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#![deny(missing_docs)] #![deny(unsafe_code)] /*! This crate provides traits for doing 2D vector geometry operations using standard types # Usage Simple vector math is implemented for vectors with the following scalar types: * `u8`-`u128` * `usize` * `i8`-`i128` * `isize` * `f32` * `f64` * Any type that implements one or more of this crate's `Scalar` traits Vectors can be of the following forms: * `[T; 2]` * `(T, T)` * Any type that implements one or more of this crate's `Vector2` traits Many 2D Vector operations are supported. Vectors do not necessarily need to be the same type to allow operation. They need only have the same `Scalar` type. The output type will be the same as the first argument. ``` use vector2math::*; let a = [2, 6]; let b = (4, -1); assert_eq!(2, a.x()); assert_eq!(-1, b.y()); assert_eq!([-2, -6], a.neg()); assert_eq!([6, 5], a.add(b)); assert_eq!([-2, 7], a.sub(b)); assert_eq!((12, -3), b.mul(3)); assert_eq!((8, -6), b.mul2(a)); assert_eq!([1, 3], a.div(2)); assert_eq!([0, -6], a.div2(b)); assert_eq!(2, a.dot(b)); ``` Floating-point vectors have additional operations: ``` use vector2math::*; assert_eq!(5.0, [3.0, 4.0].mag()); assert_eq!(10.0, [-1.0, -2.0].dist([5.0, 6.0])); let rotation_calculation = [1.0, 0.0].rotate_about([0.0; 2], std::f64::consts::PI / 4.0); let rotation_solution = [2f64.powf(0.5) / 2.0; 2]; assert!(rotation_calculation.sub(rotation_solution).mag() < std::f64::EPSILON); ``` Many types can be used to define axis-aligned rectangles: * `[[T; 2]; 2]` * `[(T, T); 2]` * `((T, T), (T, T))` * `([T; 2], [T; 2])` * `[T; 4]` * `(T, T, T, T)` * Any type that implements this crate's `Pair` trait where the associated `Item` type implements `Vector2`. ``` use vector2math::*; let rect = [1i32, 2, 4, 6]; assert_eq!([1, 2], rect.top_left()); assert_eq!([4, 6], rect.size()); assert_eq!([3, 5], rect.center()); assert_eq!(20, rect.perimeter()); assert_eq!(24, rect.area()); assert!(rect.contains([3, 5])); ``` A few types can be used to define circles: * `([T; 2], T)` * `((T, T), T)` * Any pair of types where the first implements `FloatingVector2` and the second is the vector's scalar type. ``` use vector2math::*; use std::f64; let circle = ([2.0, 3.0], 4.0); assert!((circle.circumference() - 25.132_741_228_718_345).abs() < f64::EPSILON); assert!((circle.area() - 50.265_482_457_436_69).abs() < f64::EPSILON); assert!(circle.contains([0.0, 1.0])); assert!(!circle.contains([5.0, 6.0])); ``` Vector, rectangle, and circle types can be easily mapped to different types: ``` use vector2math::*; let arrayf32: [f32; 2] = [1.0, 2.0]; let arrayf64: [f64; 2] = arrayf32.map(); let pairf64: (f64, f64) = arrayf64.map(); let arrayi16: [i16; 2] = pairf64.map_with(|f| f as i16); assert_eq!(arrayf32, arrayi16.map_f32()); let weird_rect = [(0.0, 1.0), (2.0, 5.0)]; let normal_rectf32: [f32; 4] = weird_rect.map(); let normal_rectf64: [f32; 4] = normal_rectf32.map(); let normal_rectu8: [u8; 4] = normal_rectf32.map_with(|f| f as u8); assert_eq!([0, 1, 2, 5], normal_rectu8); let pair_circlef32 = ((0.0, 1.0), 2.0); let array_circlef32 = ([0.0, 1.0], 2.0); assert_eq!