638 lines
16 KiB
Rust
638 lines
16 KiB
Rust
/*!
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# nalgebra
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**nalgebra** is a linear algebra library written for Rust targeting:
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* General-purpose linear algebra (still lacks a lot of features…)
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* Real time computer graphics.
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* Real time computer physics.
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## Using **nalgebra**
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You will need the last stable build of the [rust compiler](http://www.rust-lang.org)
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and the official package manager: [cargo](https://github.com/rust-lang/cargo).
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Simply add the following to your `Cargo.toml` file:
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```.ignore
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[dependencies]
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nalgebra = "0.16"
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```
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Most useful functionalities of **nalgebra** are grouped in the root module `nalgebra::`.
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However, the recommended way to use **nalgebra** is to import types and traits
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explicitly, and call free-functions using the `na::` prefix:
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```.rust
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#[macro_use]
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extern crate approx; // For the macro relative_eq!
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extern crate nalgebra as na;
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use na::{Vector3, Rotation3};
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fn main() {
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let axis = Vector3::x_axis();
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let angle = 1.57;
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let b = Rotation3::from_axis_angle(&axis, angle);
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relative_eq!(b.axis().unwrap(), axis);
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relative_eq!(b.angle(), angle);
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}
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```
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## Features
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**nalgebra** is meant to be a general-purpose, low-dimensional, linear algebra library, with
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an optimized set of tools for computer graphics and physics. Those features include:
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* A single parametrizable type `Matrix` for vectors, (square or rectangular) matrices, and slices
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with dimensions known either at compile-time (using type-level integers) or at runtime.
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* Matrices and vectors with compile-time sizes are statically allocated while dynamic ones are
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allocated on the heap.
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* Convenient aliases for low-dimensional matrices and vectors: `Vector1` to `Vector6` and
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`Matrix1x1` to `Matrix6x6`, including rectangular matrices like `Matrix2x5`.
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* Points sizes known at compile time, and convenience aliases: `Point1` to `Point6`.
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* Translation (seen as a transformation that composes by multiplication): `Translation2`,
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`Translation3`.
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* Rotation matrices: `Rotation2`, `Rotation3`.
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* Quaternions: `Quaternion`, `UnitQuaternion` (for 3D rotation).
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* Unit complex numbers can be used for 2D rotation: `UnitComplex`.
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* Algebraic entities with a norm equal to one: `Unit<T>`, e.g., `Unit<Vector3<f32>>`.
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* Isometries (translation ⨯ rotation): `Isometry2`, `Isometry3`
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* Similarity transformations (translation ⨯ rotation ⨯ uniform scale): `Similarity2`, `Similarity3`.
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* Affine transformations stored as an homogeneous matrix: `Affine2`, `Affine3`.
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* Projective (i.e. invertible) transformations stored as an homogeneous matrix: `Projective2`,
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`Projective3`.
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* General transformations that does not have to be invertible, stored as an homogeneous matrix:
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`Transform2`, `Transform3`.
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* 3D projections for computer graphics: `Perspective3`, `Orthographic3`.
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* Matrix factorizations: `Cholesky`, `QR`, `LU`, `FullPivLU`, `SVD`, `RealSchur`, `Hessenberg`, `SymmetricEigen`.
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* Insertion and removal of rows of columns of a matrix.
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* Implements traits from the [alga](https://crates.io/crates/alga) crate for
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generic programming.
