geo_types/geometry/
point.rs

1use crate::{point, Coord, CoordFloat, CoordNum};
2
3use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
4
5/// A single point in 2D space.
6///
7/// # Semantics
8///
9/// The _interior_ of the point is itself (a singleton set),
10/// and its _boundary_ is empty. A point is _valid_ if and
11/// only if the `Coord` is valid.
12///
13/// # Creating a Point
14///
15/// There are many ways to construct a point.
16/// ```
17/// use geo_types::{coord, point, Point};
18///
19/// let p1 = Point::new(0., 1.);
20///
21/// let p2 = point! { x: 1000.0, y: 2000.0 };
22///
23/// let p3: Point = (0., 1.).into();
24///
25/// let c = coord! { x: 10., y: 20. };
26/// let p4: Point = c.into();
27/// ```
28///
29/// See the `From` impl section for a complete list of conversions.
30///
31/// ## Coordinate order for geographic points
32///
33/// For geographic points, typically `x` corresponds to longitude and `y` to latitude.
34///
35/// Geographic methods in the [`geo`](https://crates.io/crates/geo) crate expect this common
36/// lon/lat order, but different conventions exist in other coordinate systems,
37/// notably EPSG:4326, which uses lat/lon ordering.
38/// ```
39/// use geo_types::{coord, point, Point};
40///
41/// let lon = 179.9;
42/// let lat = 45.0;
43/// let geographic_point = Point::new(lon, lat);
44/// ```
45///
46#[derive(Eq, PartialEq, Clone, Copy, Hash, Default)]
47#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
48pub struct Point<T: CoordNum = f64>(pub Coord<T>);
49
50impl<T: CoordNum> From<Coord<T>> for Point<T> {
51    fn from(x: Coord<T>) -> Self {
52        Point(x)
53    }
54}
55
56impl<T: CoordNum> From<(T, T)> for Point<T> {
57    fn from(coords: (T, T)) -> Self {
58        Point::new(coords.0, coords.1)
59    }
60}
61
62impl<T: CoordNum> From<[T; 2]> for Point<T> {
63    fn from(coords: [T; 2]) -> Self {
64        Point::new(coords[0], coords[1])
65    }
66}
67
68impl<T: CoordNum> From<Point<T>> for (T, T) {
69    fn from(point: Point<T>) -> Self {
70        point.0.into()
71    }
72}
73
74impl<T: CoordNum> From<Point<T>> for [T; 2] {
75    fn from(point: Point<T>) -> Self {
76        point.0.into()
77    }
78}
79
80impl<T: CoordNum> Point<T> {
81    /// Creates a new point.
82    ///
83    /// # Examples
84    ///
85    /// ```
86    /// use geo_types::Point;
87    ///
88    /// let p = Point::new(1.234, 2.345);
89    ///
90    /// assert_eq!(p.x(), 1.234);
91    /// assert_eq!(p.y(), 2.345);
92    /// ```
93    pub fn new(x: T, y: T) -> Self {
94        point! { x: x, y: y }
95    }
96
97    /// Returns the x/horizontal component of the point.
98    ///
99    /// Typically, `x` is the horizontal position, or longitude for geographic coordinates,
100    /// but its interpretation can vary across coordinate systems.
101    ///
102    /// # Examples
103    ///
104    /// ```
105    /// use geo_types::Point;
106    ///
107    /// let p = Point::new(1.234, 2.345);
108    ///
109    /// assert_eq!(p.x(), 1.234);
110    /// ```
111    pub fn x(self) -> T {
112        self.0.x
113    }
114
115    /// Sets the x/horizontal component of the point.
116    ///
117    /// Typically, `x` is the horizontal position, or longitude for geographic coordinates,
118    /// but its interpretation can vary across coordinate systems.
119    ///
120    /// # Examples
121    ///
122    /// ```
123    /// use geo_types::Point;
124    ///
125    /// let mut p = Point::new(1.234, 2.345);
126    /// p.set_x(9.876);
127    ///
128    /// assert_eq!(p.x(), 9.876);
129    /// ```
130    pub fn set_x(&mut self, x: T) -> &mut Self {
131        self.0.x = x;
132        self
133    }
134
135    /// Returns a mutable reference to the x/horizontal component of the point
136    ///
137    /// Typically, `x` is the horizontal position, or longitude for geographic coordinates,
138    /// but its interpretation can vary across coordinate systems.
