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
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
use num::{One, Zero};
use std::fmt;
use std::hash;

#[cfg(feature = "serde-serialize-no-std")]
use serde::{Deserialize, Deserializer, Serialize, Serializer};

use crate::base::allocator::Allocator;
use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
use crate::base::storage::Owned;
use crate::base::{Const, DefaultAllocator, OMatrix, OVector, SVector, Scalar};
use crate::ClosedDivAssign;
use crate::ClosedMulAssign;

use crate::geometry::Point;

#[cfg(feature = "rkyv-serialize")]
use rkyv::bytecheck;

/// A scale which supports non-uniform scaling.
#[repr(C)]
#[cfg_attr(
    feature = "rkyv-serialize-no-std",
    derive(rkyv::Archive, rkyv::Serialize, rkyv::Deserialize),
    archive(
        as = "Scale<T::Archived, D>",
        bound(archive = "
        T: rkyv::Archive,
        SVector<T, D>: rkyv::Archive<Archived = SVector<T::Archived, D>>
    ")
    )
)]
#[cfg_attr(feature = "rkyv-serialize", derive(bytecheck::CheckBytes))]
#[derive(Copy, Clone)]
pub struct Scale<T, const D: usize> {
    /// The scale coordinates, i.e., how much is multiplied to a point's coordinates when it is
    /// scaled.
    pub vector: SVector<T, D>,
}

impl<T: fmt::Debug, const D: usize> fmt::Debug for Scale<T, D> {
    fn fmt(&self, formatter: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
        self.vector.as_slice().fmt(formatter)
    }
}

impl<T: Scalar + hash::Hash, const D: usize> hash::Hash for Scale<T, D>
where
    Owned<T, Const<D>>: hash::Hash,
{
    fn hash<H: hash::Hasher>(&self, state: &mut H) {
        self.vector.hash(state)
    }
}

#[cfg(feature = "bytemuck")]
unsafe impl<T, const D: usize> bytemuck::Zeroable for Scale<T, D>
where
    T: Scalar + bytemuck::Zeroable,
    SVector<T, D>: bytemuck::Zeroable,
{
}

#[cfg(feature = "bytemuck")]
unsafe impl<T, const D: usize> bytemuck::Pod for Scale<T, D>
where
    T: Scalar + bytemuck::Pod,
    SVector<T, D>: bytemuck::Pod,
{
}

#[cfg(feature = "serde-serialize-no-std")]
impl<T: Scalar, const D: usize> Serialize for Scale<T, D>
where
    Owned<T, Const<D>>: Serialize,
{
    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
    where
        S: Serializer,
    {
        self.vector.serialize(serializer)
    }
}

#[cfg(feature = "serde-serialize-no-std")]
impl<'a, T: Scalar, const D: usize> Deserialize<'a> for Scale<T, D>
where
    Owned<T, Const<D>>: Deserialize<'a>,
{
    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
    where
        Des: Deserializer<'a>,
    {
        let matrix = SVector::<T, D>::deserialize(deserializer)?;

        Ok(Scale::from(matrix))
    }
}

impl<T: Scalar, const D: usize> Scale<T, D> {
    /// Inverts `self`.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::{Scale2, Scale3};
    /// let t = Scale3::new(1.0, 2.0, 3.0);
    /// assert_eq!(t * t.try_inverse().unwrap(), Scale3::identity());
    /// assert_eq!(t.try_inverse().unwrap() * t, Scale3::identity());
    ///
    /// // Work in all dimensions.
    /// let t = Scale2::new(1.0, 2.0);
    /// assert_eq!(t * t.try_inverse().unwrap(), Scale2::identity());
    /// assert_eq!(t.try_inverse().unwrap() * t, Scale2::identity());
    ///
    /// // Returns None if any coordinate is 0.
    /// let t = Scale2::new(0.0, 2.0);
    /// assert_eq!(t.try_inverse(), None);
    /// ```
    #[inline]
    #[must_use = "Did you mean to use try_inverse_mut()?"]
    pub fn try_inverse(&self) -> Option<Scale<T, D>>
    where
        T: ClosedDivAssign + One + Zero,
    {
        for i in 0..D {
            if self.vector[i] == T::zero() {
                return None;
            }
        }
        Some(self.vector.map(|e| T::one() / e).into())
    }