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*/
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// #![feature(plugin)]
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//
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// #![plugin(clippy)]
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#![deny(non_camel_case_types)]
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#![deny(unused_parens)]
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#![deny(non_upper_case_globals)]
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#![deny(unused_qualifications)]
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#![deny(unused_results)]
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#![deny(missing_docs)]
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#![warn(incoherent_fundamental_impls)]
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#![doc(html_favicon_url = "http://nalgebra.org/img/favicon.ico",
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html_root_url = "http://nalgebra.org/rustdoc")]
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#![cfg_attr(not(feature = "std"), no_std)]
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#![cfg_attr(all(feature = "alloc", not(feature = "std")), feature(alloc))]
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#[cfg(feature = "arbitrary")]
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extern crate quickcheck;
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#[cfg(feature = "serde")]
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extern crate serde;
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#[cfg(feature = "serde")]
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#[macro_use]
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extern crate serde_derive;
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#[cfg(feature = "abomonation-serialize")]
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extern crate abomonation;
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#[cfg(feature = "mint")]
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extern crate mint;
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#[macro_use]
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extern crate approx;
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extern crate generic_array;
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#[cfg(feature = "std")]
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extern crate matrixmultiply;
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extern crate num_complex;
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extern crate num_traits as num;
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extern crate rand;
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extern crate typenum;
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extern crate alga;
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#[cfg(all(feature = "alloc", not(feature = "std")))]
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extern crate alloc;
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#[cfg(not(feature = "std"))]
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extern crate core as std;
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pub mod base;
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#[cfg(feature = "debug")]
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pub mod debug;
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pub mod geometry;
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pub mod linalg;
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#[cfg(feature = "std")]
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#[deprecated(
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note = "The 'core' module is being renamed to 'base' to avoid conflicts with the 'core' crate."
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)]
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pub use base as core;
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pub use base::*;
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pub use geometry::*;
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pub use linalg::*;
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use std::cmp::{self, Ordering, PartialOrd};
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use alga::general::{
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Additive, AdditiveGroup, Identity, Inverse, JoinSemilattice, Lattice, MeetSemilattice,
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Multiplicative, SupersetOf,
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};
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use alga::linear::SquareMatrix as AlgaSquareMatrix;
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use alga::linear::{EuclideanSpace, FiniteDimVectorSpace, InnerSpace, NormedSpace};
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use num::Signed;
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pub use alga::general::{Id, Real};
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/*
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*
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* Multiplicative identity.
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*
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*/
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/// Gets the ubiquitous multiplicative identity element.
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///
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/// Same as `Id::new()`.
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#[inline]
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pub fn id() -> Id {
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Id::new()
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}
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/// Gets the multiplicative identity element.
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///
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/// # See also:
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///
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/// * [`origin`](../nalgebra/fn.origin.html)
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/// * [`zero`](fn.zero.html)
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#[inline]
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pub fn one<T: Identity<Multiplicative>>() -> T {
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T::identity()
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}
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/// Gets the additive identity element.
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///
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/// # See also:
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///
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/// * [`one`](fn.one.html)
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/// * [`origin`](../nalgebra/fn.origin.html)
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#[inline]
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pub fn zero<T: Identity<Additive>>() -> T {
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T::identity()
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}
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/// Gets the origin of the given point.
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///
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/// # See also:
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///
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/// * [`one`](fn.one.html)
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/// * [`zero`](fn.zero.html)
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#[inline]
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pub fn origin<P: EuclideanSpace>() -> P {
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P::origin()
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}
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/*
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*
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* Dimension
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*
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*/
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/// The dimension of the given algebraic entity seen as a vector space.
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#[inline]
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pub fn dimension<V: FiniteDimVectorSpace>() -> usize {
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V::dimension()
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}
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/*
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*
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* Ordering
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*
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*/
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// XXX: this is very naive and could probably be optimized for specific types.
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// XXX: also, we might just want to use divisions, but assuming `val` is usually not far from `min`
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// or `max`, would it still be more efficient?
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/// Wraps `val` into the range `[min, max]` using modular arithmetics.
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///
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/// The range must not be empty.
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#[inline]
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pub fn wrap<T>(mut val: T, min: T, max: T) -> T
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where T: Copy + PartialOrd + AdditiveGroup {
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assert!(min < max, "Invalid wrapping bounds.");
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let width = max - min;
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if val < min {
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val += width;
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while val < min {
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val += width
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}
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val
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} else if val > max {
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val -= width;
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while val > max {
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val -= width
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}
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val
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} else {
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val
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}
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}
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/// Returns a reference to the input value clamped to the interval `[min, max]`.
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///
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/// In particular:
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/// * If `min < val < max`, this returns `val`.
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/// * If `val <= min`, this returns `min`.
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/// * If `val >= max`, this returns `max`.
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#[inline]
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pub fn clamp<T: PartialOrd>(val: T, min: T, max: T) -> T {
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if val > min {
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if val < max {
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val
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} else {
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max
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}
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} else {
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min
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}
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}
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/// Same as `cmp::max`.