139    ///
140    /// # Examples
141    ///
142    /// ```
143    /// use approx::assert_relative_eq;
144    /// use geo_types::Point;
145    /// let mut p = Point::new(1.234, 2.345);
146    /// let mut p_x = p.x_mut();
147    /// *p_x += 1.0;
148    /// assert_relative_eq!(p.x(), 2.234);
149    /// ```
150    pub fn x_mut(&mut self) -> &mut T {
151        &mut self.0.x
152    }
153
154    /// Returns the y/vertical component of the point.
155    ///
156    /// Typically, `y` is the vertical position, or latitude for geographic coordinates,
157    /// but its interpretation can vary across coordinate systems.
158    ///
159    /// # Examples
160    ///
161    /// ```
162    /// use geo_types::Point;
163    ///
164    /// let p = Point::new(1.234, 2.345);
165    ///
166    /// assert_eq!(p.y(), 2.345);
167    /// ```
168    pub fn y(self) -> T {
169        self.0.y
170    }
171
172    /// Sets the y/vertical component of the point.
173    ///
174    /// Typically, `y` is the vertical position, or latitude for geographic coordinates,
175    /// but its interpretation can vary across coordinate systems.
176    ///
177    /// # Examples
178    ///
179    /// ```
180    /// use geo_types::Point;
181    ///
182    /// let mut p = Point::new(1.234, 2.345);
183    /// p.set_y(9.876);
184    ///
185    /// assert_eq!(p.y(), 9.876);
186    /// ```
187    pub fn set_y(&mut self, y: T) -> &mut Self {
188        self.0.y = y;
189        self
190    }
191
192    /// Returns a mutable reference to the x/horizontal component of the point
193    ///
194    /// Typically, `y` is the vertical position, or latitude for geographic coordinates,
195    /// but its interpretation can vary across coordinate systems.
196    ///
197    /// # Examples
198    ///
199    /// ```
200    /// use approx::assert_relative_eq;
201    /// use geo_types::Point;
202    /// let mut p = Point::new(1.234, 2.345);
203    /// let mut p_y = p.y_mut();
204    /// *p_y += 1.0;
205    /// assert_relative_eq!(p.y(), 3.345);
206    /// ```
207    pub fn y_mut(&mut self) -> &mut T {
208        &mut self.0.y
209    }
210
211    /// Returns a tuple that contains the x/horizontal & y/vertical component of the point.
212    ///
213    /// # Examples
214    ///
215    /// ```
216    /// use geo_types::Point;
217    ///
218    /// let mut p = Point::new(1.234, 2.345);
219    /// let (x, y) = p.x_y();
220    ///
221    /// assert_eq!(y, 2.345);
222    /// assert_eq!(x, 1.234);
223    /// ```
224    pub fn x_y(self) -> (T, T) {
225        (self.0.x, self.0.y)
226    }
227    /// Returns the longitude/horizontal component of the point.
228    ///
229    /// # Examples
230    ///
231    /// ```
232    /// use geo_types::Point;
233    ///
234    /// let p = Point::new(1.234, 2.345);
235    ///
236    /// assert_eq!(p.x(), 1.234);
237    /// ```
238    #[deprecated = "use `Point::x` instead, it's less ambiguous"]
239    pub fn lng(self) -> T {
240        self.x()
241    }
242
243    /// Sets the longitude/horizontal component of the point.
244    ///
245    /// # Examples
246    ///
247    /// ```
248    /// use geo_types::Point;
249    ///
250    /// let mut p = Point::new(1.234, 2.345);
251    /// #[allow(deprecated)]
252    /// p.set_lng(9.876);
253    ///
254    /// assert_eq!(p.x(), 9.876);
255    /// ```
256    #[deprecated = "use `Point::set_x` instead, it's less ambiguous"]
257    pub fn set_lng(&mut self, lng: T) -> &mut Self {
258        self.set_x(lng)
259    }
260
261    /// Returns the latitude/vertical component of the point.
262    ///
263    /// # Examples
264    ///
265    /// ```
266    /// use geo_types::Point;
267    ///
268    /// let p = Point::new(1.234, 2.345);
269    ///
270    /// assert_eq!(p.y(), 2.345);
271    /// ```
272    #[deprecated = "use `Point::y` instead, it's less ambiguous"]
273    pub fn lat(self) -> T {
274        self.y()
275    }
276    /// Sets the latitude/vertical component of the point.
