forked from M-Labs/nalgebra
541 lines
14 KiB
Rust
541 lines
14 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](https://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 = "0.23"
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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 a homogeneous matrix: `Affine2`, `Affine3`.
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* Projective (i.e. invertible) transformations stored as a homogeneous matrix: `Projective2`,
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`Projective3`.
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* General transformations that does not have to be invertible, stored as a 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`, `Schur`, `Hessenberg`, `SymmetricEigen`.
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* Insertion and removal of rows of columns of a matrix.
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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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#![doc(
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html_favicon_url = "https://nalgebra.org/img/favicon.ico",
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html_root_url = "https://nalgebra.org/rustdoc"
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)]
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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-serialize")]
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#[macro_use]
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extern crate serde;
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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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#[cfg(feature = "std")]
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extern crate matrixmultiply;
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extern crate num_traits as num;
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#[cfg(feature = "std")]
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extern crate rand_distr;
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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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#[cfg(feature = "io")]
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extern crate pest;
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#[macro_use]
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#[cfg(feature = "io")]
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extern crate pest_derive;
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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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#[cfg(feature = "io")]
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pub mod io;
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pub mod linalg;
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#[cfg(feature = "sparse")]
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pub mod sparse;
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pub use crate::base::*;
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pub use crate::geometry::*;
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pub use crate::linalg::*;
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#[cfg(feature = "sparse")]
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pub use crate::sparse::*;
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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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use simba::scalar::SupersetOf;
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use std::cmp::{self, Ordering, PartialOrd};
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use num::{One, Signed, Zero};
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use base::allocator::Allocator;
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pub use num_complex::Complex;
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pub use simba::scalar::{
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ClosedAdd, ClosedDiv, ClosedMul, ClosedSub, ComplexField, Field, RealField,
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};
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pub use simba::simd::{SimdBool, SimdComplexField, SimdPartialOrd, SimdRealField};
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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: One>() -> T {
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T::one()
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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: Zero>() -> T {
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T::zero()
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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
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T: Copy + PartialOrd + ClosedAdd + ClosedSub,
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{
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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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///
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/// Deprecated: Use [Matrix::abs] or [RealField::abs] instead.
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#[deprecated(note = "use the inherent method `Matrix::abs` or `RealField::abs` instead")]
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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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#[deprecated(note = "use the inherent method `Matrix::inf` instead")]
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#[inline]
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pub fn inf<N, R: Dim, C: Dim>(a: &MatrixMN<N, R, C>, b: &MatrixMN<N, R, C>) -> MatrixMN<N, R, C>
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where
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N: Scalar + SimdPartialOrd,
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DefaultAllocator: Allocator<N, R, C>,
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{
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a.inf(b)
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}
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/// Returns the supremum of `a` and `b`.
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#[deprecated(note = "use the inherent method `Matrix::sup` instead")]
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#[inline]
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pub fn sup<N, R: Dim, C: Dim>(a: &MatrixMN<N, R, C>, b: &MatrixMN<N, R, C>) -> MatrixMN<N, R, C>
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where
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N: Scalar + SimdPartialOrd,
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DefaultAllocator: Allocator<N, R, C>,
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{
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a.sup(b)
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}
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/// Returns simultaneously the infimum and supremum of `a` and `b`.
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#[deprecated(note = "use the inherent method `Matrix::inf_sup` instead")]
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#[inline]
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pub fn inf_sup<N, R: Dim, C: Dim>(
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a: &MatrixMN<N, R, C>,
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b: &MatrixMN<N, R, C>,
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) -> (MatrixMN<N, R, C>, MatrixMN<N, R, C>)
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where
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N: Scalar + SimdPartialOrd,
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DefaultAllocator: Allocator<N, R, C>,
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{
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a.inf_sup(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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|
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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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|
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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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* Point operations.
|
||
*
|
||
*/
|
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/// The center of two points.
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||
///
|
||
/// # See also:
|
||
///
|
||
/// * [distance](fn.distance.html)
|
||
/// * [distance_squared](fn.distance_squared.html)
|
||
#[inline]
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pub fn center<N: SimdComplexField, D: DimName>(p1: &Point<N, D>, p2: &Point<N, D>) -> Point<N, D>
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where
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DefaultAllocator: Allocator<N, D>,
|
||
{
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((&p1.coords + &p2.coords) * convert::<_, N>(0.5)).into()
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}
|
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|
||
/// The distance between two points.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [center](fn.center.html)
|
||
/// * [distance_squared](fn.distance_squared.html)
|
||
#[inline]
|
||
pub fn distance<N: SimdComplexField, D: DimName>(
|
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p1: &Point<N, D>,
|
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p2: &Point<N, D>,
|
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) -> N::SimdRealField
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
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(&p2.coords - &p1.coords).norm()
|
||
}
|
||
|
||
/// The squared distance between two points.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [center](fn.center.html)
|
||
/// * [distance](fn.distance.html)
|
||
#[inline]
|
||
pub fn distance_squared<N: SimdComplexField, D: DimName>(
|
||
p1: &Point<N, D>,
|
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p2: &Point<N, D>,
|
||
) -> N::SimdRealField
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
(&p2.coords - &p1.coords).norm_squared()
|
||
}
|
||
|
||
/*
|
||
* Cast
|
||
*/
|
||
/// Converts an object from one type to an equivalent or more general one.
|
||
///
|
||
/// 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 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 fn convert_ref_unchecked<From: SupersetOf<To>, To>(t: &From) -> To {
|
||
t.to_subset_unchecked()
|
||
}
|