    /// Inverts `self`.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::{Scale2, Scale3};
    ///
    /// unsafe {
    ///     let t = Scale3::new(1.0, 2.0, 3.0);
    ///     assert_eq!(t * t.inverse_unchecked(), Scale3::identity());
    ///     assert_eq!(t.inverse_unchecked() * t, Scale3::identity());
    ///
    ///     // Work in all dimensions.
    ///     let t = Scale2::new(1.0, 2.0);
    ///     assert_eq!(t * t.inverse_unchecked(), Scale2::identity());
    ///     assert_eq!(t.inverse_unchecked() * t, Scale2::identity());
    /// }
    /// ```
    ///
    /// # Safety
    ///
    /// Should only be used if all scaling is known to be non-zero.
    #[inline]
    #[must_use]
    pub unsafe fn inverse_unchecked(&self) -> Scale<T, D>
    where
        T: ClosedDivAssign + One,
    {
        self.vector.map(|e| T::one() / e).into()
    }

    /// Inverts `self`.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::{Scale2, Scale3};
    /// let t = Scale3::new(1.0, 2.0, 3.0);
    /// assert_eq!(t * t.pseudo_inverse(), Scale3::identity());
    /// assert_eq!(t.pseudo_inverse() * t, Scale3::identity());
    ///
    /// // Work in all dimensions.
    /// let t = Scale2::new(1.0, 2.0);
    /// assert_eq!(t * t.pseudo_inverse(), Scale2::identity());
    /// assert_eq!(t.pseudo_inverse() * t, Scale2::identity());
    ///
    /// // Inverts only non-zero coordinates.
    /// let t = Scale2::new(0.0, 2.0);
    /// assert_eq!(t * t.pseudo_inverse(), Scale2::new(0.0, 1.0));
    /// assert_eq!(t.pseudo_inverse() * t, Scale2::new(0.0, 1.0));
    /// ```
    #[inline]
    #[must_use]
    pub fn pseudo_inverse(&self) -> Scale<T, D>
    where
        T: ClosedDivAssign + One + Zero,
    {
        self.vector
            .map(|e| {
                if e != T::zero() {
                    T::one() / e
                } else {
                    T::zero()
                }
            })
            .into()
    }

    /// Converts this Scale into its equivalent homogeneous transformation matrix.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::{Scale2, Scale3, Matrix3, Matrix4};
    /// let t = Scale3::new(10.0, 20.0, 30.0);
    /// let expected = Matrix4::new(10.0, 0.0, 0.0, 0.0,
    ///                             0.0, 20.0, 0.0, 0.0,
    ///                             0.0, 0.0, 30.0, 0.0,
    ///                             0.0, 0.0, 0.0, 1.0);
    /// assert_eq!(t.to_homogeneous(), expected);
    ///
    /// let t = Scale2::new(10.0, 20.0);
    /// let expected = Matrix3::new(10.0, 0.0, 0.0,
    ///                             0.0, 20.0, 0.0,
    ///                             0.0, 0.0, 1.0);
    /// assert_eq!(t.to_homogeneous(), expected);
    /// ```
    #[inline]
    #[must_use]
    pub fn to_homogeneous(&self) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
    where
        T: Zero + One + Clone,
        Const<D>: DimNameAdd<U1>,
        DefaultAllocator: Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
            + Allocator<DimNameSum<Const<D>, U1>, U1>,
    {
        // TODO: use self.vector.push() instead. We can’t right now because
        //       that would require the DimAdd bound (but here we use DimNameAdd).
        //       This should be fixable once Rust gets a more complete support of
        //       const-generics.
        let mut v = OVector::from_element(T::one());
        for i in 0..D {
            v[i] = self.vector[i].clone();
        }
        OMatrix::from_diagonal(&v)
    }