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#[inline]
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pub fn max<T: Ord>(a: T, b: T) -> T {
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cmp::max(a, b)
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}
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/// Same as `cmp::min`.
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#[inline]
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pub fn min<T: Ord>(a: T, b: T) -> T {
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cmp::min(a, b)
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}
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/// The absolute value of `a`.
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#[inline]
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pub fn abs<T: Signed>(a: &T) -> T {
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a.abs()
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}
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/// Returns the infimum of `a` and `b`.
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#[inline]
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pub fn inf<T: MeetSemilattice>(a: &T, b: &T) -> T {
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a.meet(b)
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}
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/// Returns the supremum of `a` and `b`.
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#[inline]
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pub fn sup<T: JoinSemilattice>(a: &T, b: &T) -> T {
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a.join(b)
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}
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/// Returns simultaneously the infimum and supremum of `a` and `b`.
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#[inline]
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pub fn inf_sup<T: Lattice>(a: &T, b: &T) -> (T, T) {
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a.meet_join(b)
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}
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/// Compare `a` and `b` using a partial ordering relation.
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#[inline]
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pub fn partial_cmp<T: PartialOrd>(a: &T, b: &T) -> Option<Ordering> {
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a.partial_cmp(b)
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}
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/// Returns `true` iff `a` and `b` are comparable and `a < b`.
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#[inline]
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pub fn partial_lt<T: PartialOrd>(a: &T, b: &T) -> bool {
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a.lt(b)
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}
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/// Returns `true` iff `a` and `b` are comparable and `a <= b`.
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#[inline]
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pub fn partial_le<T: PartialOrd>(a: &T, b: &T) -> bool {
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a.le(b)
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}
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/// Returns `true` iff `a` and `b` are comparable and `a > b`.
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#[inline]
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pub fn partial_gt<T: PartialOrd>(a: &T, b: &T) -> bool {
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a.gt(b)
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}
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/// Returns `true` iff `a` and `b` are comparable and `a >= b`.
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#[inline]
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pub fn partial_ge<T: PartialOrd>(a: &T, b: &T) -> bool {
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a.ge(b)
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}
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/// Return the minimum of `a` and `b` if they are comparable.
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#[inline]
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pub fn partial_min<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
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if let Some(ord) = a.partial_cmp(b) {
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match ord {
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Ordering::Greater => Some(b),
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_ => Some(a),
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}
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} else {
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None
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}
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}
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/// Return the maximum of `a` and `b` if they are comparable.
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#[inline]
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pub fn partial_max<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
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if let Some(ord) = a.partial_cmp(b) {
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match ord {
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Ordering::Less => Some(b),
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_ => Some(a),
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}
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} else {
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None
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}
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}
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/// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to
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/// `min` or `max`.
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#[inline]
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pub fn partial_clamp<'a, T: PartialOrd>(value: &'a T, min: &'a T, max: &'a T) -> Option<&'a T> {
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if let (Some(cmp_min), Some(cmp_max)) = (value.partial_cmp(min), value.partial_cmp(max)) {
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if cmp_min == Ordering::Less {
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Some(min)
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} else if cmp_max == Ordering::Greater {
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Some(max)
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} else {
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Some(value)
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}
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} else {
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None
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}
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}
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/// Sorts two values in increasing order using a partial ordering.
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#[inline]
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pub fn partial_sort2<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<(&'a T, &'a T)> {
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if let Some(ord) = a.partial_cmp(b) {
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match ord {
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Ordering::Less => Some((a, b)),
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_ => Some((b, a)),
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}
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} else {
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None
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}
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}
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/*
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* Inverse
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*/
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/// Tries to gets an inverted copy of a square matrix.
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///
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/// # See also:
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///
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/// * [`inverse`](fn.inverse.html)
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#[inline]
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pub fn try_inverse<M: AlgaSquareMatrix>(m: &M) -> Option<M> {
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m.try_inverse()
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}
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/// Computes the multiplicative inverse of an (always invertible) algebraic entity.
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///
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/// # See also:
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///
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/// * [`try_inverse`](fn.try_inverse.html)
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#[inline]
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pub fn inverse<M: Inverse<Multiplicative>>(m: &M) -> M {
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m.inverse()
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}
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/*
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* Inner vector space
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*/
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/// Computes the dot product of two vectors.
