Move traits into common module
This commit is contained in:
Brendan Zabarauskas
parent
e9671e6070
commit
8dd2874b59
204
src/angle.rs
204
src/angle.rs
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@ -21,10 +21,11 @@ use std::ops::*;
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use rand::{Rand, Rng};
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use rand::{Rand, Rng};
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use rand::distributions::range::SampleRange;
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use rand::distributions::range::SampleRange;
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use rust_num::{Float, Zero};
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use rust_num::{Float, Zero};
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use rust_num::traits::cast;
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use rust_num::traits::cast;
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use structure::Angle;
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use approx::ApproxEq;
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use approx::ApproxEq;
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use num::BaseFloat;
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use num::BaseFloat;
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@ -61,207 +62,6 @@ impl<S> From<Deg<S>> for Rad<S> where S: BaseFloat {
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}
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}
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}
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}
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/// Angles and their associated trigonometric functions.
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///
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/// Typed angles allow for the writing of self-documenting code that makes it
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/// clear when semantic violations have occured - for example, adding degrees to
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/// radians, or adding a number to an angle.
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///
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pub trait Angle where
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Self: Copy + Clone,
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Self: PartialEq + PartialOrd,
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// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
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Self: ApproxEq<Epsilon = <Self as Angle>::Unitless>,
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Self: Neg<Output = Self>,
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Self: Add<Self, Output = Self>,
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Self: Sub<Self, Output = Self>,
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Self: Rem<Self, Output = Self>,
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Self: Mul<<Self as Angle>::Unitless, Output = Self>,
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Self: Div<Self, Output = <Self as Angle>::Unitless>,
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Self: Div<<Self as Angle>::Unitless, Output = Self>,
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{
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type Unitless: BaseFloat;
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/// Return the angle, normalized to the range `[0, full_turn)`.
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#[inline]
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fn normalize(self) -> Self {
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let rem = self % Self::full_turn();
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if rem < Self::zero() { rem + Self::full_turn() } else { rem }
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}
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/// Return the angle rotated by half a turn.
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#[inline]
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fn opposite(self) -> Self {
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Self::normalize(self + Self::turn_div_2())
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}
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/// Returns the interior bisector of the two angles.
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#[inline]
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fn bisect(self, other: Self) -> Self {
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let half = cast(0.5f64).unwrap();
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Self::normalize((self - other) * half + self)
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}
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/// The additive identity.
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///
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/// Adding this to another angle has no affect.
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///
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/// For example:
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Deg;
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///
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/// let v = Deg::new(180.0);
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/// assert_eq!(v + Deg::zero(), v);
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/// ```
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fn zero() -> Self;
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/// A full rotation.
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fn full_turn() -> Self;
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/// Half of a full rotation.
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fn turn_div_2() -> Self;
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/// A third of a full rotation.
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fn turn_div_3() -> Self;
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/// A quarter of a full rotation.
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fn turn_div_4() -> Self;
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/// A sixth of a full rotation.
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fn turn_div_6() -> Self;
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/// Compute the sine of the angle, returning a unitless ratio.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle = Rad::new(35.0);
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/// let ratio: f32 = Rad::sin(angle);
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/// ```
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fn sin(self) -> Self::Unitless;
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/// Compute the cosine of the angle, returning a unitless ratio.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle = Rad::new(35.0);
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/// let ratio: f32 = Rad::cos(angle);
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/// ```
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fn cos(self) -> Self::Unitless;
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/// Compute the tangent of the angle, returning a unitless ratio.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle = Rad::new(35.0);
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/// let ratio: f32 = Rad::tan(angle);
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/// ```
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fn tan(self) -> Self::Unitless;
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/// Compute the sine and cosine of the angle, returning the result as a
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/// pair.
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///
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/// This does not have any performance benefits, but calculating both the
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/// sine and cosine of a single angle is a common operation.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle = Rad::new(35.0);
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/// let (s, c) = Rad::sin_cos(angle);
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/// ```
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fn sin_cos(self) -> (Self::Unitless, Self::Unitless);
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/// Compute the cosecant of the angle.
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///
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/// This is the same as computing the reciprocal of `Self::sin`.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle = Rad::new(35.0);
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/// let ratio: f32 = Rad::csc(angle);
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/// ```
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#[inline]
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fn csc(self) -> Self::Unitless {
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Self::sin(self).recip()
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}
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/// Compute the secant of the angle.
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///
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/// This is the same as computing the reciprocal of `Self::tan`.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle = Rad::new(35.0);
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/// let ratio: f32 = Rad::cot(angle);
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/// ```
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#[inline]
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fn cot(self) -> Self::Unitless {
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Self::tan(self).recip()
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}
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/// Compute the cotatangent of the angle.
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///
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/// This is the same as computing the reciprocal of `Self::cos`.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle = Rad::new(35.0);
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/// let ratio: f32 = Rad::sec(angle);
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/// ```
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#[inline]
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fn sec(self) -> Self::Unitless {
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Self::cos(self).recip()
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}
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/// Compute the arcsine of the ratio, returning the resulting angle.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle: Rad<f32> = Rad::asin(0.5);
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/// ```
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fn asin(ratio: Self::Unitless) -> Self;
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/// Compute the arccosine of the ratio, returning the resulting angle.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle: Rad<f32> = Rad::acos(0.5);
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/// ```
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fn acos(ratio: Self::Unitless) -> Self;
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/// Compute the arctangent of the ratio, returning the resulting angle.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Rad;
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///
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/// let angle: Rad<f32> = Rad::atan(0.5);
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/// ```
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fn atan(ratio: Self::Unitless) -> Self;
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fn atan2(a: Self::Unitless, b: Self::Unitless) -> Self;
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}
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macro_rules! impl_angle {
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macro_rules! impl_angle {
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($Angle:ident, $fmt:expr, $full_turn:expr, $hi:expr) => {
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($Angle:ident, $fmt:expr, $full_turn:expr, $hi:expr) => {
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impl<S: BaseFloat> $Angle<S> {
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impl<S: BaseFloat> $Angle<S> {
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86
src/array.rs
86
src/array.rs
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@ -1,86 +0,0 @@
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// Copyright 2013 The OMath Developers. For a full listing of the authors,
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// refer to the Cargo.toml file at the top-level directory of this distribution.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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use std::ptr;
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use std::ops::*;
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use num::PartialOrd;
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/// An array containing elements of type `Element`
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pub trait Array where
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// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
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Self: Index<usize, Output = <Self as Array>::Element>,
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Self: IndexMut<usize, Output = <Self as Array>::Element>,
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{
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type Element: Copy;
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/// Construct a vector from a single value, replicating it.
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///
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/// ```rust
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/// use cgmath::prelude::*;
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/// use cgmath::Vector3;
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///
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/// assert_eq!(Vector3::from_value(1),
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/// Vector3::new(1, 1, 1));
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/// ```
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fn from_value(value: Self::Element) -> Self;
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/// Get the pointer to the first element of the array.
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#[inline]
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fn as_ptr(&self) -> *const Self::Element {
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&self[0]
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}
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/// Get a mutable pointer to the first element of the array.
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#[inline]
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fn as_mut_ptr(&mut self) -> *mut Self::Element {
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&mut self[0]
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}
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/// Swap the elements at indices `i` and `j` in-place.
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#[inline]
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fn swap_elements(&mut self, i: usize, j: usize) {
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// Yeah, ok borrow checker – I know what I'm doing here
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unsafe { ptr::swap(&mut self[i], &mut self[j]) };
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}
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/// The sum of the elements of the array.
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fn sum(self) -> Self::Element where Self::Element: Add<Output = <Self as Array>::Element>;
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/// The product of the elements of the array.
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fn product(self) -> Self::Element where Self::Element: Mul<Output = <Self as Array>::Element>;
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/// The minimum element of the array.
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fn min(self) -> Self::Element where Self::Element: PartialOrd;
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/// The maximum element of the array.
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fn max(self) -> Self::Element where Self::Element: PartialOrd;
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}
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/// Element-wise arithmetic operations. These are supplied for pragmatic
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/// reasons, but will usually fall outside of traditional algebraic properties.