277    ///
278    /// # Examples
279    ///
280    /// ```
281    /// use geo_types::Point;
282    ///
283    /// let mut p = Point::new(1.234, 2.345);
284    /// #[allow(deprecated)]
285    /// p.set_lat(9.876);
286    ///
287    /// assert_eq!(p.y(), 9.876);
288    /// ```
289    #[deprecated = "use `Point::set_y` instead, it's less ambiguous"]
290    pub fn set_lat(&mut self, lat: T) -> &mut Self {
291        self.set_y(lat)
292    }
293}
294
295impl<T: CoordNum> Point<T> {
296    /// Returns the dot product of the two points:
297    /// `dot = x1 * x2 + y1 * y2`
298    ///
299    /// # Examples
300    ///
301    /// ```
302    /// use geo_types::{point, Point};
303    ///
304    /// let point = point! { x: 1.5, y: 0.5 };
305    /// let dot = point.dot(point! { x: 2.0, y: 4.5 });
306    ///
307    /// assert_eq!(dot, 5.25);
308    /// ```
309    pub fn dot(self, other: Self) -> T {
310        self.x() * other.x() + self.y() * other.y()
311    }
312
313    /// Returns the cross product of 3 points. A positive value implies
314    /// `self` → `point_b` → `point_c` is counter-clockwise, negative implies
315    /// clockwise.
316    ///
317    /// # Note on Robustness
318    ///
319    /// This function is **not** robust against floating-point errors.
320    /// The [`geo`](https://docs.rs/geo) crate
321    /// offers robust predicates for standard numeric types using the
322    /// [`Kernel`](https://docs.rs/geo/algorithm/kernels/trait.Kernel.html)
323    /// trait, and these should be preferred if possible.
324    ///
325    /// # Examples
326    ///
327    /// ```
328    /// use geo_types::point;
329    ///
330    /// let point_a = point! { x: 1., y: 2. };
331    /// let point_b = point! { x: 3., y: 5. };
332    /// let point_c = point! { x: 7., y: 12. };
333    ///
334    /// let cross = point_a.cross_prod(point_b, point_c);
335    ///
336    /// assert_eq!(cross, 2.0)
337    /// ```
338    pub fn cross_prod(self, point_b: Self, point_c: Self) -> T {
339        (point_b.x() - self.x()) * (point_c.y() - self.y())
340            - (point_b.y() - self.y()) * (point_c.x() - self.x())
341    }
342}
343
344impl<T: CoordFloat> Point<T> {
345    /// Converts the (x,y) components of Point to degrees
346    ///
347    /// # Example
348    /// ```
349    /// use geo_types::Point;
350    ///
351    /// let p = Point::new(1.234, 2.345);
352    /// let (x, y): (f32, f32) = p.to_degrees().x_y();
353    /// assert_eq!(x.round(), 71.0);
354    /// assert_eq!(y.round(), 134.0);
355    /// ```
356    pub fn to_degrees(self) -> Self {
357        let (x, y) = self.x_y();
358        let x = x.to_degrees();
359        let y = y.to_degrees();
360        Point::new(x, y)
361    }
362
363    /// Converts the (x,y) components of Point to radians
364    ///
365    /// # Example
366    /// ```
367    /// use geo_types::Point;
368    ///
369    /// let p = Point::new(180.0, 341.5);
370    /// let (x, y): (f32, f32) = p.to_radians().x_y();
371    /// assert_eq!(x.round(), 3.0);
372    /// assert_eq!(y.round(), 6.0);
373    /// ```
374    pub fn to_radians(self) -> Self {
375        let (x, y) = self.x_y();
376        let x = x.to_radians();
377        let y = y.to_radians();
378        Point::new(x, y)
379    }
380}
381
382impl<T> Neg for Point<T>
383where
384    T: CoordNum + Neg<Output = T>,
385{
386    type Output = Self;
387
388    /// Returns a point with the x and y components negated.
389    ///
390    /// # Examples
391    ///
392    /// ```
393    /// use geo_types::Point;
394    ///
395    /// let p = -Point::new(-1.25, 2.5);
396    ///
397    /// assert_eq!(p.x(), 1.25);
398    /// assert_eq!(p.y(), -2.5);
399    /// ```
400    fn neg(self) -> Self::Output {
401        Point::from(-self.0)
402    }
403}
404
405impl<T: CoordNum> Add for Point<T> {
406    type Output = Self;
407
408    /// Add a point to the given point.
