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
use crate::{Padding, Point, Radians, Size, Vector};

/// An axis-aligned rectangle.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
pub struct Rectangle<T = f32> {
    /// X coordinate of the top-left corner.
    pub x: T,

    /// Y coordinate of the top-left corner.
    pub y: T,

    /// Width of the rectangle.
    pub width: T,

    /// Height of the rectangle.
    pub height: T,
}

impl<T> Rectangle<T>
where
    T: Default,
{
    /// Creates a new [`Rectangle`] with its top-left corner at the origin
    /// and with the provided [`Size`].
    pub fn with_size(size: Size<T>) -> Self {
        Self {
            x: T::default(),
            y: T::default(),
            width: size.width,
            height: size.height,
        }
    }
}

impl Rectangle<f32> {
    /// A rectangle starting at [`Point::ORIGIN`] with infinite width and height.
    pub const INFINITE: Self = Self::new(Point::ORIGIN, Size::INFINITY);

    /// Creates a new [`Rectangle`] with its top-left corner in the given
    /// [`Point`] and with the provided [`Size`].
    pub const fn new(top_left: Point, size: Size) -> Self {
        Self {
            x: top_left.x,
            y: top_left.y,
            width: size.width,
            height: size.height,
        }
    }

    /// Creates a new square [`Rectangle`] with the center at the origin and
    /// with the given radius.
    pub fn with_radius(radius: f32) -> Self {
        Self {
            x: -radius,
            y: -radius,
            width: radius * 2.0,
            height: radius * 2.0,
        }
    }

    /// Creates a new axis-aligned [`Rectangle`] from the given vertices; returning the
    /// rotation in [`Radians`] that must be applied to the axis-aligned [`Rectangle`]
    /// to obtain the desired result.
    pub fn with_vertices(
        top_left: Point,
        top_right: Point,
        bottom_left: Point,
    ) -> (Rectangle, Radians) {
        let width = (top_right.x - top_left.x).hypot(top_right.y - top_left.y);

        let height =
            (bottom_left.x - top_left.x).hypot(bottom_left.y - top_left.y);

        let rotation =
            (top_right.y - top_left.y).atan2(top_right.x - top_left.x);

        let rotation = if rotation < 0.0 {
            2.0 * std::f32::consts::PI + rotation
        } else {
            rotation
        };

        let position = {
            let center = Point::new(
                (top_right.x + bottom_left.x) / 2.0,
                (top_right.y + bottom_left.y) / 2.0,
            );

            let rotation = -rotation - std::f32::consts::PI * 2.0;

            Point::new(
                center.x + (top_left.x - center.x) * rotation.cos()
                    - (top_left.y - center.y) * rotation.sin(),
                center.y
                    + (top_left.x - center.x) * rotation.sin()
                    + (top_left.y - center.y) * rotation.cos(),
            )
        };

        (
            Rectangle::new(position, Size::new(width, height)),
            Radians(rotation),
        )
    }

    /// Returns the [`Point`] at the center of the [`Rectangle`].
    pub fn center(&self) -> Point {
        Point::new(self.center_x(), self.center_y())
    }

    /// Returns the X coordinate of the [`Point`] at the center of the
    /// [`Rectangle`].
    pub fn center_x(&self) -> f32 {
        self.x + self.width / 2.0
    }

    /// Returns the Y coordinate of the [`Point`] at the center of the
    /// [`Rectangle`].
    pub fn center_y(&self) -> f32 {
        self.y + self.height / 2.0
    }

    /// Returns the position of the top left corner of the [`Rectangle`].
    pub fn position(&self) -> Point {
        Point::new(self.x, self.y)
    }

    /// Returns the [`Size`] of the [`Rectangle`].
    pub fn size(&self) -> Size {
        Size::new(self.width, self.height)
    }

    /// Returns the area of the [`Rectangle`].
    pub fn area(&self) -> f32 {
        self.width * self.height
    }

    /// Returns true if the given [`Point`] is contained in the [`Rectangle`].
    pub fn contains(&self, point: Point) -> bool {
        self.x <= point.x
            && point.x < self.x + self.width
            && self.y <= point.y
            && point.y < self.y + self.height
    }

    /// Returns true if the given [`Point`] is contained in the [`Rectangle`].
    /// The [`Point`] must be strictly contained, i.e. it must not be on the
    /// border.
    pub fn contains_strict(&self, point: Point) -> bool {
        self.x < point.x
            && point.x < self.x + self.width
            && self.y < point.y
            && point.y < self.y + self.height
    }

    /// Returns true if the current [`Rectangle`] is completely within the given
    /// `container`.
    pub fn is_within(&self, container: &Rectangle) -> bool {
        container.contains(self.position())
            && container.contains(
                self.position() + Vector::new(self.width, self.height),
            )
    }