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pub trait ElementWise<Rhs = Self> {
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fn add_element_wise(self, rhs: Rhs) -> Self;
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fn sub_element_wise(self, rhs: Rhs) -> Self;
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fn mul_element_wise(self, rhs: Rhs) -> Self;
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fn div_element_wise(self, rhs: Rhs) -> Self;
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fn rem_element_wise(self, rhs: Rhs) -> Self;
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fn add_assign_element_wise(&mut self, rhs: Rhs);
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fn sub_assign_element_wise(&mut self, rhs: Rhs);
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fn mul_assign_element_wise(&mut self, rhs: Rhs);
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fn div_assign_element_wise(&mut self, rhs: Rhs);
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fn rem_assign_element_wise(&mut self, rhs: Rhs);
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}
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25
src/lib.rs
25
src/lib.rs
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// Re-exports
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// Re-exports
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pub use array::*;
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pub use approx::*;
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pub use matrix::*;
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pub use num::*;
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pub use quaternion::*;
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pub use structure::*;
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pub use vector::*;
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pub use angle::*;
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pub use matrix::{Matrix2, Matrix3, Matrix4};
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pub use point::*;
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pub use quaternion::Quaternion;
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pub use vector::{Vector2, Vector3, Vector4, dot, vec2, vec3, vec4};
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pub use angle::{Deg, Rad, deg, rad};
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pub use point::{Point2, Point3};
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pub use rotation::*;
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pub use rotation::*;
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pub use transform::*;
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pub use transform::*;
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pub use projection::*;
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pub use projection::*;
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pub use approx::ApproxEq;
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pub use num::*;
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pub use rust_num::{One, Zero, one, zero};
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pub use rust_num::{One, Zero, one, zero};
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// Modules
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// Modules
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@ -79,7 +79,9 @@ pub mod prelude;
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mod macros;
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mod macros;
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mod array;
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mod approx;
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mod num;
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mod structure;
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mod matrix;
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mod matrix;
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mod quaternion;
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mod quaternion;
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@ -91,6 +93,3 @@ mod rotation;
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mod transform;
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mod transform;
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mod projection;
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mod projection;
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mod approx;
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mod num;
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156
src/matrix.rs
156
src/matrix.rs
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@ -13,23 +13,21 @@
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// See the License for the specific language governing permissions and
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// limitations under the License.
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use rand::{Rand, Rng};
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use rust_num::{Zero, One};
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use rust_num::traits::cast;
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use std::fmt;
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use std::fmt;
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use std::mem;
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use std::mem;
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use std::ops::*;
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use std::ops::*;
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use std::ptr;
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use std::ptr;
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use rand::{Rand, Rng};
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use structure::*;
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use rust_num::{Zero, One};
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use angle::Rad;
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use rust_num::traits::cast;
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use angle::{Angle, Rad};
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use approx::ApproxEq;
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use approx::ApproxEq;
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use array::Array;
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use num::BaseFloat;
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use num::BaseFloat;
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use point::{EuclideanSpace, Point3};
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use point::Point3;
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use quaternion::Quaternion;
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use quaternion::Quaternion;
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use vector::{VectorSpace, InnerSpace};
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use vector::{Vector2, Vector3, Vector4};
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use vector::{Vector2, Vector3, Vector4};
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/// A 2 x 2, column major matrix
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/// A 2 x 2, column major matrix
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|
@ -288,148 +286,6 @@ impl<S: BaseFloat> VectorSpace for Matrix4<S> {
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
/// A column-major matrix of arbitrary dimensions.
|
|
||||||
///
|
|
||||||
/// Because this is constrained to the `VectorSpace` trait, this means that
|
|
||||||
/// following operators are required to be implemented:
|
|
||||||
///
|
|
||||||
/// Matrix addition:
|
|
||||||
///
|
|
||||||
/// - `Add<Output = Self>`
|
|
||||||
/// - `Sub<Output = Self>`
|
|
||||||
/// - `Neg<Output = Self>`
|
|
||||||
///
|
|
||||||
/// Scalar multiplication:
|
|
||||||
///
|
|
||||||
/// - `Mul<Self::Scalar, Output = Self>`
|
|
||||||
/// - `Div<Self::Scalar, Output = Self>`
|
|
||||||
/// - `Rem<Self::Scalar, Output = Self>`
|
|
||||||
///
|
|
||||||
/// Note that matrix multiplication is not required for implementors of this
|
|
||||||
/// trait. This is due to the complexities of implementing these operators with
|
|
||||||
/// Rust's current type system. For the multiplication of square matrices,
|
|
||||||
/// see `SquareMatrix`.
|
|
||||||
pub trait Matrix: VectorSpace where
|
|
||||||
Self::Scalar: BaseFloat,
|
|
||||||
|
|
||||||
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
|
||||||
Self: Index<usize, Output = <Self as Matrix>::Column>,
|
|
||||||
Self: IndexMut<usize, Output = <Self as Matrix>::Column>,
|
|
||||||
Self: ApproxEq<Epsilon = <Self as VectorSpace>::Scalar>,
|
|
||||||
{
|
|
||||||
/// The row vector of the matrix.
|
|
||||||
type Row: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>;
|
|
||||||
|
|
||||||
/// The column vector of the matrix.
|
|
||||||
type Column: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>;
|
|
||||||
|
|
||||||
/// The result of transposing the matrix
|
|
||||||
type Transpose: Matrix<Scalar = Self::Scalar, Row = Self::Column, Column = Self::Row>;
|
|
||||||
|
|
||||||
/// Get the pointer to the first element of the array.
|
|
||||||
#[inline]
|
|
||||||
fn as_ptr(&self) -> *const Self::Scalar {
|
|
||||||
&self[0][0]
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Get a mutable pointer to the first element of the array.
|
|
||||||
#[inline]
|
|
||||||
fn as_mut_ptr(&mut self) -> *mut Self::Scalar {
|
|
||||||
&mut self[0][0]
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Replace a column in the array.
|
|
||||||
#[inline]
|
|
||||||
fn replace_col(&mut self, c: usize, src: Self::Column) -> Self::Column {
|
|
||||||
mem::replace(&mut self[c], src)
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Get a row from this matrix by-value.
|
|
||||||
fn row(&self, r: usize) -> Self::Row;
|
|
||||||
|
|
||||||
/// Swap two rows of this array.
|
|
||||||
fn swap_rows(&mut self, a: usize, b: usize);
|
|
||||||
/// Swap two columns of this array.
|
|
||||||
fn swap_columns(&mut self, a: usize, b: usize);
|
|
||||||
/// Swap the values at index `a` and `b`
|
|
||||||
fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize));
|
|
||||||
|
|
||||||
/// Transpose this matrix, returning a new matrix.
|
|
||||||
fn transpose(&self) -> Self::Transpose;
|
|
||||||
}
|
|
||||||
|
|
||||||
/// A column-major major matrix where the rows and column vectors are of the same dimensions.
|
|
||||||
pub trait SquareMatrix where
|
|
||||||
Self::Scalar: BaseFloat,
|
|
||||||
|
|
||||||
Self: Matrix<
|
|
||||||
// FIXME: Can be cleaned up once equality constraints in where clauses are implemented
|
|
||||||
Column = <Self as SquareMatrix>::ColumnRow,
|
|
||||||
Row = <Self as SquareMatrix>::ColumnRow,
|
|
||||||
Transpose = Self,
|
|
||||||
>,
|
|
||||||
Self: Mul<<Self as SquareMatrix>::ColumnRow, Output = <Self as SquareMatrix>::ColumnRow>,
|
|
||||||
Self: Mul<Self, Output = Self>,
|
|
||||||
{
|
|
||||||
// FIXME: Will not be needed once equality constraints in where clauses are implemented
|
|
||||||
/// The row/column vector of the matrix.
|
|
||||||
///
|
|
||||||
/// This is used to constrain the column and rows to be of the same type in lieu of equality
|
|
||||||
/// constraints being implemented for `where` clauses. Once those are added, this type will
|
|
||||||
/// likely go away.
|
|
||||||
type ColumnRow: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>;
|
|
||||||
|
|
||||||
/// Create a new diagonal matrix using the supplied value.
|
|
||||||
fn from_value(value: Self::Scalar) -> Self;
|
|
||||||
/// Create a matrix from a non-uniform scale
|
|
||||||
fn from_diagonal(diagonal: Self::ColumnRow) -> Self;
|
|
||||||
|
|
||||||
/// The [identity matrix](https://en.wikipedia.org/wiki/Identity_matrix). Multiplying this
|
|
||||||
/// matrix with another has no effect.
|
|
||||||
fn identity() -> Self;
|
|
||||||
|
|
||||||
/// Transpose this matrix in-place.
|
|
||||||
fn transpose_self(&mut self);
|
|
||||||
/// Take the determinant of this matrix.
|
|
||||||
fn determinant(&self) -> Self::Scalar;
|
|
||||||
|
|
||||||
/// Return a vector containing the diagonal of this matrix.
|
|
||||||
fn diagonal(&self) -> Self::ColumnRow;
|
|
||||||
|
|
||||||
/// Return the trace of this matrix. That is, the sum of the diagonal.
|
|
||||||
#[inline]
|
|
||||||
fn trace(&self) -> Self::Scalar { self.diagonal().sum() }
|
|
||||||
|
|
||||||
/// Invert this matrix, returning a new matrix. `m.mul_m(m.invert())` is
|
|
||||||
/// the identity matrix. Returns `None` if this matrix is not invertible
|
|
||||||
/// (has a determinant of zero).
|
|
||||||
#[must_use]
|
|
||||||
fn invert(&self) -> Option<Self>;
|
|
||||||
|
|
||||||
/// Invert this matrix in-place.
|
|
||||||
#[inline]
|
|
||||||
fn invert_self(&mut self) {
|
|
||||||
*self = self.invert().expect("Attempted to invert a matrix with zero determinant.");
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Test if this matrix is invertible.
