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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)); ``` 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()); ``` Both vector and rectangle 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; 2]>()); 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); ``` Implementing `Vector2` and `Rectangle` 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}; /// 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.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; 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.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, 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 getting the sine of a number pub trait Sin { /// The output type type Output; /// Get the sine fn sin(self) -> Self::Output; } impl Sin for f32 { type Output = f32; fn sin(self) -> Self::Output { f32::sin(self) } } impl Sin for f64 { type Output = f64; fn sin(self) -> Self::Output { f64::sin(self) } } /// Trait for getting the cosine of a number pub trait Cos { /// The output type type Output; /// Get the cosine fn cos(self) -> Self::Output; } impl Cos for f32 { type Output = f32; fn cos(self) -> Self::Output { f32::cos(self) } } impl Cos for f64 { type Output = f64; fn cos(self) -> Self::Output { f64::cos(self) } } /// 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> + ZeroOneTwo { /// Get the max of this `Scalar` and another fn max(self, other: Self) -> Self { if self > other { self } else { other } } /// Get the min of this `Scalar` and another fn min(self, other: Self) -> Self { if self < other { self } else { other } } } 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> + ZeroOneTwo { } /// Trait for scalars that can be negated pub trait NegScalar: Scalar + Neg<Output = Self> { /// Get the abolute value of this `Scalar` fn abs(self) -> Self; } impl<T> NegScalar for T where T: Scalar + Neg<Output = Self>, { /// Get the absolute value fn abs(self) -> Self { if self >= Self::ZERO { self } else { self.neg() } } } /// Trait for floating-point scalar numbers pub trait FloatingScalar: NegScalar + Pow<Self, Output = Self> + Sin<Output = Self> + Cos<Output = Self> { } impl<T> FloatingScalar for T where T: NegScalar + Pow<Self, Output = Self> + Sin<Output = T> + Cos<Output = T> { } /// 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; /// 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 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())) } /// 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()) } } 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 negatable 2D vectors pub trait NegVector2: Vector2 where Self::Scalar: NegScalar, { /// Negate the vector fn neg(self) -> Self { Self::new(-self.x(), -self.y()) } /// Get the value of the dimmension with the higher magnitude fn max_dim(self) -> Self::Scalar { if self.x().abs() > self.y().abs() { self.x() } else { self.y() } } } impl<T> NegVector2 for T where T: Vector2, T::Scalar: NegScalar, { } /// 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) } /// 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) } } impl<T> FloatingVector2 for T where T: Vector2, T::Scalar: FloatingScalar, { } /// Trait for manipulating axis-aligned rectangles 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) } /// 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 ractangle to a ractangle 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 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 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 width fn width(self) -> Self::Scalar { self.size().x() } /// Get the height fn height(self) -> Self::Scalar { self.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 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)) } } 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() } }