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#[inline]
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pub fn dot<V: FiniteDimVectorSpace>(a: &V, b: &V) -> V::Field {
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a.dot(b)
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}
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/// Computes the smallest angle between two vectors.
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#[inline]
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pub fn angle<V: InnerSpace>(a: &V, b: &V) -> V::Real {
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a.angle(b)
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}
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/*
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* Normed space
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*/
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/// Computes the L2 (Euclidean) norm of a vector.
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///
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/// # See also:
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///
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/// * [`magnitude`](fn.magnitude.html)
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/// * [`magnitude_squared`](fn.magnitude_squared.html)
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/// * [`norm_squared`](fn.norm_squared.html)
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#[inline]
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pub fn norm<V: NormedSpace>(v: &V) -> V::Field {
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v.norm()
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}
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/// Computes the squared L2 (Euclidean) norm of the vector `v`.
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///
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/// # See also:
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///
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/// * [`magnitude`](fn.magnitude.html)
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/// * [`magnitude_squared`](fn.magnitude_squared.html)
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/// * [`norm`](fn.norm.html)
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#[inline]
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pub fn norm_squared<V: NormedSpace>(v: &V) -> V::Field {
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v.norm_squared()
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}
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/// A synonym for [`norm`](fn.norm.html), aka length.
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///
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/// # See also:
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///
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/// * [`magnitude_squared`](fn.magnitude_squared.html)
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/// * [`norm`](fn.norm.html)
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/// * [`norm_squared`](fn.norm_squared.html)
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#[inline]
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pub fn magnitude<V: NormedSpace>(v: &V) -> V::Field {
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v.norm()
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}
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/// A synonym for [`norm_squared`](fn.norm_squared.html),
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/// aka length squared.
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///
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/// # See also:
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///
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/// * [`magnitude`](fn.magnitude.html)
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/// * [`norm`](fn.norm.html)
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/// * [`norm_squared`](fn.norm_squared.html)
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#[inline]
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pub fn magnitude_squared<V: NormedSpace>(v: &V) -> V::Field {
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v.norm_squared()
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}
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/// Computes the normalized version of the vector `v`.
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#[inline]
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pub fn normalize<V: NormedSpace>(v: &V) -> V {
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v.normalize()
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}
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/// Computes the normalized version of the vector `v` or returns `None` if its norm is smaller than `min_norm`.
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#[inline]
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pub fn try_normalize<V: NormedSpace>(v: &V, min_norm: V::Field) -> Option<V> {
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v.try_normalize(min_norm)
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}
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/*
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*
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* Point operations.
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*
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*/
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/// The center of two points.
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///
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/// # See also:
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///
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/// * [distance](fn.distance.html)
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/// * [distance_squared](fn.distance_squared.html)
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#[inline]
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pub fn center<P: EuclideanSpace>(p1: &P, p2: &P) -> P {
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P::from_coordinates((p1.coordinates() + p2.coordinates()) * convert(0.5))
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}
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/// The distance between two points.
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///
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/// # See also:
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///
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/// * [center](fn.center.html)
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/// * [distance_squared](fn.distance_squared.html)
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#[inline]
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pub fn distance<P: EuclideanSpace>(p1: &P, p2: &P) -> P::Real {
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(p2.coordinates() - p1.coordinates()).norm()
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}
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/// The squared distance between two points.
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///
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/// # See also:
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///
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/// * [center](fn.center.html)
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/// * [distance](fn.distance.html)
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#[inline]
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pub fn distance_squared<P: EuclideanSpace>(p1: &P, p2: &P) -> P::Real {
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(p2.coordinates() - p1.coordinates()).norm_squared()
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}
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/*
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* Cast
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*/
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/// Converts an object from one type to an equivalent or more general one.