|
|
||||||
#[inline]
|
|
||||||
fn is_invertible(&self) -> bool { !self.determinant().approx_eq(&Self::Scalar::zero()) }
|
|
||||||
|
|
||||||
/// Test if this matrix is the identity matrix. That is, it is diagonal
|
|
||||||
/// and every element in the diagonal is one.
|
|
||||||
#[inline]
|
|
||||||
fn is_identity(&self) -> bool { self.approx_eq(&Self::identity()) }
|
|
||||||
|
|
||||||
/// Test if this is a diagonal matrix. That is, every element outside of
|
|
||||||
/// the diagonal is 0.
|
|
||||||
fn is_diagonal(&self) -> bool;
|
|
||||||
|
|
||||||
/// Test if this matrix is symmetric. That is, it is equal to its
|
|
||||||
/// transpose.
|
|
||||||
fn is_symmetric(&self) -> bool;
|
|
||||||
}
|
|
||||||
|
|
||||||
impl<S: BaseFloat> Matrix for Matrix2<S> {
|
impl<S: BaseFloat> Matrix for Matrix2<S> {
|
||||||
type Column = Vector2<S>;
|
type Column = Vector2<S>;
|
||||||
type Row = Vector2<S>;
|
type Row = Vector2<S>;
|
||||||
|
|
|
||||||
91
src/point.rs
91
src/point.rs
|
|
@ -23,10 +23,11 @@ use std::ops::*;
|
||||||
|
|
||||||
use rust_num::{One, Zero};
|
use rust_num::{One, Zero};
|
||||||
|
|
||||||
|
use structure::*;
|
||||||
|
|
||||||
use approx::ApproxEq;
|
use approx::ApproxEq;
|
||||||
use array::Array;
|
|
||||||
use num::{BaseNum, BaseFloat};
|
use num::{BaseNum, BaseFloat};
|
||||||
use vector::*;
|
use vector::{Vector2, Vector3, Vector4};
|
||||||
|
|
||||||
/// A point in 2-dimensional space.
|
/// A point in 2-dimensional space.
|
||||||
///
|
///
|
||||||
|
|
@ -77,92 +78,6 @@ impl<S: BaseNum> Point3<S> {
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
/// Points in a [Euclidean space](https://en.wikipedia.org/wiki/Euclidean_space)
|
|
||||||
/// with an associated space of displacement vectors.
|
|
||||||
///
|
|
||||||
/// # Point-Vector distinction
|
|
||||||
///
|
|
||||||
/// `cgmath` distinguishes between points and vectors in the following way:
|
|
||||||
///
|
|
||||||
/// - Points are _locations_ relative to an origin
|
|
||||||
/// - Vectors are _displacements_ between those points
|
|
||||||
///
|
|
||||||
/// For example, to find the midpoint between two points, you can write the
|
|
||||||
/// following:
|
|
||||||
///
|
|
||||||
/// ```rust
|
|
||||||
/// use cgmath::Point3;
|
|
||||||
///
|
|
||||||
/// let p0 = Point3::new(1.0, 2.0, 3.0);
|
|
||||||
/// let p1 = Point3::new(-3.0, 1.0, 2.0);
|
|
||||||
/// let midpoint: Point3<f32> = p0 + (p1 - p0) * 0.5;
|
|
||||||
/// ```
|
|
||||||
///
|
|
||||||
/// Breaking the expression up, and adding explicit types makes it clearer
|
|
||||||
/// to see what is going on:
|
|
||||||
///
|
|
||||||
/// ```rust
|
|
||||||
/// # use cgmath::{Point3, Vector3};
|
|
||||||
/// #
|
|
||||||
/// # let p0 = Point3::new(1.0, 2.0, 3.0);
|
|
||||||
/// # let p1 = Point3::new(-3.0, 1.0, 2.0);
|
|
||||||
/// #
|
|
||||||
/// let dv: Vector3<f32> = p1 - p0;
|
|
||||||
/// let half_dv: Vector3<f32> = dv * 0.5;
|
|
||||||
/// let midpoint: Point3<f32> = p0 + half_dv;
|
|
||||||
/// ```
|
|
||||||
///
|
|
||||||
/// ## Converting between points and vectors
|
|
||||||
///
|
|
||||||
/// Points can be converted to and from displacement vectors using the
|
|
||||||
/// `EuclideanSpace::{from_vec, to_vec}` methods. Note that under the hood these
|
|
||||||
/// are implemented as inlined a type conversion, so should not have any
|
|
||||||
/// performance implications.
|
|
||||||
///
|
|
||||||
/// ## References
|
|
||||||
///
|
|
||||||
/// - [CGAL 4.7 - 2D and 3D Linear Geometry Kernel: 3.1 Points and Vectors](http://doc.cgal.org/latest/Kernel_23/index.html#Kernel_23PointsandVectors)
|
|
||||||
/// - [What is the difference between a point and a vector](http://math.stackexchange.com/q/645827)
|
|
||||||
///
|
|
||||||
pub trait EuclideanSpace: Copy + Clone where
|
|
||||||
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
|
||||||
Self: Array<Element = <Self as EuclideanSpace>::Scalar>,
|
|
||||||
|
|
||||||
Self: Add<<Self as EuclideanSpace>::Diff, Output = Self>,
|
|
||||||
Self: Sub<Self, Output = <Self as EuclideanSpace>::Diff>,
|
|
||||||
|
|
||||||
Self: Mul<<Self as EuclideanSpace>::Scalar, Output = Self>,
|
|
||||||
Self: Div<<Self as EuclideanSpace>::Scalar, Output = Self>,
|
|
||||||
Self: Rem<<Self as EuclideanSpace>::Scalar, Output = Self>,
|
|
||||||
{
|
|
||||||
/// The associated scalar over which the space is defined.
|
|
||||||
///
|
|
||||||
/// Due to the equality constraints demanded by `Self::Diff`, this is effectively just an
|
|
||||||
/// alias to `Self::Diff::Scalar`.
|
|
||||||
type Scalar: BaseNum;
|
|
||||||
|
|
||||||
/// The associated space of displacement vectors.
|
|
||||||
type Diff: VectorSpace<Scalar = Self::Scalar>;
|
|
||||||
|
|
||||||
/// The point at the origin of the Euclidean space.
|
|
||||||
fn origin() -> Self;
|
|
||||||
|
|
||||||
/// Convert a displacement vector to a point.
|
|
||||||
///
|
|
||||||
/// This can be considered equivalent to the addition of the displacement
|
|
||||||
/// vector `v` to to `Self::origin()`.
|
|
||||||
fn from_vec(v: Self::Diff) -> Self;
|
|
||||||
|
|
||||||
/// Convert a point to a displacement vector.
|
|
||||||
///
|
|
||||||
/// This can be seen as equivalent to the displacement vector from
|
|
||||||
/// `Self::origin()` to `self`.
|
|
||||||
fn to_vec(self) -> Self::Diff;
|
|
||||||
|
|
||||||
/// This is a weird one, but its useful for plane calculations.
|
|
||||||
fn dot(self, v: Self::Diff) -> Self::Scalar;
|
|
||||||
}
|
|
||||||
|
|
||||||
macro_rules! impl_point {
|
macro_rules! impl_point {
|
||||||
($PointN:ident { $($field:ident),+ }, $VectorN:ident, $n:expr) => {
|
($PointN:ident { $($field:ident),+ }, $VectorN:ident, $n:expr) => {
|
||||||
impl<S: BaseNum> Array for $PointN<S> {
|
impl<S: BaseNum> Array for $PointN<S> {
|
||||||
|
|
|
||||||
|
|
@ -2,15 +2,7 @@
|
||||||
//! glob-importing this module, you can avoid the need to import each trait
|
//! glob-importing this module, you can avoid the need to import each trait
|
||||||
//! individually, while still being selective about what types you import.
|
//! individually, while still being selective about what types you import.