(((0.0, 1.0), 2.0), array_circlef32.map::<((f64, f64), f64)>()); ``` Implementing these traits for your own types is simple. Just make sure that your type is `Copy` ``` use vector2math::*; #[derive(Clone, Copy)] struct MyVector { x: f64, y: f64, } impl Vector2 for MyVector { type Scalar = f64; fn new(x: f64, y: f64) -> Self { MyVector { x, y } } fn x(self) -> f64 { self.x } fn y(self) -> f64 { self.y } } #[derive(Clone, Copy)] struct MyRectangle { top_left: MyVector, size: MyVector, } impl Rectangle for MyRectangle { type Scalar = f64; type Vector = MyVector; fn new(top_left: MyVector, size: MyVector) -> Self { MyRectangle { top_left, size } } fn top_left(self) -> MyVector { self.top_left } fn size(self) -> MyVector { self.size } } let rect: MyRectangle = [1, 2, 3, 4].map(); assert_eq!(12.0, rect.area()); assert_eq!(6.0, rect.bottom()); ``` */ use std::{ ops::{Add, Div, Mul, Neg, Sub}, vec, }; pub use Rectangle as _; /// Module containing standard f32 types /// /// Import the contents of this module if your project uses `f32`s in geometry pub mod f32 { /// The scalar type used by this module pub type Dim = f32; /// A standard 2D vector type pub type Vec2 = [Dim; 2]; /// A standard rectangle type pub type Rect = [Dim; 4]; /// A standard circle type pub type Circ = ([Dim; 2], Dim); } /// Module containing standard f64 types /// /// Import the contents of this module if your project uses `f64`s in geometry pub mod f64 { /// The scalar type used by this module pub type Dim = f64; /// A standard 2D vector type pub type Vec2 = [Dim; 2]; /// A standard rectangle type pub type Rect = [Dim; 4]; /// A standard circle type pub type Circ = ([Dim; 2], Dim); } /// Trait for defining a pair of items of the same type. /// /// This trait is meant to generalize having two similar things. /// It is implemented for `(T, T)` and `[T; 2]` with `Item = T`. /// However, because a pair does not necessarily have to be an /// actual *pair* It is also implemented for `(T, T, T, T)` and /// `[T; 4]` with `Item = (T, T)` and `Item = [T; 2]` respectively. pub trait Pair { /// The type of the pair's item type Item; /// Get the first thing fn first(self) -> Self::Item; /// Get the second thing fn second(self) -> Self::Item; /// Create a pair from two items fn from_items(a: Self::Item, b: Self::Item) -> Self; } impl<T> Pair for (T, T) where T: Clone, { type Item = T; fn first(self) -> Self::Item { self.0 } fn second(self) -> Self::Item { self.1 } fn from_items(a: Self::Item, b: Self::Item) -> Self { (a, b) } } impl<T> Pair for [T; 2] where T: Clone, { type Item = T; fn first(self) -> Self::Item { self[0].clone() } fn second(self) -> Self::Item { self[1].clone() } fn from_items(a: Self::Item, b: Self::Item) -> Self { [a, b] } } impl<T> Pair for (T, T, T, T) where T: Clone, { type Item = (T, T); fn first(self) -> Self::Item { (self.0, self.1) } fn second(self) -> Self::Item { (self.2, self.3) } fn from_items(a: Self::Item, b: Self::Item) -> Self { (a.0, a.1, b.0, b.1) } } impl<T> Pair for [T; 4] where T: Clone, { type Item = [T; 2]; fn first(self) -> Self::Item { [self[0].clone(), self[1].clone()] } fn second(self) -> Self::Item { [self[2].clone(), self[3].clone()] } fn from_items(a: Self::Item, b: Self::Item) -> Self { [a[0].clone(), a[1].clone(), b[0].clone(), b[1].clone()] } } /// Trait for trigonometric operations pub trait Trig: Copy + Div<Output = Self> { /// Get the cosine fn cos(self) -> Self; /// Get the sine fn sin(self) -> Self; /// Get the tangent fn tan(self) -> Self { self.sin() / self.cos() } /// Get the four-quadrant arctangent fn atan2(self, other: Self) -> Self; } impl Trig for f32 { fn cos(self) -> Self { f32::cos(self) } fn sin(self) -> Self { f32::sin(self) } fn atan2(self, other: Self) -> Self { self.atan2(other) } } impl Trig for f64 { fn cos(self) -> Self { f64::cos(self) } fn sin(self) -> Self { f64::sin(self) } fn atan2(self, other: Self) -> Self { self.atan2(other) } } /// Trait for retrieving an absolute value of a number pub trait Abs { /// Get the absolute value of the number fn abs(self) -> Self; } macro_rules! abs_unsigned_impl { ($type:ty) => { impl Abs for $type { fn abs(self) -> Self { self } } }; } macro_rules! abs_signed_impl { ($type:ty) => { impl Abs for $type { fn abs(self) -> Self { Self::abs(self) } } }; } abs_unsigned_impl! {u8} abs_unsigned_impl! {u16} abs_unsigned_impl! {u32} abs_unsigned_impl! {u64} abs_unsigned_impl! {u128} abs_unsigned_impl! {usize} abs_signed_impl! {i8} abs_signed_impl! {i16} abs_signed_impl! {i32} abs_signed_impl! {i64} abs_signed_impl! {i128} abs_signed_impl! {isize} abs_signed_impl! {f32} abs_signed_impl! {f64} /// Trait for raising numbers to a power pub trait Pow<P> { /// The output type type Output; /// Raise this number to a power fn pow(self, power: P) -> Self::Output; } macro_rules! pow_float_impl { ($type:ty) => { impl Pow<Self> for $type { type Output = Self; fn pow(self, power: Self) -> Self::Output { self.powf(power) } } }; } pow_float_impl! {f32} pow_float_impl! {f64} /// Trait for defining small-number constants pub trait ZeroOneTwo: Copy { /// This type's value for zero, i.e. `0` const ZERO: Self; /// This type's value for one, i.e. `1` const ONE: Self; /// This type's value for two, i.e. `2` const TWO: Self; } macro_rules! zot_int_impl { ($type:ty) => { impl ZeroOneTwo for $type { const ZERO: Self = 0; const ONE: Self = 1; const TWO: Self = 2; } }; } zot_int_impl! {u8} zot_int_impl! {u16} zot_int_impl! {u32} zot_int_impl! {u64} zot_int_impl! {u128} zot_int_impl! {usize} zot_int_impl! {i8} zot_int_impl! {i16} zot_int_impl! {i32} zot_int_impl! {i64} zot_int_impl! {i128} zot_int_impl! {isize} macro_rules! zot_float_impl { ($type:ty) => { impl ZeroOneTwo for $type { const ZERO: Self = 0.0; const ONE: Self = 1.0; const TWO: Self = 2.0; } }; } zot_float_impl! {f32} zot_float_impl! {f64} /// Trait for math with scalar numbers pub trait Scalar: Add<Self, Output = Self> + Copy + PartialEq + PartialOrd + Sub<Self, Output = Self> + Mul<Self, Output = Self> + Div<Self, Output = Self> + Abs + ZeroOneTwo { /// Get the max of this `Scalar` and another /// /// This function is named to not conflict with the /// `Scalar`'s default `max` function fn maxx(self, other: Self) -> Self { if self > other { self } else { other } } /// Get the min of this `Scalar` and another /// /// This function is named to not conflict with the /// `Scalar`'s default `min` function fn minn(self, other: Self) -> Self { if self < other { self } else { other } } /// Create a square `Vector` from this `Scalar` fn square(self) -> [Self; 2] { Vector2::square(self) } } impl<T> Scalar for T where T: Copy + PartialEq + PartialOrd + Add<T, Output = T> + Sub<T, Output = T> + Mul<T, Output = T> + Div<T, Output = T> + Abs + ZeroOneTwo { } /// Trait for floating-point scalar numbers pub trait FloatingScalar: Scalar + Pow<Self, Output = Self> + Trig { /// The value of Pi const PI: Self; /// The epsilon value const EPSILON: Self; /// Get the value of Tau, or 2π fn tau() -> Self { Self::PI * Self::TWO } /// Linear interpolate the scalar with another fn lerp(self, other: Self, t: Self) -> Self { (Self::ONE - t) * self + t * other } /// Get the unit vector corresponding to an angle in radians defined by the scalar fn angle_as_vector(self) -> [Self; 2] { [self.cos(), self.sin()] } /// Check if the value is within its epsilon range fn is_zero(self) -> bool { self.abs() < Self::EPSILON } } impl FloatingScalar for f32 { const PI: Self = std::f32::consts::PI; const EPSILON: Self = std::f32::EPSILON; } impl FloatingScalar for f64 { const PI: Self = std::f64::consts::PI; const EPSILON: Self = std::f64::EPSILON; } /// Trait for manipulating 2D vectors pub trait Vector2: Copy { /// The scalar type type Scalar: Scalar; /// Get the x component fn x(self) -> Self::Scalar; /// Get the y component fn y(self) -> Self::Scalar; /// Create a new vector from an x and y component fn new(x: Self::Scalar, y: Self::Scalar) -> Self; /// Set the x component fn set_x(&mut self, x: Self::Scalar) { *self = Vector2::new(x, self.y()) } /// Set the y component fn set_y(&mut self, y: Self::Scalar) { *self = Vector2::new(self.x(), y) } /// Get this vector with a different x component fn with_x(self, x: Self::Scalar) -> Self { Self::new(x, self.y()) } /// Get this vector with a different y component fn with_y(self, y: Self::Scalar) -> Self { Self::new(self.x(), y) } /// Create a new square vector fn square(s: Self::Scalar) -> Self { Self::new(s, s) } /// Map this vector to a vector of another type fn map<V>(self) -> V where V: Vector2, V::Scalar: From<Self::Scalar>, { V::new(V::Scalar::from(self.x()), V::Scalar::from(self.y())) } /// Map this vector to a `[f32;2]` /// /// This is an alias for Vector2::map::<[f32;2]>() that is more concise fn map_f32(self) -> [f32; 2] where f32: From<Self::Scalar>, { self.map() } /// Map this vector to a `[f64;2]` /// /// This is an alias for Vector2::map::<[f64;2]>() that is more concise fn map_f64(self) -> [f64; 2] where f64: From<Self::Scalar>, { self.map() } /// Map this vector to a vector of another type using a function fn map_with<V, F>(self, mut f: F) -> V where V: Vector2, F: FnMut(Self::Scalar) -> V::Scalar, { V::new(f(self.x()), f(self.y())) } /// Negate the vector fn neg(self) -> Self where Self::Scalar: Neg<Output = Self::Scalar>, { Self::new(-self.x(), -self.y()) } /// Add the vector to another fn add<V>(self, other: V) -> Self where V: Vector2<Scalar = Self::Scalar>, { Self::new(self.x() + other.x(), self.y() + other.y()) } /// Subtract another vector from this one fn sub<V>(self, other: V) -> Self where V: Vector2<Scalar = Self::Scalar>, { Self::new(self.x() - other.x(), self.y() - other.y()) } /// Multiply this vector by a scalar fn mul(self, by: Self::Scalar) -> Self { Self::new(self.x() * by, self.y() * by) } /// Multiply this vector component-wise by another fn mul2<V>(self, other: V) -> Self where V: Vector2<Scalar = Self::Scalar>, { Self::new(self.x() * other.x(), self.y() * other.y()) } /// Divide this vector by a scalar fn div(self, by: Self::Scalar) -> Self { Self::new(self.x() / by, self.y() / by) } /// Divide this vector component-wise by another fn div2<V>(self, other: V) -> Self where V: Vector2<Scalar = Self::Scalar>, { Self::new(self.x() / other.x(), self.y() / other.y()) } /// Get the value of the dimension with the higher magnitude fn max_dim(self) -> Self::Scalar { if self.x().abs() > self.y().abs() { self.x() } else { self.y() } } /// Get the value of the dimension with the lower magnitude fn min_dim(self) -> Self::Scalar { if self.x().abs() < self.y().abs() { self.x() } else { self.y() } } /// Get the dot product of this vector and another fn dot<V>(self, other: V) -> Self::Scalar where V: Vector2<Scalar = Self::Scalar>, { self.x() * other.x() + self.y() * other.y() } } impl<P> Vector2 for P where P: Pair + Copy, P::Item: Scalar, { type Scalar = P::Item; fn x(self) -> P::Item { self.first() } fn y(self) -> P::Item { self.second() } fn new(x: P::Item, y: P::Item) -> Self { Self::from_items(x, y) } } /// Trait for manipulating floating-point 2D vectors pub trait FloatingVector2: Vector2 where Self::Scalar: FloatingScalar, { /// Get the distance between this vector and another fn dist<V>(self, to: V) -> Self::Scalar where V: Vector2<Scalar = Self::Scalar>, { ((self.x() - to.x()).pow(Self::Scalar::TWO) + (self.y() - to.y()).pow(Self::Scalar::TWO)) .pow(Self::Scalar::ONE / Self::Scalar::TWO) } /// Get the vector's magnitude fn mag(self) -> Self::Scalar { (self.x().pow(Self::Scalar::TWO) + self.y().pow(Self::Scalar::TWO)) .pow(Self::Scalar::ONE / Self::Scalar::TWO) } /// Get the unit vector fn unit(self) -> Self { let mag = self.mag(); if mag < Self::Scalar::EPSILON { Self::new(Self::Scalar::ZERO, Self::Scalar::ZERO) } else { self.div(mag) } } /// Rotate the vector some number of radians about a pivot fn rotate_about<V>(self, pivot: V, radians: Self::Scalar) -> Self where V: Vector2<Scalar = Self::Scalar> + Clone, { let sin = radians.sin(); let cos = radians.cos(); let origin_point = self.sub(pivot); let rotated_point = Self::new( origin_point.x() * cos - origin_point.y() * sin, origin_point.x() * sin + origin_point.y() * cos, ); rotated_point.add(pivot) } /// Linear interpolate the vector with another fn lerp<V>(self, other: V, t: Self::Scalar) -> Self where V: Vector2<Scalar = Self::Scalar>, { Self::new(self.x().lerp(other.x(), t), self.y().lerp(other.y(), t)) } /// Get the arctangent of the vector, which corresponds to /// the angle it represents bounded between -π to π fn atan(self) -> Self::Scalar { self.y().atan2(self.x()) } } impl<T> FloatingVector2 for T where T: Vector2, T::Scalar: FloatingScalar, { } /** Trait for manipulating axis-aligned rectangles Because the primary expected use for this crate is in 2D graphics and alignment implementations, a coordinate system where the positive Y direction is "down" is assumed. # Note Methods of the form `abs_*` account for the case where the size is negative. If the size is not negative, they are identical to their non-`abs_*` counterparts. ``` use vector2math::*; let pos_size = [1, 2, 3, 4]; assert_eq!(pos_size.right(), pos_size.abs_right()); let neg_size = [1, 2, -3, -4]; assert_ne!(neg_size.right(), neg_size.abs_right()); let points = vec![ [-1, 0], [1, 5], [3, 2], ]; let bounding_rect: [i32; 4] = Rectangle::bounding(points).unwrap(); assert_eq!( bounding_rect, [-1, 0, 4, 5] ); ``` */ pub trait Rectangle: Copy { /// The scalar type type Scalar: Scalar; /// The vector type type Vector: Vector2<Scalar = Self::Scalar>; /// Create a new rectangle from a top-left corner position and a size fn new(top_left: Self::Vector, size: Self::Vector) -> Self; /// Get the top-left corner position fn top_left(self) -> Self::Vector; /// Get the size fn size(self) -> Self::Vector; /// Create a new square from a top-left corner position and a side length fn square(top_left: Self::Vector, side_length: Self::Scalar) -> Self { Self::new(top_left, Self::Vector::square(side_length)) } /// Create a new rectangle from a center position and a size fn centered(center: Self::Vector, size: Self::Vector) -> Self { Self::new(center.sub(size.div(Self::Scalar::TWO)), size) } /// Create a new square from a top-left corner position and a side length fn square_centered(center: Self::Vector, side_length: Self::Scalar) -> Self { Self::centered(center, Self::Vector::square(side_length)) } /// Map this rectangle to a rectangle of another type fn map<R>(self) -> R where R: Rectangle, R::Scalar: From<Self::Scalar>, { R::new( R::Vector::new(R::Scalar::from(self.left()), R::Scalar::from(self.top())), R::Vector::new( R::Scalar::from(self.width()), R::Scalar::from(self.height()), ), ) } /// Map this rectangle to a `[f32;4]` /// /// This is an alias for `Rectangle::map::<[f32;4]>()` that is more concise fn map_f32(self) -> [f32; 4] where f32: From<Self::Scalar>, { self.map() } /// Map this rectangle to a `[f64;4]` /// /// This is an alias for `Rectangle::map::<[f64;4]>()` that is more concise fn map_f64(self) -> [f64; 4] where f64: From<Self::Scalar>, { self.map() } /// Map this rectangle to a rectangle of another type using a function fn map_with<R, F>(self, mut f: F) -> R where R: Rectangle, F: FnMut(Self::Scalar) -> <<R as Rectangle>::Vector as Vector2>::Scalar, { R::new( R::Vector::new(f(self.left()), f(self.top())), R::Vector::new(f(self.width()), f(self.height())), ) } /// Get the absolute size fn abs_size(self) -> Self::Vector { Self::Vector::new(self.size().x().abs(), self.size().y().abs()) } /// Get the top-right corner position fn top_right(self) -> Self::Vector { Self::Vector::new(self.top_left().x() + self.size().x(), self.top_left().y()) } /// Get the bottom-left corner position fn bottom_left(self) -> Self::Vector { Self::Vector::new(self.top_left().x(), self.top_left().y() + self.size().y()) } /// Get the bottom-right corner position fn bottom_right(self) -> Self::Vector { self.top_left().add(self.size()) } /// Get the absolute top-left corner position fn abs_top_left(self) -> Self::Vector { let tl = self.top_left(); let size = self.size(); Self::Vector::new( tl.x().minn(tl.x() + size.x()), tl.y().minn(tl.y() + size.y()), ) } /// Get the absolute top-right corner position fn abs_top_right(self) -> Self::Vector { Self::Vector::new( self.abs_top_left().x() + self.abs_size().x(), self.abs_top_left().y(), ) } /// Get the absolute bottom-left corner position fn abs_bottom_left(self) -> Self::Vector { Self::Vector::new( self.abs_top_left().x(), self.abs_top_left().y() + self.abs_size().y(), ) } /// Get the absolute bottom-right corner position fn abs_bottom_right(self) -> Self::Vector { self.abs_top_left().add(self.abs_size()) } /// Get the top y fn top(self) -> Self::Scalar { self.top_left().y() } /// Get the bottom y fn bottom(self) -> Self::Scalar { self.top_left().y() + self.size().y() } /// Get the left x fn left(self) -> Self::Scalar { self.top_left().x() } /// Get the right x fn right(self) -> Self::Scalar { self.top_left().x() + self.size().x() } /// Get the absolute top y fn abs_top(self) -> Self::Scalar { self.abs_top_left().y() } /// Get the absolute bottom y fn abs_bottom(self) -> Self::Scalar { self.abs_top_left().y() + self.abs_size().y() } /// Get the absolute left x fn abs_left(self) -> Self::Scalar { self.abs_top_left().x() } /// Get the absolute right x fn abs_right(self) -> Self::Scalar { self.abs_top_left().x() + self.abs_size().x() } /// Get the width fn width(self) -> Self::Scalar { self.size().x() } /// Get the height fn height(self) -> Self::Scalar { self.size().y() } /// Get the absolute width fn abs_width(self) -> Self::Scalar { self.abs_size().x() } /// Get the absolute height fn abs_height(self) -> Self::Scalar { self.abs_size().y() } /// Get the position of the center fn center(self) -> Self::Vector { self.top_left().add(self.size().div(Self::Scalar::TWO)) } /// Transform the rectangle into one with a different top-left corner position fn with_top_left(self, top_left: Self::Vector) -> Self { Self::new(top_left, self.size()) } /// Transform the rectangle into one with a