    /// Returns true if the current [`Rectangle`] is completely within the given
    /// `container`. The [`Rectangle`] must be strictly contained, i.e. it must
    /// not be on the border.
    pub fn is_within_strict(&self, container: &Rectangle) -> bool {
        container.contains_strict(self.position())
            && container.contains_strict(
                self.position() + Vector::new(self.width, self.height),
            )
    }

    /// Computes the intersection with the given [`Rectangle`].
    pub fn intersection(
        &self,
        other: &Rectangle<f32>,
    ) -> Option<Rectangle<f32>> {
        let x = self.x.max(other.x);
        let y = self.y.max(other.y);

        let lower_right_x = (self.x + self.width).min(other.x + other.width);
        let lower_right_y = (self.y + self.height).min(other.y + other.height);

        let width = lower_right_x - x;
        let height = lower_right_y - y;

        if width > 0.0 && height > 0.0 {
            Some(Rectangle {
                x,
                y,
                width,
                height,
            })
        } else {
            None
        }
    }

    /// Returns whether the [`Rectangle`] intersects with the given one.
    pub fn intersects(&self, other: &Self) -> bool {
        self.intersection(other).is_some()
    }

    /// Computes the union with the given [`Rectangle`].
    pub fn union(&self, other: &Self) -> Self {
        let x = self.x.min(other.x);
        let y = self.y.min(other.y);

        let lower_right_x = (self.x + self.width).max(other.x + other.width);
        let lower_right_y = (self.y + self.height).max(other.y + other.height);

        let width = lower_right_x - x;
        let height = lower_right_y - y;

        Rectangle {
            x,
            y,
            width,
            height,
        }
    }

    /// Snaps the [`Rectangle`] to __unsigned__ integer coordinates.
    pub fn snap(self) -> Option<Rectangle<u32>> {
        let width = self.width as u32;
        let height = self.height as u32;

        if width < 1 || height < 1 {
            return None;
        }

        Some(Rectangle {
            x: self.x as u32,
            y: self.y as u32,
            width,
            height,
        })
    }

    /// Expands the [`Rectangle`] a given amount.
    pub fn expand(self, padding: impl Into<Padding>) -> Self {
        let padding = padding.into();

        Self {
            x: self.x - padding.left,
            y: self.y - padding.top,
            width: self.width + padding.horizontal(),
            height: self.height + padding.vertical(),
        }
    }

    /// Shrinks the [`Rectangle`] a given amount.
    pub fn shrink(self, padding: impl Into<Padding>) -> Self {
        let padding = padding.into();

        Self {
            x: self.x + padding.left,
            y: self.y + padding.top,
            width: self.width - padding.horizontal(),
            height: self.height - padding.vertical(),
        }
    }

    /// Rotates the [`Rectangle`] and returns the smallest [`Rectangle`]
    /// containing it.
    pub fn rotate(self, rotation: Radians) -> Self {
        let size = self.size().rotate(rotation);
        let position = Point::new(
            self.center_x() - size.width / 2.0,
            self.center_y() - size.height / 2.0,
        );

        Self::new(position, size)
    }
}

impl std::ops::Mul<f32> for Rectangle<f32> {
    type Output = Self;

    fn mul(self, scale: f32) -> Self {
        Self {
            x: self.x * scale,
            y: self.y * scale,
            width: self.width * scale,
            height: self.height * scale,
        }
    }
}

impl From<Rectangle<u32>> for Rectangle<f32> {
    fn from(rectangle: Rectangle<u32>) -> Rectangle<f32> {
        Rectangle {
            x: rectangle.x as f32,
            y: rectangle.y as f32,
            width: rectangle.width as f32,
            height: rectangle.height as f32,
        }
    }
}

impl<T> std::ops::Add<Vector<T>> for Rectangle<T>
where
    T: std::ops::Add<Output = T>,
{
    type Output = Rectangle<T>;

    fn add(self, translation: Vector<T>) -> Self {
        Rectangle {
            x: self.x + translation.x,
            y: self.y + translation.y,
            ..self
        }
    }
}

impl<T> std::ops::Sub<Vector<T>> for Rectangle<T>
where
    T: std::ops::Sub<Output = T>,
{
    type Output = Rectangle<T>;

    fn sub(self, translation: Vector<T>) -> Self {
        Rectangle {
            x: self.x - translation.x,
            y: self.y - translation.y,
            ..self
        }
    }
}

impl<T> std::ops::Mul<Vector<T>> for Rectangle<T>
where
    T: std::ops::Mul<Output = T> + Copy,
{
    type Output = Rectangle<T>;

    fn mul(self, scale: Vector<T>) -> Self {
        Rectangle {
            x: self.x * scale.x,
            y: self.y * scale.y,
            width: self.width * scale.x,
            height: self.height * scale.y,
        }
    }
}