|
||||||
|
|
||||||
pub use angle::Angle;
|
pub use structure::*;
|
||||||
|
|
||||||
pub use array::Array;
|
|
||||||
pub use array::ElementWise;
|
|
||||||
|
|
||||||
pub use matrix::Matrix;
|
|
||||||
pub use matrix::SquareMatrix;
|
|
||||||
|
|
||||||
pub use point::EuclideanSpace;
|
|
||||||
|
|
||||||
pub use rotation::Rotation;
|
pub use rotation::Rotation;
|
||||||
pub use rotation::Rotation2;
|
pub use rotation::Rotation2;
|
||||||
|
|
@ -19,6 +11,3 @@ pub use rotation::Rotation3;
|
||||||
pub use transform::Transform;
|
pub use transform::Transform;
|
||||||
pub use transform::Transform2;
|
pub use transform::Transform2;
|
||||||
pub use transform::Transform3;
|
pub use transform::Transform3;
|
||||||
|
|
||||||
pub use vector::InnerSpace;
|
|
||||||
pub use vector::VectorSpace;
|
|
||||||
|
|
|
||||||
|
|
@ -16,7 +16,9 @@
|
||||||
use rust_num::{Zero, One};
|
use rust_num::{Zero, One};
|
||||||
use rust_num::traits::cast;
|
use rust_num::traits::cast;
|
||||||
|
|
||||||
use angle::{Angle, Rad};
|
use structure::Angle;
|
||||||
|
|
||||||
|
use angle::Rad;
|
||||||
use matrix::Matrix4;
|
use matrix::Matrix4;
|
||||||
use num::BaseFloat;
|
use num::BaseFloat;
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -20,13 +20,15 @@ use rand::{Rand, Rng};
|
||||||
use rust_num::{Float, One, Zero};
|
use rust_num::{Float, One, Zero};
|
||||||
use rust_num::traits::cast;
|
use rust_num::traits::cast;
|
||||||
|
|
||||||
use angle::{Angle, Rad};
|
use structure::*;
|
||||||
|
|
||||||
|
use angle::Rad;
|
||||||
use approx::ApproxEq;
|
use approx::ApproxEq;
|
||||||
use matrix::{Matrix3, Matrix4};
|
use matrix::{Matrix3, Matrix4};
|
||||||
use num::BaseFloat;
|
use num::BaseFloat;
|
||||||
use point::Point3;
|
use point::Point3;
|
||||||
use rotation::{Rotation, Rotation3, Basis3};
|
use rotation::{Rotation, Rotation3, Basis3};
|
||||||
use vector::{Vector3, VectorSpace, InnerSpace};
|
use vector::Vector3;
|
||||||
|
|
||||||
|
|
||||||
/// A [quaternion](https://en.wikipedia.org/wiki/Quaternion) in scalar/vector
|
/// A [quaternion](https://en.wikipedia.org/wiki/Quaternion) in scalar/vector
|
||||||
|
|
|
||||||
|
|
@ -15,14 +15,15 @@
|
||||||
|
|
||||||
use std::fmt;
|
use std::fmt;
|
||||||
|
|
||||||
use angle::{Angle, Rad};
|
use structure::*;
|
||||||
|
|
||||||
|
use angle::Rad;
|
||||||
use approx::ApproxEq;
|
use approx::ApproxEq;
|
||||||
use matrix::SquareMatrix;
|
|
||||||
use matrix::{Matrix2, Matrix3};
|
use matrix::{Matrix2, Matrix3};
|
||||||
use num::BaseFloat;
|
use num::BaseFloat;
|
||||||
use point::{EuclideanSpace, Point2, Point3};
|
use point::{Point2, Point3};
|
||||||
use quaternion::Quaternion;
|
use quaternion::Quaternion;
|
||||||
use vector::{InnerSpace, Vector2, Vector3};
|
use vector::{Vector2, Vector3};
|
||||||
|
|
||||||
/// A trait for a generic rotation. A rotation is a transformation that
|
/// A trait for a generic rotation. A rotation is a transformation that
|
||||||
/// creates a circular motion, and preserves at least one point in the space.
|
/// creates a circular motion, and preserves at least one point in the space.
|
||||||
|
|
|
||||||
664
src/structure.rs
Normal file
664
src/structure.rs
Normal file
|
|
@ -0,0 +1,664 @@
|
||||||
|
// Copyright 2016 The CGMath Developers. For a full listing of the authors,
|
||||||
|
// refer to the Cargo.toml file at the top-level directory of this distribution.
|
||||||
|
//
|
||||||
|
// Licensed under the Apache License, Version 2.0 (the "License");
|
||||||
|
// you may not use this file except in compliance with the License.
|
||||||
|
// You may obtain a copy of the License at
|
||||||
|
//
|
||||||
|
// http://www.apache.org/licenses/LICENSE-2.0
|
||||||
|
//
|
||||||
|
// Unless required by applicable law or agreed to in writing, software
|
||||||
|
// distributed under the License is distributed on an "AS IS" BASIS,
|
||||||
|
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||||||
|
// See the License for the specific language governing permissions and
|
||||||
|
// limitations under the License.
|
||||||
|
|
||||||
|
//! Generic algebraic structures
|
||||||
|
|
||||||
|
use rust_num::{cast, Float, One, Zero};
|
||||||
|
use std::cmp;
|
||||||
|
use std::ops::*;
|
||||||
|
|
||||||
|
use approx::ApproxEq;
|
||||||
|
|
||||||
|
use angle::Rad;
|
||||||
|
use num::{BaseNum, BaseFloat, PartialOrd};
|
||||||
|
|
||||||
|
/// An array containing elements of type `Element`
|
||||||
|
pub trait Array where
|
||||||
|
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
||||||
|
Self: Index<usize, Output = <Self as Array>::Element>,
|
||||||
|
Self: IndexMut<usize, Output = <Self as Array>::Element>,
|
||||||
|
{
|
||||||
|
type Element: Copy;
|
||||||
|
|
||||||
|
/// Construct a vector from a single value, replicating it.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Vector3;
|
||||||
|
///
|
||||||
|
/// assert_eq!(Vector3::from_value(1),
|
||||||
|
/// Vector3::new(1, 1, 1));
|
||||||
|
/// ```
|
||||||
|
fn from_value(value: Self::Element) -> Self;
|
||||||
|
|
||||||
|
/// Get the pointer to the first element of the array.
|
||||||
|
#[inline]
|
||||||
|
fn as_ptr(&self) -> *const Self::Element {
|
||||||
|
&self[0]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Get a mutable pointer to the first element of the array.
|
||||||
|
#[inline]
|
||||||
|
fn as_mut_ptr(&mut self) -> *mut Self::Element {
|
||||||
|
&mut self[0]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Swap the elements at indices `i` and `j` in-place.
|
||||||
|
#[inline]
|
||||||
|
fn swap_elements(&mut self, i: usize, j: usize) {
|
||||||
|
use std::ptr;
|
||||||
|
|
||||||
|
// Yeah, ok borrow checker – I know what I'm doing here
|
||||||
|
unsafe { ptr::swap(&mut self[i], &mut self[j]) };
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The sum of the elements of the array.
|
||||||
|
fn sum(self) -> Self::Element where Self::Element: Add<Output = <Self as Array>::Element>;
|
||||||
|
|
||||||
|
/// The product of the elements of the array.
|
||||||
|
fn product(self) -> Self::Element where Self::Element: Mul<Output = <Self as Array>::Element>;
|
||||||
|
|
||||||
|
/// The minimum element of the array.
|
||||||
|
fn min(self) -> Self::Element where Self::Element: PartialOrd;
|
||||||
|
|
||||||
|
/// The maximum element of the array.
|
||||||
|
fn max(self) -> Self::Element where Self::Element: PartialOrd;
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Element-wise arithmetic operations. These are supplied for pragmatic
|
||||||
|
/// reasons, but will usually fall outside of traditional algebraic properties.
|
||||||
|
pub trait ElementWise<Rhs = Self> {
|
||||||
|
fn add_element_wise(self, rhs: Rhs) -> Self;
|
||||||
|
fn sub_element_wise(self, rhs: Rhs) -> Self;
|
||||||
|
fn mul_element_wise(self, rhs: Rhs) -> Self;
|
||||||
|
fn div_element_wise(self, rhs: Rhs) -> Self;
|
||||||
|
fn rem_element_wise(self, rhs: Rhs) -> Self;
|
||||||
|
|
||||||
|
fn add_assign_element_wise(&mut self, rhs: Rhs);
|
||||||
|
fn sub_assign_element_wise(&mut self, rhs: Rhs);
|
||||||
|
fn mul_assign_element_wise(&mut self, rhs: Rhs);
|
||||||
|
fn div_assign_element_wise(&mut self, rhs: Rhs);
|
||||||
|
fn rem_assign_element_wise(&mut self, rhs: Rhs);
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Vectors that can be [added](http://mathworld.wolfram.com/VectorAddition.html)
|
||||||
|
/// together and [multiplied](https://en.wikipedia.org/wiki/Scalar_multiplication)
|
||||||
|
/// by scalars.
|
||||||
|
///
|
||||||
|
/// Examples include vectors, matrices, and quaternions.