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///
|
||
/// See also [`try_convert`](fn.try_convert.html) for conversion to more specific types.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [convert_ref](fn.convert_ref.html)
|
||
/// * [convert_ref_unchecked](fn.convert_ref_unchecked.html)
|
||
/// * [is_convertible](../nalgebra/fn.is_convertible.html)
|
||
/// * [try_convert](fn.try_convert.html)
|
||
/// * [try_convert_ref](fn.try_convert_ref.html)
|
||
#[inline]
|
||
pub fn convert<From, To: SupersetOf<From>>(t: From) -> To {
|
||
To::from_subset(&t)
|
||
}
|
||
|
||
/// Attempts to convert an object to a more specific one.
|
||
///
|
||
/// See also [`convert`](fn.convert.html) for conversion to more general types.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [convert](fn.convert.html)
|
||
/// * [convert_ref](fn.convert_ref.html)
|
||
/// * [convert_ref_unchecked](fn.convert_ref_unchecked.html)
|
||
/// * [is_convertible](../nalgebra/fn.is_convertible.html)
|
||
/// * [try_convert_ref](fn.try_convert_ref.html)
|
||
#[inline]
|
||
pub fn try_convert<From: SupersetOf<To>, To>(t: From) -> Option<To> {
|
||
t.to_subset()
|
||
}
|
||
|
||
/// Indicates if [`try_convert`](fn.try_convert.html) will succeed without
|
||
/// actually performing the conversion.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [convert](fn.convert.html)
|
||
/// * [convert_ref](fn.convert_ref.html)
|
||
/// * [convert_ref_unchecked](fn.convert_ref_unchecked.html)
|
||
/// * [try_convert](fn.try_convert.html)
|
||
/// * [try_convert_ref](fn.try_convert_ref.html)
|
||
#[inline]
|
||
pub fn is_convertible<From: SupersetOf<To>, To>(t: &From) -> bool {
|
||
t.is_in_subset()
|
||
}
|
||
|
||
/// Use with care! Same as [`try_convert`](fn.try_convert.html) but
|
||
/// without any property checks.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [convert](fn.convert.html)
|
||
/// * [convert_ref](fn.convert_ref.html)
|
||
/// * [convert_ref_unchecked](fn.convert_ref_unchecked.html)
|
||
/// * [is_convertible](../nalgebra/fn.is_convertible.html)
|
||
/// * [try_convert](fn.try_convert.html)
|
||
/// * [try_convert_ref](fn.try_convert_ref.html)
|
||
#[inline]
|
||
pub unsafe fn convert_unchecked<From: SupersetOf<To>, To>(t: From) -> To {
|
||
t.to_subset_unchecked()
|
||
}
|
||
|
||
/// Converts an object from one type to an equivalent or more general one.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [convert](fn.convert.html)
|
||
/// * [convert_ref_unchecked](fn.convert_ref_unchecked.html)
|
||
/// * [is_convertible](../nalgebra/fn.is_convertible.html)
|
||
/// * [try_convert](fn.try_convert.html)
|
||
/// * [try_convert_ref](fn.try_convert_ref.html)
|
||
#[inline]
|
||
pub fn convert_ref<From, To: SupersetOf<From>>(t: &From) -> To {
|
||
To::from_subset(t)
|
||
}
|
||
|
||
/// Attempts to convert an object to a more specific one.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [convert](fn.convert.html)
|
||
/// * [convert_ref](fn.convert_ref.html)
|
||
/// * [convert_ref_unchecked](fn.convert_ref_unchecked.html)
|
||
/// * [is_convertible](../nalgebra/fn.is_convertible.html)
|
||
/// * [try_convert](fn.try_convert.html)
|
||
#[inline]
|
||
pub fn try_convert_ref<From: SupersetOf<To>, To>(t: &From) -> Option<To> {
|
||
t.to_subset()
|
||
}
|
||
|
||
/// Use with care! Same as [`try_convert`](fn.try_convert.html) but
|
||
/// without any property checks.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [convert](fn.convert.html)
|
||
/// * [convert_ref](fn.convert_ref.html)
|
||
/// * [is_convertible](../nalgebra/fn.is_convertible.html)
|
||
/// * [try_convert](fn.try_convert.html)
|
||
/// * [try_convert_ref](fn.try_convert_ref.html)
|
||
#[inline]
|
||
pub unsafe fn convert_ref_unchecked<From: SupersetOf<To>, To>(t: &From) -> To {
|
||
t.to_subset_unchecked()
|
||
}
|