409    ///
410    /// # Examples
411    ///
412    /// ```
413    /// use geo_types::Point;
414    ///
415    /// let p = Point::new(1.25, 2.5) + Point::new(1.5, 2.5);
416    ///
417    /// assert_eq!(p.x(), 2.75);
418    /// assert_eq!(p.y(), 5.0);
419    /// ```
420    fn add(self, rhs: Self) -> Self::Output {
421        Point::from(self.0 + rhs.0)
422    }
423}
424
425impl<T: CoordNum> AddAssign for Point<T> {
426    /// Add a point to the given point and assign it to the original point.
427    ///
428    /// # Examples
429    ///
430    /// ```
431    /// use geo_types::Point;
432    ///
433    /// let mut p = Point::new(1.25, 2.5);
434    /// p += Point::new(1.5, 2.5);
435    ///
436    /// assert_eq!(p.x(), 2.75);
437    /// assert_eq!(p.y(), 5.0);
438    /// ```
439    fn add_assign(&mut self, rhs: Self) {
440        self.0 = self.0 + rhs.0;
441    }
442}
443
444impl<T: CoordNum> Sub for Point<T> {
445    type Output = Self;
446
447    /// Subtract a point from the given point.
448    ///
449    /// # Examples
450    ///
451    /// ```
452    /// use geo_types::Point;
453    ///
454    /// let p = Point::new(1.25, 3.0) - Point::new(1.5, 2.5);
455    ///
456    /// assert_eq!(p.x(), -0.25);
457    /// assert_eq!(p.y(), 0.5);
458    /// ```
459    fn sub(self, rhs: Self) -> Self::Output {
460        Point::from(self.0 - rhs.0)
461    }
462}
463
464impl<T: CoordNum> SubAssign for Point<T> {
465    /// Subtract a point from the given point and assign it to the original point.
466    ///
467    /// # Examples
468    ///
469    /// ```
470    /// use geo_types::Point;
471    ///
472    /// let mut p = Point::new(1.25, 2.5);
473    /// p -= Point::new(1.5, 2.5);
474    ///
475    /// assert_eq!(p.x(), -0.25);
476    /// assert_eq!(p.y(), 0.0);
477    /// ```
478    fn sub_assign(&mut self, rhs: Self) {
479        self.0 = self.0 - rhs.0;
480    }
481}
482
483impl<T: CoordNum> Mul<T> for Point<T> {
484    type Output = Self;
485
486    /// Scaler multiplication of a point
487    ///
488    /// # Examples
489    ///
490    /// ```
491    /// use geo_types::Point;
492    ///
493    /// let p = Point::new(2.0, 3.0) * 2.0;
494    ///
495    /// assert_eq!(p.x(), 4.0);
496    /// assert_eq!(p.y(), 6.0);
497    /// ```
498    fn mul(self, rhs: T) -> Self::Output {
499        Point::from(self.0 * rhs)
500    }
501}
502
503impl<T: CoordNum> MulAssign<T> for Point<T> {
504    /// Scaler multiplication of a point in place
505    ///
506    /// # Examples
507    ///
508    /// ```
509    /// use geo_types::Point;
510    ///
511    /// let mut p = Point::new(2.0, 3.0);
512    /// p *= 2.0;
513    ///
514    /// assert_eq!(p.x(), 4.0);
515    /// assert_eq!(p.y(), 6.0);
516    /// ```
517    fn mul_assign(&mut self, rhs: T) {
518        self.0 = self.0 * rhs
519    }
520}
521
522impl<T: CoordNum> Div<T> for Point<T> {
523    type Output = Self;
524
525    /// Scaler division of a point
526    ///
527    /// # Examples
528    ///
529    /// ```
530    /// use geo_types::Point;
531    ///
532    /// let p = Point::new(2.0, 3.0) / 2.0;
533    ///
534    /// assert_eq!(p.x(), 1.0);
535    /// assert_eq!(p.y(), 1.5);
536    /// ```
537    fn div(self, rhs: T) -> Self::Output {
538        Point::from(self.0 / rhs)
539    }
540}
541
542impl<T: CoordNum> DivAssign<T> for Point<T> {
543    /// Scaler division of a point in place
544    ///
545    /// # Examples
546    ///
547    /// ```
548    /// use geo_types::Point;
549    ///
550    /// let mut p = Point::new(2.0, 3.0);
551    /// p /= 2.0;
552    ///
553    /// assert_eq!(p.x(), 1.0);
554    /// assert_eq!(p.y(), 1.5);
555    /// ```
556    fn div_assign(&mut self, rhs: T) {
557        self.0 = self.0 / rhs
558    }
559}
560
561#[cfg(any(feature = "approx", test))]
562mod approx_integration {
563    use super::*;
564    use approx::{AbsDiffEq, RelativeEq, UlpsEq};
565
566    impl<T> RelativeEq for Point<T>
567    where
568        T: CoordNum + RelativeEq<Epsilon = T>,
569    {
570        #[inline]
571        fn default_max_relative() -> Self::Epsilon {
572            T::default_max_relative()
573        }
574
575        /// Equality assertion within a relative limit.