|
||||||
|
///
|
||||||
|
/// # Required operators
|
||||||
|
///
|
||||||
|
/// ## Vector addition
|
||||||
|
///
|
||||||
|
/// Vectors can be added, subtracted, or negated via the following traits:
|
||||||
|
///
|
||||||
|
/// - `Add<Output = Self>`
|
||||||
|
/// - `Sub<Output = Self>`
|
||||||
|
/// - `Neg<Output = Self>`
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::Vector3;
|
||||||
|
///
|
||||||
|
/// let velocity0 = Vector3::new(1, 2, 0);
|
||||||
|
/// let velocity1 = Vector3::new(1, 1, 0);
|
||||||
|
///
|
||||||
|
/// let total_velocity = velocity0 + velocity1;
|
||||||
|
/// let velocity_diff = velocity1 - velocity0;
|
||||||
|
/// let reversed_velocity0 = -velocity0;
|
||||||
|
/// ```
|
||||||
|
///
|
||||||
|
/// ## Scalar multiplication
|
||||||
|
///
|
||||||
|
/// Vectors can be multiplied or divided by their associated scalars via the
|
||||||
|
/// following traits:
|
||||||
|
///
|
||||||
|
/// - `Mul<Self::Scalar, Output = Self>`
|
||||||
|
/// - `Div<Self::Scalar, Output = Self>`
|
||||||
|
/// - `Rem<Self::Scalar, Output = Self>`
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::Vector2;
|
||||||
|
///
|
||||||
|
/// let translation = Vector2::new(3.0, 4.0);
|
||||||
|
/// let scale_factor = 2.0;
|
||||||
|
///
|
||||||
|
/// let upscaled_translation = translation * scale_factor;
|
||||||
|
/// let downscaled_translation = translation / scale_factor;
|
||||||
|
/// ```
|
||||||
|
pub trait VectorSpace: Copy + Clone where
|
||||||
|
Self: Add<Self, Output = Self>,
|
||||||
|
Self: Sub<Self, Output = Self>,
|
||||||
|
|
||||||
|
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
||||||
|
Self: Mul<<Self as VectorSpace>::Scalar, Output = Self>,
|
||||||
|
Self: Div<<Self as VectorSpace>::Scalar, Output = Self>,
|
||||||
|
Self: Rem<<Self as VectorSpace>::Scalar, Output = Self>,
|
||||||
|
{
|
||||||
|
/// The associated scalar.
|
||||||
|
type Scalar: BaseNum;
|
||||||
|
|
||||||
|
/// The additive identity.
|
||||||
|
///
|
||||||
|
/// Adding this to another `Self` value has no effect.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Vector2;
|
||||||
|
///
|
||||||
|
/// let v = Vector2::new(1, 2);
|
||||||
|
/// assert_eq!(v + Vector2::zero(), v);
|
||||||
|
/// ```
|
||||||
|
fn zero() -> Self;
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Vectors that also have a [dot](https://en.wikipedia.org/wiki/Dot_product)
|
||||||
|
/// (or [inner](https://en.wikipedia.org/wiki/Inner_product_space)) product.
|
||||||
|
///
|
||||||
|
/// The dot product allows for the definition of other useful operations, like
|
||||||
|
/// finding the magnitude of a vector or normalizing it.
|
||||||
|
///
|
||||||
|
/// Examples include vectors and quaternions.
|
||||||
|
pub trait InnerSpace: VectorSpace + Sized where
|
||||||
|
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
||||||
|
<Self as VectorSpace>::Scalar: BaseFloat,
|
||||||
|
Self: ApproxEq<Epsilon = <Self as VectorSpace>::Scalar>,
|
||||||
|
{
|
||||||
|
/// Vector dot (or inner) product.
|
||||||
|
fn dot(self, other: Self) -> Self::Scalar;
|
||||||
|
|
||||||
|
/// Returns `true` if the vector is perpendicular (at right angles) to the
|
||||||
|
/// other vector.
|
||||||
|
fn is_perpendicular(self, other: Self) -> bool {
|
||||||
|
Self::dot(self, other).approx_eq(&Self::Scalar::zero())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Returns the squared magnitude of the vector.
|
||||||
|
///
|
||||||
|
/// This does not perform an expensive square root operation like in
|
||||||
|
/// `Vector::magnitude` method, and so can be used to compare vectors more
|
||||||
|
/// efficiently.
|
||||||
|
#[inline]
|
||||||
|
fn magnitude2(self) -> Self::Scalar {
|
||||||
|
Self::dot(self, self)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The distance from the tail to the tip of the vector.
|
||||||
|
#[inline]
|
||||||
|
fn magnitude(self) -> Self::Scalar {
|
||||||
|
use rust_num::Float;
|
||||||
|
|
||||||
|
// FIXME: Not sure why we can't use method syntax for `sqrt` here...
|
||||||
|
Float::sqrt(self.magnitude2())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Returns the angle between two vectors in radians.
|
||||||
|
fn angle(self, other: Self) -> Rad<Self::Scalar> {
|
||||||
|
Rad::acos(Self::dot(self, other) / (self.magnitude() * other.magnitude()))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Returns a vector with the same direction, but with a magnitude of `1`.
|
||||||
|
#[inline]
|
||||||
|
#[must_use]
|
||||||
|
fn normalize(self) -> Self {
|
||||||
|
self.normalize_to(Self::Scalar::one())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Returns a vector with the same direction and a given magnitude.
|
||||||
|
#[inline]
|
||||||
|
#[must_use]
|
||||||
|
fn normalize_to(self, magnitude: Self::Scalar) -> Self {
|
||||||
|
self * (magnitude / self.magnitude())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Returns the result of linearly interpolating the magnitude of the vector
|
||||||
|
/// towards the magnitude of `other` by the specified amount.
|
||||||
|
#[inline]
|
||||||
|
#[must_use]
|
||||||
|
fn lerp(self, other: Self, amount: Self::Scalar) -> Self {
|
||||||
|
self + ((other - self) * amount)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Points in a [Euclidean space](https://en.wikipedia.org/wiki/Euclidean_space)
|
||||||
|
/// with an associated space of displacement vectors.
|
||||||
|
///
|
||||||
|
/// # Point-Vector distinction
|
||||||
|
///
|
||||||
|
/// `cgmath` distinguishes between points and vectors in the following way:
|
||||||
|
///
|
||||||
|
/// - Points are _locations_ relative to an origin
|
||||||
|
/// - Vectors are _displacements_ between those points
|
||||||
|
///
|
||||||
|
/// For example, to find the midpoint between two points, you can write the
|
||||||
|
/// following:
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::Point3;
|
||||||
|
///
|
||||||
|
/// let p0 = Point3::new(1.0, 2.0, 3.0);
|
||||||
|
/// let p1 = Point3::new(-3.0, 1.0, 2.0);
|
||||||
|
/// let midpoint: Point3<f32> = p0 + (p1 - p0) * 0.5;
|
||||||
|
/// ```
|
||||||
|
///
|
||||||
|
/// Breaking the expression up, and adding explicit types makes it clearer
|
||||||
|
/// to see what is going on:
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// # use cgmath::{Point3, Vector3};
|
||||||
|
/// #
|
||||||
|
/// # let p0 = Point3::new(1.0, 2.0, 3.0);
|
||||||
|
/// # let p1 = Point3::new(-3.0, 1.0, 2.0);
|
||||||
|
/// #
|
||||||
|
/// let dv: Vector3<f32> = p1 - p0;
|
||||||
|
/// let half_dv: Vector3<f32> = dv * 0.5;
|
||||||
|
/// let midpoint: Point3<f32> = p0 + half_dv;
|
||||||
|
/// ```
|
||||||
|
///
|
||||||
|
/// ## Converting between points and vectors
|
||||||
|
///
|
||||||
|
/// Points can be converted to and from displacement vectors using the
|
||||||
|
/// `EuclideanSpace::{from_vec, to_vec}` methods. Note that under the hood these
|
||||||
|
/// are implemented as inlined a type conversion, so should not have any
|
||||||
|
/// performance implications.
|
||||||
|
///
|
||||||
|
/// ## References
|
||||||
|
///
|
||||||
|
/// - [CGAL 4.7 - 2D and 3D Linear Geometry Kernel: 3.1 Points and Vectors](http://doc.cgal.org/latest/Kernel_23/index.html#Kernel_23PointsandVectors)
|
||||||
|
/// - [What is the difference between a point and a vector](http://math.stackexchange.com/q/645827)
|
||||||
|
///
|
||||||
|
pub trait EuclideanSpace: Copy + Clone where
|
||||||
|
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
||||||
|
Self: Array<Element = <Self as EuclideanSpace>::Scalar>,
|
||||||
|
|
||||||
|
Self: Add<<Self as EuclideanSpace>::Diff, Output = Self>,
|
||||||
|
Self: Sub<Self, Output = <Self as EuclideanSpace>::Diff>,
|
||||||
|
|
||||||
|
Self: Mul<<Self as EuclideanSpace>::Scalar, Output = Self>,
|
||||||
|
Self: Div<<Self as EuclideanSpace>::Scalar, Output = Self>,
|
||||||
|
Self: Rem<<Self as EuclideanSpace>::Scalar, Output = Self>,
|
||||||
|
{
|
||||||
|
/// The associated scalar over which the space is defined.
|
||||||
|
///
|
||||||
|
/// Due to the equality constraints demanded by `Self::Diff`, this is effectively just an
|
||||||
|
/// alias to `Self::Diff::Scalar`.
|
||||||
|
type Scalar: BaseNum;
|
||||||
|
|
||||||
|
/// The associated space of displacement vectors.
|
||||||
|
type Diff: VectorSpace<Scalar = Self::Scalar>;
|
||||||
|
|
||||||
|
/// The point at the origin of the Euclidean space.
|
||||||
|
fn origin() -> Self;
|
||||||
|
|
||||||
|
/// Convert a displacement vector to a point.
|
||||||
|
///
|
||||||
|
/// This can be considered equivalent to the addition of the displacement
|
||||||
|
/// vector `v` to to `Self::origin()`.
