::origin());
        /// assert_relative_eq!(iso * Vector3::x(), -Vector3::z());
        /// ```
        #[inline]
        pub fn look_at_rh(eye:    &Point3<N>,
                          target: &Point3<N>,
                          up:     &Vector3<N>)
                          -> Self {
            let rotation = $RotId::look_at_rh(&(target - eye), up);
            let trans    = &rotation * (-eye);

            Self::from_parts(Translation::from(trans.coords), rotation)
        }

        /// Builds a left-handed look-at view matrix.
        ///
        /// It maps the view direction `target - eye` to the **positive** `z` axis and the `eye` to the origin.
        /// This conforms to the common notion of right handed camera look-at **view matrix** from
        /// the computer graphics community, i.e. the camera is assumed to look toward its local `z` axis.
        ///
        /// # Arguments
        ///   * eye - The eye position.
        ///   * target - The target position.
        ///   * up - A vector approximately aligned with required the vertical axis. The only
        ///   requirement of this parameter is to not be collinear to `target - eye`.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
        /// let eye = Point3::new(1.0, 2.0, 3.0);
        /// let target = Point3::new(2.0, 2.0, 3.0);
        /// let up = Vector3::y();
        ///
        /// // Isometry with its rotation part represented as a UnitQuaternion
        /// let iso = Isometry3::look_at_lh(&eye, &target, &up);
        /// assert_eq!(iso * eye, Point3::origin());
        /// assert_relative_eq!(iso * Vector3::x(), Vector3::z());
        ///
        /// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
        /// let iso = IsometryMatrix3::look_at_lh(&eye, &target, &up);
        /// assert_eq!(iso * eye, Point3::origin());
        /// assert_relative_eq!(iso * Vector3::x(), Vector3::z());
        /// ```
        #[inline]
        pub fn look_at_lh(eye:    &Point3<N>,
                          target: &Point3<N>,
                          up:     &Vector3<N>)
                          -> Self {
            let rotation = $RotId::look_at_lh(&(target - eye), up);
            let trans    = &rotation * (-eye);

            Self::from_parts(Translation::from(trans.coords), rotation)
        }
    }
);

/// # Construction from a 3D vector and/or an axis-angle
impl<N: SimdRealField> Isometry3<N>
where
    N::Element: SimdRealField,
{
    basic_isometry_construction_impl!(UnitQuaternion<N>);

    /// Cast the components of `self` to another type.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::Isometry3;
    /// let iso = Isometry3::<f64>::identity();
    /// let iso2 = iso.cast::<f32>();
    /// assert_eq!(iso2, Isometry3::<f32>::identity());
    /// ```
    pub fn cast<To: Scalar>(self) -> Isometry3<To>
    where
        Isometry3<To>: SupersetOf<Self>,
    {
        crate::convert(self)
    }
}

impl<N: SimdRealField> IsometryMatrix3<N>
where
    N::Element: SimdRealField,
{
    basic_isometry_construction_impl!(Rotation3<N>);

    /// Cast the components of `self` to another type.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::IsometryMatrix3;
    /// let iso = IsometryMatrix3::<f64>::identity();
    /// let iso2 = iso.cast::<f32>();
    /// assert_eq!(iso2, IsometryMatrix3::<f32>::identity());
    /// ```
    pub fn cast<To: Scalar>(self) -> IsometryMatrix3<To>
    where
        IsometryMatrix3<To>: SupersetOf<Self>,
    {
        crate::convert(self)
    }
}

/// # Construction from a 3D eye position and target point
impl<N: SimdRealField> Isometry3<N>
where
    N::Element: SimdRealField,
{
    look_at_isometry_construction_impl!(UnitQuaternion<N>);
}

impl<N: SimdRealField> IsometryMatrix3<N>
where
    N::Element: SimdRealField,
{
    look_at_isometry_construction_impl!(Rotation3<N>);
}