576        ///
577        /// # Examples
578        ///
579        /// ```
580        /// use geo_types::Point;
581        ///
582        /// let a = Point::new(2.0, 3.0);
583        /// let b = Point::new(2.0, 3.01);
584        ///
585        /// approx::assert_relative_eq!(a, b, max_relative=0.1)
586        /// ```
587        #[inline]
588        fn relative_eq(
589            &self,
590            other: &Self,
591            epsilon: Self::Epsilon,
592            max_relative: Self::Epsilon,
593        ) -> bool {
594            self.0.relative_eq(&other.0, epsilon, max_relative)
595        }
596    }
597
598    impl<T> AbsDiffEq for Point<T>
599    where
600        T: CoordNum + AbsDiffEq<Epsilon = T>,
601    {
602        type Epsilon = T::Epsilon;
603
604        #[inline]
605        fn default_epsilon() -> Self::Epsilon {
606            T::default_epsilon()
607        }
608
609        /// Equality assertion with an absolute limit.
610        ///
611        /// # Examples
612        ///
613        /// ```
614        /// use geo_types::Point;
615        ///
616        /// let a = Point::new(2.0, 3.0);
617        /// let b = Point::new(2.0, 3.0000001);
618        ///
619        /// approx::assert_relative_eq!(a, b, epsilon=0.1)
620        /// ```
621        #[inline]
622        fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
623            self.0.abs_diff_eq(&other.0, epsilon)
624        }
625    }
626
627    impl<T> UlpsEq for Point<T>
628    where
629        T: CoordNum + UlpsEq<Epsilon = T>,
630    {
631        fn default_max_ulps() -> u32 {
632            T::default_max_ulps()
633        }
634
635        fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
636            self.0.ulps_eq(&other.0, epsilon, max_ulps)
637        }
638    }
639}
640
641#[cfg(feature = "rstar_0_8")]
642// These are required for rstar RTree
643impl<T> ::rstar_0_8::Point for Point<T>
644where
645    T: ::num_traits::Float + ::rstar_0_8::RTreeNum,
646{
647    type Scalar = T;
648
649    const DIMENSIONS: usize = 2;
650
651    fn generate(generator: impl Fn(usize) -> Self::Scalar) -> Self {
652        Point::new(generator(0), generator(1))
653    }
654
655    fn nth(&self, index: usize) -> Self::Scalar {
656        match index {
657            0 => self.0.x,
658            1 => self.0.y,
659            _ => unreachable!(),
660        }
661    }
662    fn nth_mut(&mut self, index: usize) -> &mut Self::Scalar {
663        match index {
664            0 => &mut self.0.x,
665            1 => &mut self.0.y,
666            _ => unreachable!(),
667        }
668    }
669}
670
671#[cfg(feature = "rstar_0_9")]
672impl<T> ::rstar_0_9::Point for Point<T>
673where
674    T: ::num_traits::Float + ::rstar_0_9::RTreeNum,
675{
676    type Scalar = T;
677
678    const DIMENSIONS: usize = 2;
679
680    fn generate(mut generator: impl FnMut(usize) -> Self::Scalar) -> Self {
681        Point::new(generator(0), generator(1))
682    }
683
684    fn nth(&self, index: usize) -> Self::Scalar {
685        match index {
686            0 => self.0.x,
687            1 => self.0.y,
688            _ => unreachable!(),
689        }
690    }
691    fn nth_mut(&mut self, index: usize) -> &mut Self::Scalar {
692        match index {
693            0 => &mut self.0.x,
694            1 => &mut self.0.y,
695            _ => unreachable!(),
696        }
697    }
698}
699
700#[cfg(feature = "rstar_0_10")]
701impl<T> ::rstar_0_10::Point for Point<T>
702where
703    T: ::num_traits::Float + ::rstar_0_10::RTreeNum,
704{
705    type Scalar = T;
706
707    const DIMENSIONS: usize = 2;
708
709    fn generate(mut generator: impl FnMut(usize) -> Self::Scalar) -> Self {