|
||||||
|
fn from_vec(v: Self::Diff) -> Self;
|
||||||
|
|
||||||
|
/// Convert a point to a displacement vector.
|
||||||
|
///
|
||||||
|
/// This can be seen as equivalent to the displacement vector from
|
||||||
|
/// `Self::origin()` to `self`.
|
||||||
|
fn to_vec(self) -> Self::Diff;
|
||||||
|
|
||||||
|
/// This is a weird one, but its useful for plane calculations.
|
||||||
|
fn dot(self, v: Self::Diff) -> Self::Scalar;
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A column-major matrix of arbitrary dimensions.
|
||||||
|
///
|
||||||
|
/// Because this is constrained to the `VectorSpace` trait, this means that
|
||||||
|
/// following operators are required to be implemented:
|
||||||
|
///
|
||||||
|
/// Matrix addition:
|
||||||
|
///
|
||||||
|
/// - `Add<Output = Self>`
|
||||||
|
/// - `Sub<Output = Self>`
|
||||||
|
/// - `Neg<Output = Self>`
|
||||||
|
///
|
||||||
|
/// Scalar multiplication:
|
||||||
|
///
|
||||||
|
/// - `Mul<Self::Scalar, Output = Self>`
|
||||||
|
/// - `Div<Self::Scalar, Output = Self>`
|
||||||
|
/// - `Rem<Self::Scalar, Output = Self>`
|
||||||
|
///
|
||||||
|
/// Note that matrix multiplication is not required for implementors of this
|
||||||
|
/// trait. This is due to the complexities of implementing these operators with
|
||||||
|
/// Rust's current type system. For the multiplication of square matrices,
|
||||||
|
/// see `SquareMatrix`.
|
||||||
|
pub trait Matrix: VectorSpace where
|
||||||
|
Self::Scalar: BaseFloat,
|
||||||
|
|
||||||
|
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
||||||
|
Self: Index<usize, Output = <Self as Matrix>::Column>,
|
||||||
|
Self: IndexMut<usize, Output = <Self as Matrix>::Column>,
|
||||||
|
Self: ApproxEq<Epsilon = <Self as VectorSpace>::Scalar>,
|
||||||
|
{
|
||||||
|
/// The row vector of the matrix.
|
||||||
|
type Row: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>;
|
||||||
|
|
||||||
|
/// The column vector of the matrix.
|
||||||
|
type Column: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>;
|
||||||
|
|
||||||
|
/// The result of transposing the matrix
|
||||||
|
type Transpose: Matrix<Scalar = Self::Scalar, Row = Self::Column, Column = Self::Row>;
|
||||||
|
|
||||||
|
/// Get the pointer to the first element of the array.
|
||||||
|
#[inline]
|
||||||
|
fn as_ptr(&self) -> *const Self::Scalar {
|
||||||
|
&self[0][0]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Get a mutable pointer to the first element of the array.
|
||||||
|
#[inline]
|
||||||
|
fn as_mut_ptr(&mut self) -> *mut Self::Scalar {
|
||||||
|
&mut self[0][0]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Replace a column in the array.
|
||||||
|
#[inline]
|
||||||
|
fn replace_col(&mut self, c: usize, src: Self::Column) -> Self::Column {
|
||||||
|
use std::mem;
|
||||||
|
|
||||||
|
mem::replace(&mut self[c], src)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Get a row from this matrix by-value.
|
||||||
|
fn row(&self, r: usize) -> Self::Row;
|
||||||
|
|
||||||
|
/// Swap two rows of this array.
|
||||||
|
fn swap_rows(&mut self, a: usize, b: usize);
|
||||||
|
/// Swap two columns of this array.
|
||||||
|
fn swap_columns(&mut self, a: usize, b: usize);
|
||||||
|
/// Swap the values at index `a` and `b`
|
||||||
|
fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize));
|
||||||
|
|
||||||
|
/// Transpose this matrix, returning a new matrix.
|
||||||
|
fn transpose(&self) -> Self::Transpose;
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A column-major major matrix where the rows and column vectors are of the same dimensions.
|
||||||
|
pub trait SquareMatrix where
|
||||||
|
Self::Scalar: BaseFloat,
|
||||||
|
|
||||||
|
Self: Matrix<
|
||||||
|
// FIXME: Can be cleaned up once equality constraints in where clauses are implemented
|
||||||
|
Column = <Self as SquareMatrix>::ColumnRow,
|
||||||
|
Row = <Self as SquareMatrix>::ColumnRow,
|
||||||
|
Transpose = Self,
|
||||||
|
>,
|
||||||
|
Self: Mul<<Self as SquareMatrix>::ColumnRow, Output = <Self as SquareMatrix>::ColumnRow>,
|
||||||
|
Self: Mul<Self, Output = Self>,
|
||||||
|
{
|
||||||
|
// FIXME: Will not be needed once equality constraints in where clauses are implemented
|
||||||
|
/// The row/column vector of the matrix.
|
||||||
|
///
|
||||||
|
/// This is used to constrain the column and rows to be of the same type in lieu of equality
|
||||||
|
/// constraints being implemented for `where` clauses. Once those are added, this type will
|
||||||
|
/// likely go away.
|
||||||
|
type ColumnRow: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>;
|
||||||
|
|
||||||
|
/// Create a new diagonal matrix using the supplied value.
|
||||||
|
fn from_value(value: Self::Scalar) -> Self;
|
||||||
|
/// Create a matrix from a non-uniform scale
|
||||||
|
fn from_diagonal(diagonal: Self::ColumnRow) -> Self;
|
||||||
|
|
||||||
|
/// The [identity matrix](https://en.wikipedia.org/wiki/Identity_matrix). Multiplying this
|
||||||
|
/// matrix with another has no effect.
|
||||||
|
fn identity() -> Self;
|
||||||
|
|
||||||
|
/// Transpose this matrix in-place.
|
||||||
|
fn transpose_self(&mut self);
|
||||||
|
/// Take the determinant of this matrix.
|
||||||
|
fn determinant(&self) -> Self::Scalar;
|
||||||
|
|
||||||
|
/// Return a vector containing the diagonal of this matrix.
|
||||||
|
fn diagonal(&self) -> Self::ColumnRow;
|
||||||
|
|
||||||
|
/// Return the trace of this matrix. That is, the sum of the diagonal.
|
||||||
|
#[inline]
|
||||||
|
fn trace(&self) -> Self::Scalar { self.diagonal().sum() }
|
||||||
|
|
||||||
|
/// Invert this matrix, returning a new matrix. `m.mul_m(m.invert())` is
|
||||||
|
/// the identity matrix. Returns `None` if this matrix is not invertible
|
||||||
|
/// (has a determinant of zero).
|
||||||
|
#[must_use]
|
||||||
|
fn invert(&self) -> Option<Self>;
|
||||||
|
|
||||||
|
/// Invert this matrix in-place.
|
||||||
|
#[inline]
|
||||||
|
fn invert_self(&mut self) {
|
||||||
|
*self = self.invert().expect("Attempted to invert a matrix with zero determinant.");
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Test if this matrix is invertible.
|
||||||
|
#[inline]
|
||||||
|
fn is_invertible(&self) -> bool { !self.determinant().approx_eq(&Self::Scalar::zero()) }
|
||||||
|
|
||||||
|
/// Test if this matrix is the identity matrix. That is, it is diagonal
|
||||||
|
/// and every element in the diagonal is one.
|
||||||
|
#[inline]
|
||||||
|
fn is_identity(&self) -> bool { self.approx_eq(&Self::identity()) }
|
||||||
|
|
||||||
|
/// Test if this is a diagonal matrix. That is, every element outside of
|
||||||
|
/// the diagonal is 0.
|
||||||
|
fn is_diagonal(&self) -> bool;
|
||||||
|
|
||||||
|
/// Test if this matrix is symmetric. That is, it is equal to its
|
||||||
|
/// transpose.
|
||||||
|
fn is_symmetric(&self) -> bool;
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Angles and their associated trigonometric functions.
|
||||||
|
///
|
||||||
|
/// Typed angles allow for the writing of self-documenting code that makes it
|
||||||
|
/// clear when semantic violations have occured - for example, adding degrees to
|
||||||
|
/// radians, or adding a number to an angle.
|
||||||
|
///
|
||||||
|
pub trait Angle where
|
||||||
|
Self: Copy + Clone,
|
||||||
|
Self: PartialEq + cmp::PartialOrd,
|
||||||
|
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
||||||
|
Self: ApproxEq<Epsilon = <Self as Angle>::Unitless>,
|
||||||
|
|
||||||
|
Self: Neg<Output = Self>,
|
||||||
|
Self: Add<Self, Output = Self>,
|
||||||
|
Self: Sub<Self, Output = Self>,
|
||||||
|
Self: Rem<Self, Output = Self>,
|
||||||
|
Self: Mul<<Self as Angle>::Unitless, Output = Self>,
|
||||||
|
Self: Div<Self, Output = <Self as Angle>::Unitless>,
|
||||||
|
Self: Div<<Self as Angle>::Unitless, Output = Self>,
|
||||||
|
{
|
||||||
|
type Unitless: BaseFloat;
|
||||||
|
|
||||||
|
/// Return the angle, normalized to the range `[0, full_turn)`.