    /// Inverts `self` in-place.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::{Scale2, Scale3};
    /// let t = Scale3::new(1.0, 2.0, 3.0);
    /// let mut inv_t = Scale3::new(1.0, 2.0, 3.0);
    /// assert!(inv_t.try_inverse_mut());
    /// assert_eq!(t * inv_t, Scale3::identity());
    /// assert_eq!(inv_t * t, Scale3::identity());
    ///
    /// // Work in all dimensions.
    /// let t = Scale2::new(1.0, 2.0);
    /// let mut inv_t = Scale2::new(1.0, 2.0);
    /// assert!(inv_t.try_inverse_mut());
    /// assert_eq!(t * inv_t, Scale2::identity());
    /// assert_eq!(inv_t * t, Scale2::identity());
    ///
    /// // Does not perform any operation if a coordinate is 0.
    /// let mut t = Scale2::new(0.0, 2.0);
    /// assert!(!t.try_inverse_mut());
    /// ```
    #[inline]
    pub fn try_inverse_mut(&mut self) -> bool
    where
        T: ClosedDivAssign + One + Zero,
    {
        if let Some(v) = self.try_inverse() {
            self.vector = v.vector;
            true
        } else {
            false
        }
    }
}

impl<T: Scalar + ClosedMulAssign, const D: usize> Scale<T, D> {
    /// Translate the given point.
    ///
    /// This is the same as the multiplication `self * pt`.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::{Scale3, Point3};
    /// let t = Scale3::new(1.0, 2.0, 3.0);
    /// let transformed_point = t.transform_point(&Point3::new(4.0, 5.0, 6.0));
    /// assert_eq!(transformed_point, Point3::new(4.0, 10.0, 18.0));
    /// ```
    #[inline]
    #[must_use]
    pub fn transform_point(&self, pt: &Point<T, D>) -> Point<T, D> {
        self * pt
    }
}

impl<T: Scalar + ClosedDivAssign + ClosedMulAssign + One + Zero, const D: usize> Scale<T, D> {
    /// Translate the given point by the inverse of this Scale.
    ///
    /// # Example
    /// ```
    /// # use nalgebra::{Scale3, Point3};
    /// let t = Scale3::new(1.0, 2.0, 3.0);
    /// let transformed_point = t.try_inverse_transform_point(&Point3::new(4.0, 6.0, 6.0)).unwrap();
    /// assert_eq!(transformed_point, Point3::new(4.0, 3.0, 2.0));
    ///
    /// // Returns None if the inverse doesn't exist.
    /// let t = Scale3::new(1.0, 0.0, 3.0);
    /// let transformed_point = t.try_inverse_transform_point(&Point3::new(4.0, 6.0, 6.0));
    /// assert_eq!(transformed_point, None);
    /// ```
    #[inline]
    #[must_use]
    pub fn try_inverse_transform_point(&self, pt: &Point<T, D>) -> Option<Point<T, D>> {
        self.try_inverse().map(|s| s * pt)
    }
}

impl<T: Scalar + Eq, const D: usize> Eq for Scale<T, D> {}

impl<T: Scalar + PartialEq, const D: usize> PartialEq for Scale<T, D> {
    #[inline]
    fn eq(&self, right: &Scale<T, D>) -> bool {
        self.vector == right.vector
    }
}

impl<T: Scalar + AbsDiffEq, const D: usize> AbsDiffEq for Scale<T, D>
where
    T::Epsilon: Clone,
{
    type Epsilon = T::Epsilon;

    #[inline]
    fn default_epsilon() -> Self::Epsilon {
        T::default_epsilon()
    }

    #[inline]
    fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
        self.vector.abs_diff_eq(&other.vector, epsilon)
    }
}

impl<T: Scalar + RelativeEq, const D: usize> RelativeEq for Scale<T, D>
where
    T::Epsilon: Clone,
{
    #[inline]
    fn default_max_relative() -> Self::Epsilon {
        T::default_max_relative()
    }

    #[inline]
    fn relative_eq(
        &self,
        other: &Self,
        epsilon: Self::Epsilon,
        max_relative: Self::Epsilon,
    ) -> bool {
        self.vector
            .relative_eq(&other.vector, epsilon, max_relative)
    }
}

impl<T: Scalar + UlpsEq, const D: usize> UlpsEq for Scale<T, D>
where
    T::Epsilon: Clone,
{
    #[inline]
    fn default_max_ulps() -> u32 {
        T::default_max_ulps()
    }

    #[inline]
    fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
        self.vector.ulps_eq(&other.vector, epsilon, max_ulps)
    }
}

/*
 *
 * Display
 *
 */
impl<T: Scalar + fmt::Display, const D: usize> fmt::Display for Scale<T, D> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        let precision = f.precision().unwrap_or(3);

        writeln!(f, "Scale {{")?;
        write!(f, "{:.*}", precision, self.vector)?;
        writeln!(f, "}}")
    }
}