different center position fn with_center(self, center: Self::Vector) -> Self { Self::centered(center, self.size()) } /// Transform the rectangle into one with a different size fn with_size(self, size: Self::Vector) -> Self { Self::new(self.top_left(), size) } /// Get the perimeter fn perimeter(self) -> Self::Scalar { self.width() * Self::Scalar::TWO + self.height() * Self::Scalar::TWO } /// Get the area fn area(self) -> Self::Scalar { self.width() * self.height() } /// Get the rectangle that is this one translated by some vector fn translated(self, offset: Self::Vector) -> Self { self.with_top_left(self.top_left().add(offset)) } /// Get the rectangle that is this one with a scalar-scaled size fn scaled(self, scale: Self::Scalar) -> Self { self.with_size(self.size().mul(scale)) } /// Get the rectangle that is this one with a vector-scaled size fn scaled2(self, scale: Self::Vector) -> Self { self.with_size(self.size().mul2(scale)) } /// Get an iterator over the rectangle's four corners fn corners(self) -> vec::IntoIter<Self::Vector> { vec![ self.top_left(), self.top_right(), self.bottom_right(), self.bottom_left(), ] .into_iter() } /// Check that the rectangle contains the given point. Includes edges. fn contains(self, point: Self::Vector) -> bool { let in_x_bounds = self.abs_left() <= point.x() && point.x() <= self.abs_right(); let in_y_bounds = || self.abs_top() <= point.y() && point.y() <= self.abs_bottom(); in_x_bounds && in_y_bounds() } /// Check that the rectangle contains all points fn contains_all<I>(self, points: I) -> bool where I: IntoIterator<Item = Self::Vector>, { points.into_iter().all(|point| self.contains(point)) } /// Check that the rectangle contains any point fn contains_any<I>(self, points: I) -> bool where I: IntoIterator<Item = Self::Vector>, { points.into_iter().any(|point| self.contains(point)) } /// Get the smallest rectangle that contains all the points /// /// Returns `None` if the iterator is empty fn bounding<I>(points: I) -> Option<Self> where I: IntoIterator<Item = Self::Vector>, { let mut points = points.into_iter(); if let Some(first) = points.next() { let mut tl = first; let mut br = first; for point in points { tl = Self::Vector::new(tl.x().minn(point.x()), tl.y().minn(point.y())); br = Self::Vector::new(br.x().maxx(point.x()), br.y().maxx(point.y())); } Some(Self::new(tl, br.sub(tl))) } else { None } } /// Get the rectangle that is inside this one with the given /// margin on all sides fn inner_margin(self, margin: Self::Scalar) -> Self { self.inner_margins([margin; 4]) } /// Get the rectangle that is inside this one with the given margins /// /// Margins should be ordered `[left, right, top, bottom]` fn inner_margins(self, [left, right, top, bottom]: [Self::Scalar; 4]) -> Self { Self::new( self.abs_top_left().add(Self::Vector::new(left, top)), self.abs_size() .sub(Self::Vector::new(left + right, top + bottom)), ) } /// Get the rectangle that is outside this one with the given /// margin on all sides fn outer_margin(self, margin: Self::Scalar) -> Self { self.outer_margins([margin; 4]) } /// Get the rectangle that is outside this one with the given margins /// /// Margins should be ordered `[left, right, top, bottom]` fn outer_margins(self, [left, right, top, bottom]: [Self::Scalar; 4]) -> Self { Self::new( self.abs_top_left().sub(Self::Vector::new(left, top)), self.abs_size() .add(Self::Vector::new(left + right, top + bottom)), ) } } impl<P> Rectangle for P where P: Pair + Copy, P::Item: Vector2, { type Scalar = <P::Item as Vector2>::Scalar; type Vector = P::Item; fn new(top_left: Self::Vector, size: Self::Vector) -> Self { Self::from_items(top_left, size) } fn top_left(self) -> Self::Vector { self.first() } fn size(self) -> Self::Vector { self.second() } } /// Trait for manipulating circles pub trait Circle: Copy { /// The scalar type type Scalar: FloatingScalar; /// The vector type type Vector: FloatingVector2<Scalar = Self::Scalar>; /// Create a new circle from a center coordinate and a radius fn new(center: Self::Vector, radius: Self::Scalar) -> Self; /// Get the circle's center fn center(self) -> Self::Vector; /// Get the circle's radius fn radius(self) -> Self::Scalar; /// Map this circle to a circle of another type fn map<C>(self) -> C where C: Circle, C::Scalar: From<Self::Scalar>, { C::new( C::Vector::new( C::Scalar::from(self.center().x()), C::Scalar::from(self.center().y()), ), C::Scalar::from(self.radius()), ) } /// Map this circle to a circle of another type using a function fn map_with<C, F>(self, mut f: F) -> C where C: Circle, F: FnMut(Self::Scalar) -> <<C as Circle>::Vector as Vector2>::Scalar, { C::new( C::Vector::new(f(self.center().x()), f(self.center().y())), f(self.radius()), ) } /// Transform the circle into one with a different top-left corner position fn with_center(self, center: Self::Vector) -> Self { Self::new(center, self.radius()) } /// Transform the circle into one with a different size fn with_radius(self, radius: Self::Scalar) -> Self { Self::new(self.center(), radius) } /// Get the circle's diameter fn diameter(self) -> Self::Scalar { self.radius() * Self::Scalar::TWO } /// Get the circle's circumference fn circumference(self) -> Self::Scalar { self.diameter() * Self::Scalar::PI } /// Get the circle's area fn area(self) -> Self::Scalar { self.radius().pow(Self::Scalar::TWO) * Self::Scalar::PI } /// Get the circle that is this one translated by some vector fn translated(self, offset: Self::Vector) -> Self { self.with_center(self.center().add(offset)) } /// Get the circle that is this one with a scalar-scaled size fn scaled(self, scale: Self::Scalar) -> Self { self.with_radius(self.radius() * scale) } /// Get the smallest square that this circle fits inside fn to_square<R>(self) -> R where R: Rectangle<Scalar = Self::Scalar, Vector = Self::Vector>, { R::new( self.center().sub(R::Vector::square(self.radius())), R::Vector::square(self.radius() * R::Scalar::TWO), ) } /// Check that the circle contains the given point fn contains(self, point: Self::Vector) -> bool { self.center().dist(point) <= self.radius().abs() } /// Alias for `Rectangle::contains` /// /// Useful when `contains` is ambiguous fn cntains(self, point: Self::Vector) -> bool { self.contains(point) } /// Check that the circle contains all points fn contains_all<I>(self, points: I) -> bool where I: IntoIterator<Item = Self::Vector>, { points.into_iter().all(|point| self.contains(point)) } /// Check that the circle contains any point fn contains_any<I>(self, points: I) -> bool where I: IntoIterator<Item = Self::Vector>, { points.into_iter().any(|point| self.contains(point)) } } impl<S, V> Circle for (V, S) where S: FloatingScalar, V: FloatingVector2<Scalar = S>, { type Scalar = S; type Vector = V; fn new(center: Self::Vector, radius: Self::Scalar) -> Self { (center, radius) } fn center(self) -> Self::Vector { self.0 } fn radius(self) -> Self::Scalar { self.1 } } #[cfg(test)] mod test { use super::*; #[test] fn margins() { let rect = [0, 0, 8, 8]; assert!(rect.contains([1, 1])); assert!(!rect.inner_margin(2).contains([1, 1])); } }