|
||||||
|
#[inline]
|
||||||
|
fn normalize(self) -> Self {
|
||||||
|
let rem = self % Self::full_turn();
|
||||||
|
if rem < Self::zero() { rem + Self::full_turn() } else { rem }
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Return the angle rotated by half a turn.
|
||||||
|
#[inline]
|
||||||
|
fn opposite(self) -> Self {
|
||||||
|
Self::normalize(self + Self::turn_div_2())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Returns the interior bisector of the two angles.
|
||||||
|
#[inline]
|
||||||
|
fn bisect(self, other: Self) -> Self {
|
||||||
|
let half = cast(0.5f64).unwrap();
|
||||||
|
Self::normalize((self - other) * half + self)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The additive identity.
|
||||||
|
///
|
||||||
|
/// Adding this to another angle has no affect.
|
||||||
|
///
|
||||||
|
/// For example:
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Deg;
|
||||||
|
///
|
||||||
|
/// let v = Deg::new(180.0);
|
||||||
|
/// assert_eq!(v + Deg::zero(), v);
|
||||||
|
/// ```
|
||||||
|
fn zero() -> Self;
|
||||||
|
|
||||||
|
/// A full rotation.
|
||||||
|
fn full_turn() -> Self;
|
||||||
|
|
||||||
|
/// Half of a full rotation.
|
||||||
|
fn turn_div_2() -> Self;
|
||||||
|
|
||||||
|
/// A third of a full rotation.
|
||||||
|
fn turn_div_3() -> Self;
|
||||||
|
|
||||||
|
/// A quarter of a full rotation.
|
||||||
|
fn turn_div_4() -> Self;
|
||||||
|
|
||||||
|
/// A sixth of a full rotation.
|
||||||
|
fn turn_div_6() -> Self;
|
||||||
|
|
||||||
|
/// Compute the sine of the angle, returning a unitless ratio.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle = Rad::new(35.0);
|
||||||
|
/// let ratio: f32 = Rad::sin(angle);
|
||||||
|
/// ```
|
||||||
|
fn sin(self) -> Self::Unitless;
|
||||||
|
|
||||||
|
/// Compute the cosine of the angle, returning a unitless ratio.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle = Rad::new(35.0);
|
||||||
|
/// let ratio: f32 = Rad::cos(angle);
|
||||||
|
/// ```
|
||||||
|
fn cos(self) -> Self::Unitless;
|
||||||
|
|
||||||
|
/// Compute the tangent of the angle, returning a unitless ratio.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle = Rad::new(35.0);
|
||||||
|
/// let ratio: f32 = Rad::tan(angle);
|
||||||
|
/// ```
|
||||||
|
fn tan(self) -> Self::Unitless;
|
||||||
|
|
||||||
|
/// Compute the sine and cosine of the angle, returning the result as a
|
||||||
|
/// pair.
|
||||||
|
///
|
||||||
|
/// This does not have any performance benefits, but calculating both the
|
||||||
|
/// sine and cosine of a single angle is a common operation.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle = Rad::new(35.0);
|
||||||
|
/// let (s, c) = Rad::sin_cos(angle);
|
||||||
|
/// ```
|
||||||
|
fn sin_cos(self) -> (Self::Unitless, Self::Unitless);
|
||||||
|
|
||||||
|
/// Compute the cosecant of the angle.
|
||||||
|
///
|
||||||
|
/// This is the same as computing the reciprocal of `Self::sin`.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle = Rad::new(35.0);
|
||||||
|
/// let ratio: f32 = Rad::csc(angle);
|
||||||
|
/// ```
|
||||||
|
#[inline]
|
||||||
|
fn csc(self) -> Self::Unitless {
|
||||||
|
Self::sin(self).recip()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Compute the secant of the angle.
|
||||||
|
///
|
||||||
|
/// This is the same as computing the reciprocal of `Self::tan`.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle = Rad::new(35.0);
|
||||||
|
/// let ratio: f32 = Rad::cot(angle);
|
||||||
|
/// ```
|
||||||
|
#[inline]
|
||||||
|
fn cot(self) -> Self::Unitless {
|
||||||
|
Self::tan(self).recip()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Compute the cotatangent of the angle.
|
||||||
|
///
|
||||||
|
/// This is the same as computing the reciprocal of `Self::cos`.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle = Rad::new(35.0);
|
||||||
|
/// let ratio: f32 = Rad::sec(angle);
|
||||||
|
/// ```
|
||||||
|
#[inline]
|
||||||
|
fn sec(self) -> Self::Unitless {
|
||||||
|
Self::cos(self).recip()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Compute the arcsine of the ratio, returning the resulting angle.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle: Rad<f32> = Rad::asin(0.5);
|
||||||
|
/// ```
|
||||||
|
fn asin(ratio: Self::Unitless) -> Self;
|
||||||
|
|
||||||
|
/// Compute the arccosine of the ratio, returning the resulting angle.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle: Rad<f32> = Rad::acos(0.5);
|
||||||
|
/// ```
|
||||||
|
fn acos(ratio: Self::Unitless) -> Self;
|
||||||
|
|
||||||
|
/// Compute the arctangent of the ratio, returning the resulting angle.
|
||||||
|
///
|
||||||
|
/// ```rust
|
||||||
|
/// use cgmath::prelude::*;
|
||||||
|
/// use cgmath::Rad;
|
||||||
|
///
|
||||||
|
/// let angle: Rad<f32> = Rad::atan(0.5);
|
||||||
|
/// ```
|
||||||
|
fn atan(ratio: Self::Unitless) -> Self;
|
||||||
|
|
||||||
|
fn atan2(a: Self::Unitless, b: Self::Unitless) -> Self;
|
||||||
|
}
|
||||||
|
|
@ -17,12 +17,14 @@ use std::fmt;
|
||||||
|
|
||||||
use rust_num::{Zero, One};
|
use rust_num::{Zero, One};
|
||||||
|
|
||||||
|
use structure::*;
|
||||||
|
|
||||||
use approx::ApproxEq;
|
use approx::ApproxEq;
|
||||||
use matrix::*;
|
use matrix::{Matrix2, Matrix3, Matrix4};
|
||||||
use num::*;
|
use num::{BaseFloat, BaseNum};
|
||||||
use point::*;
|
use point::{Point2, Point3};
|
||||||
use rotation::*;
|
use rotation::*;
|
||||||
use vector::*;
|
use vector::{Vector2, Vector3};
|
||||||
|
|
||||||
/// A trait representing an [affine
|
/// A trait representing an [affine
|
||||||
/// transformation](https://en.wikipedia.org/wiki/Affine_transformation) that
|
/// transformation](https://en.wikipedia.org/wiki/Affine_transformation) that
|
||||||
|
|
@ -87,7 +89,7 @@ impl<P: EuclideanSpace, R: Rotation<P>> Transform<P> for Decomposed<P::Diff, R>
|
||||||
#[inline]
|
#[inline]
|
||||||
fn one() -> Decomposed<P::Diff, R> {
|
fn one() -> Decomposed<P::Diff, R> {
|
||||||
Decomposed {
|
Decomposed {
|
||||||
scale: <P as EuclideanSpace>::Scalar::one(),
|
scale: P::Scalar::one(),
|
||||||
rot: R::one(),
|
rot: R::one(),
|
||||||
disp: P::Diff::zero(),
|
disp: P::Diff::zero(),
|
||||||
}
|
}
|
||||||
|
|
@ -98,7 +100,7 @@ impl<P: EuclideanSpace, R: Rotation<P>> Transform<P> for Decomposed<P::Diff, R>
|
||||||
let rot = R::look_at(center - eye, up);
|
let rot = R::look_at(center - eye, up);
|
||||||
let disp = rot.rotate_vector(P::origin() - eye);
|
let disp = rot.rotate_vector(P::origin() - eye);
|
||||||
Decomposed {
|
Decomposed {
|
||||||
scale: <P as EuclideanSpace>::Scalar::one(),
|
scale: P::Scalar::one(),
|
||||||
rot: rot,
|
rot: rot,
|
||||||
disp: disp,
|
disp: disp,
|
||||||
}
|
}
|
||||||
|
|
@ -123,10 +125,10 @@ impl<P: EuclideanSpace, R: Rotation<P>> Transform<P> for Decomposed<P::Diff, R>
|
||||||
}
|
}
|
||||||
|
|
||||||
fn invert(&self) -> Option<Decomposed<P::Diff, R>> {
|
fn invert(&self) -> Option<Decomposed<P::Diff, R>> {
|
||||||
if self.scale.approx_eq(&<P as EuclideanSpace>::Scalar::zero()) {
|
if self.scale.approx_eq(&P::Scalar::zero()) {
|
||||||
None
|
None
|
||||||
} else {
|
} else {
|
||||||
let s = <P as EuclideanSpace>::Scalar::one() / self.scale;
|
let s = P::Scalar::one() / self.scale;
|
||||||
let r = self.rot.invert();
|
let r = self.rot.invert();
|
||||||
let d = r.rotate_vector(self.disp.clone()) * -s;
|
let d = r.rotate_vector(self.disp.clone()) * -s;
|
||||||
Some(Decomposed {
|
Some(Decomposed {
|
||||||
|
|
|
||||||
148
src/vector.rs
148
src/vector.rs
|
|
@ -13,90 +13,18 @@
|
||||||
// See the License for the specific language governing permissions and
|
// See the License for the specific language governing permissions and
|
||||||
// limitations under the License.