710        Point::new(generator(0), generator(1))
711    }
712
713    fn nth(&self, index: usize) -> Self::Scalar {
714        match index {
715            0 => self.0.x,
716            1 => self.0.y,
717            _ => unreachable!(),
718        }
719    }
720    fn nth_mut(&mut self, index: usize) -> &mut Self::Scalar {
721        match index {
722            0 => &mut self.0.x,
723            1 => &mut self.0.y,
724            _ => unreachable!(),
725        }
726    }
727}
728
729#[cfg(feature = "rstar_0_11")]
730impl<T> ::rstar_0_11::Point for Point<T>
731where
732    T: ::num_traits::Float + ::rstar_0_11::RTreeNum,
733{
734    type Scalar = T;
735
736    const DIMENSIONS: usize = 2;
737
738    fn generate(mut generator: impl FnMut(usize) -> Self::Scalar) -> Self {
739        Point::new(generator(0), generator(1))
740    }
741
742    fn nth(&self, index: usize) -> Self::Scalar {
743        match index {
744            0 => self.0.x,
745            1 => self.0.y,
746            _ => unreachable!(),
747        }
748    }
749    fn nth_mut(&mut self, index: usize) -> &mut Self::Scalar {
750        match index {
751            0 => &mut self.0.x,
752            1 => &mut self.0.y,
753            _ => unreachable!(),
754        }
755    }
756}
757
758#[cfg(feature = "rstar_0_12")]
759impl<T> ::rstar_0_12::Point for Point<T>
760where
761    T: ::num_traits::Float + ::rstar_0_12::RTreeNum,
762{
763    type Scalar = T;
764
765    const DIMENSIONS: usize = 2;
766
767    fn generate(mut generator: impl FnMut(usize) -> Self::Scalar) -> Self {
768        Point::new(generator(0), generator(1))
769    }
770
771    fn nth(&self, index: usize) -> Self::Scalar {
772        match index {
773            0 => self.0.x,
774            1 => self.0.y,
775            _ => unreachable!(),
776        }
777    }
778    fn nth_mut(&mut self, index: usize) -> &mut Self::Scalar {
779        match index {
780            0 => &mut self.0.x,
781            1 => &mut self.0.y,
782            _ => unreachable!(),
783        }
784    }
785}
786
787impl<T: CoordNum> AsRef<Coord<T>> for Point<T> {
788    fn as_ref(&self) -> &Coord<T> {
789        &self.0
790    }
791}
792
793#[cfg(test)]
794mod test {
795    use super::*;
796
797    use approx::{AbsDiffEq, RelativeEq};
798
799    #[test]
800    fn test_abs_diff_eq() {
801        let delta = 1e-6;
802        let p = Point::new(1.0, 1.0);
803
804        let p_x = Point::new(1.0 - delta, 1.0);
805        assert!(p.abs_diff_eq(&p_x, 1e-2));
806        assert!(p.abs_diff_ne(&p_x, 1e-12));
807
808        let p_y = Point::new(1.0, 1.0 + delta);
809        assert!(p.abs_diff_eq(&p_y, 1e-2));
810        assert!(p.abs_diff_ne(&p_y, 1e-12));
811
812        let p_xy = Point::new(1.0 + delta, 1.0 - delta);
813        assert!(p.abs_diff_eq(&p_xy, 1e-2));
814        assert!(p.abs_diff_ne(&p_xy, 1e-12));
815
816        let p_inf = Point::new(f64::INFINITY, 1.);
817        assert!(p.abs_diff_ne(&p_inf, 1e-2));
818    }
819
820    #[test]
821    fn test_relative_eq() {
822        let delta = 1e-6;
823        let p = Point::new(1.0, 1.0);
824
825        let p_x = Point::new(1.0 - delta, 1.0);
826        assert!(p.relative_eq(&p_x, 1e-2, 1e-2));
827        assert!(p.relative_ne(&p_x, 1e-12, 1e-12));
828
829        let p_y = Point::new(1.0, 1.0 + delta);
830        assert!(p.relative_eq(&p_y, 1e-2, 1e-2));
831        assert!(p.relative_ne(&p_y, 1e-12, 1e-12));
832
833        let p_xy = Point::new(1.0 + delta, 1.0 - delta);
834        assert!(p.relative_eq(&p_xy, 1e-2, 1e-2));
835        assert!(p.relative_ne(&p_xy, 1e-12, 1e-12));
836
837        let p_inf = Point::new(f64::INFINITY, 1.);
838        assert!(p.relative_ne(&p_inf, 1e-2, 1e-2));
839    }
840}