|
// limitations under the License.
|
||||||
|
|
||||||
|
use rand::{Rand, Rng};
|
||||||
|
use rust_num::{NumCast, Zero, One};
|
||||||
use std::fmt;
|
use std::fmt;
|
||||||
use std::mem;
|
use std::mem;
|
||||||
use std::ops::*;
|
use std::ops::*;
|
||||||
|
|
||||||
use rand::{Rand, Rng};
|
use structure::*;
|
||||||
|
|
||||||
use rust_num::{NumCast, Zero, One};
|
use angle::Rad;
|
||||||
|
|
||||||
use angle::{Angle, Rad};
|
|
||||||
use approx::ApproxEq;
|
use approx::ApproxEq;
|
||||||
use array::{Array, ElementWise};
|
|
||||||
use num::{BaseNum, BaseFloat, PartialOrd};
|
use num::{BaseNum, BaseFloat, PartialOrd};
|
||||||
|
|
||||||
/// Vectors that can be [added](http://mathworld.wolfram.com/VectorAddition.html)
|
|
||||||
/// together and [multiplied](https://en.wikipedia.org/wiki/Scalar_multiplication)
|
|
||||||
/// by scalars.
|
|
||||||
///
|
|
||||||
/// Examples include vectors, matrices, and quaternions.
|
|
||||||
///
|
|
||||||
/// # Required operators
|
|
||||||
///
|
|
||||||
/// ## Vector addition
|
|
||||||
///
|
|
||||||
/// Vectors can be added, subtracted, or negated via the following traits:
|
|
||||||
///
|
|
||||||
/// - `Add<Output = Self>`
|
|
||||||
/// - `Sub<Output = Self>`
|
|
||||||
/// - `Neg<Output = Self>`
|
|
||||||
///
|
|
||||||
/// ```rust
|
|
||||||
/// use cgmath::Vector3;
|
|
||||||
///
|
|
||||||
/// let velocity0 = Vector3::new(1, 2, 0);
|
|
||||||
/// let velocity1 = Vector3::new(1, 1, 0);
|
|
||||||
///
|
|
||||||
/// let total_velocity = velocity0 + velocity1;
|
|
||||||
/// let velocity_diff = velocity1 - velocity0;
|
|
||||||
/// let reversed_velocity0 = -velocity0;
|
|
||||||
/// ```
|
|
||||||
///
|
|
||||||
/// ## Scalar multiplication
|
|
||||||
///
|
|
||||||
/// Vectors can be multiplied or divided by their associated scalars via the
|
|
||||||
/// following traits:
|
|
||||||
///
|
|
||||||
/// - `Mul<Self::Scalar, Output = Self>`
|
|
||||||
/// - `Div<Self::Scalar, Output = Self>`
|
|
||||||
/// - `Rem<Self::Scalar, Output = Self>`
|
|
||||||
///
|
|
||||||
/// ```rust
|
|
||||||
/// use cgmath::Vector2;
|
|
||||||
///
|
|
||||||
/// let translation = Vector2::new(3.0, 4.0);
|
|
||||||
/// let scale_factor = 2.0;
|
|
||||||
///
|
|
||||||
/// let upscaled_translation = translation * scale_factor;
|
|
||||||
/// let downscaled_translation = translation / scale_factor;
|
|
||||||
/// ```
|
|
||||||
pub trait VectorSpace: Copy + Clone where
|
|
||||||
Self: Add<Self, Output = Self>,
|
|
||||||
Self: Sub<Self, Output = Self>,
|
|
||||||
|
|
||||||
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
|
||||||
Self: Mul<<Self as VectorSpace>::Scalar, Output = Self>,
|
|
||||||
Self: Div<<Self as VectorSpace>::Scalar, Output = Self>,
|
|
||||||
Self: Rem<<Self as VectorSpace>::Scalar, Output = Self>,
|
|
||||||
{
|
|
||||||
/// The associated scalar.
|
|
||||||
type Scalar: BaseNum;
|
|
||||||
|
|
||||||
/// The additive identity.
|
|
||||||
///
|
|
||||||
/// Adding this to another `Self` value has no effect.
|
|
||||||
///
|
|
||||||
/// ```rust
|
|
||||||
/// use cgmath::prelude::*;
|
|
||||||
/// use cgmath::Vector2;
|
|
||||||
///
|
|
||||||
/// let v = Vector2::new(1, 2);
|
|
||||||
/// assert_eq!(v + Vector2::zero(), v);
|
|
||||||
/// ```
|
|
||||||
fn zero() -> Self;
|
|
||||||
}
|
|
||||||
|
|
||||||
/// A 2-dimensional vector.
|
/// A 2-dimensional vector.
|
||||||
///
|
///
|
||||||
/// This type is marked as `#[repr(C, packed)]`.
|
/// This type is marked as `#[repr(C, packed)]`.
|
||||||
|
|
@ -451,74 +379,6 @@ impl<S: BaseNum> Vector4<S> {
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
/// Vectors that also have a [dot](https://en.wikipedia.org/wiki/Dot_product)
|
|
||||||
/// (or [inner](https://en.wikipedia.org/wiki/Inner_product_space)) product.
|
|
||||||
///
|
|
||||||
/// The dot product allows for the definition of other useful operations, like
|
|
||||||
/// finding the magnitude of a vector or normalizing it.
|
|
||||||
///
|
|
||||||
/// Examples include vectors and quaternions.
|
|
||||||
pub trait InnerSpace: VectorSpace + Sized where
|
|
||||||
// FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
|
|
||||||
<Self as VectorSpace>::Scalar: BaseFloat,
|
|
||||||
Self: ApproxEq<Epsilon = <Self as VectorSpace>::Scalar>,
|
|
||||||
{
|
|
||||||
/// Vector dot (or inner) product.
|
|
||||||
fn dot(self, other: Self) -> Self::Scalar;
|
|
||||||
|
|
||||||
/// Returns `true` if the vector is perpendicular (at right angles) to the
|
|
||||||
/// other vector.
|
|
||||||
fn is_perpendicular(self, other: Self) -> bool {
|
|
||||||
Self::dot(self, other).approx_eq(&Self::Scalar::zero())
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Returns the squared magnitude of the vector.
|
|
||||||
///
|
|
||||||
/// This does not perform an expensive square root operation like in
|
|
||||||
/// `Vector::magnitude` method, and so can be used to compare vectors more
|
|
||||||
/// efficiently.
|
|
||||||
#[inline]
|
|
||||||
fn magnitude2(self) -> Self::Scalar {
|
|
||||||
Self::dot(self, self)
|
|
||||||
}
|
|
||||||
|
|
||||||
/// The distance from the tail to the tip of the vector.
|
|
||||||
#[inline]
|
|
||||||
fn magnitude(self) -> Self::Scalar {
|
|
||||||
use rust_num::Float;
|
|
||||||
|
|
||||||
// FIXME: Not sure why we can't use method syntax for `sqrt` here...
|
|
||||||
Float::sqrt(self.magnitude2())
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Returns the angle between two vectors in radians.
|
|
||||||
fn angle(self, other: Self) -> Rad<Self::Scalar> {
|
|
||||||
Rad::acos(Self::dot(self, other) / (self.magnitude() * other.magnitude()))
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Returns a vector with the same direction, but with a magnitude of `1`.
|
|
||||||
#[inline]
|
|
||||||
#[must_use]
|
|
||||||
fn normalize(self) -> Self {
|
|
||||||
self.normalize_to(Self::Scalar::one())
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Returns a vector with the same direction and a given magnitude.
|
|
||||||
#[inline]
|
|
||||||
#[must_use]
|
|
||||||
fn normalize_to(self, magnitude: Self::Scalar) -> Self {
|
|
||||||
self * (magnitude / self.magnitude())
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Returns the result of linearly interpolating the magnitude of the vector
|
|
||||||
/// towards the magnitude of `other` by the specified amount.
|
|
||||||
#[inline]
|
|
||||||
#[must_use]
|
|
||||||
fn lerp(self, other: Self, amount: Self::Scalar) -> Self {
|
|
||||||
self + ((other - self) * amount)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Dot product of two vectors.
|
/// Dot product of two vectors.
|
||||||
#[inline]
|
#[inline]
|
||||||
pub fn dot<V: InnerSpace>(a: V, b: V) -> V::Scalar where
|
pub fn dot<V: InnerSpace>(a: V, b: V) -> V::Scalar where
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue