forked from M-Labs/nalgebra
537 lines
14 KiB
Rust
537 lines
14 KiB
Rust
/*!
|
||
# nalgebra
|
||
|
||
**nalgebra** is a linear algebra library written for Rust targeting:
|
||
|
||
* General-purpose linear algebra (still lacks a lot of features…)
|
||
* Real-time computer graphics.
|
||
* Real-time computer physics.
|
||
|
||
## Using **nalgebra**
|
||
You will need the last stable build of the [rust compiler](https://www.rust-lang.org)
|
||
and the official package manager: [cargo](https://github.com/rust-lang/cargo).
|
||
|
||
Simply add the following to your `Cargo.toml` file:
|
||
|
||
```.ignore
|
||
[dependencies]
|
||
nalgebra = "0.18"
|
||
```
|
||
|
||
|
||
Most useful functionalities of **nalgebra** are grouped in the root module `nalgebra::`.
|
||
|
||
However, the recommended way to use **nalgebra** is to import types and traits
|
||
explicitly, and call free-functions using the `na::` prefix:
|
||
|
||
```.rust
|
||
#[macro_use]
|
||
extern crate approx; // For the macro relative_eq!
|
||
extern crate nalgebra as na;
|
||
use na::{Vector3, Rotation3};
|
||
|
||
fn main() {
|
||
let axis = Vector3::x_axis();
|
||
let angle = 1.57;
|
||
let b = Rotation3::from_axis_angle(&axis, angle);
|
||
|
||
relative_eq!(b.axis().unwrap(), axis);
|
||
relative_eq!(b.angle(), angle);
|
||
}
|
||
```
|
||
|
||
|
||
## Features
|
||
**nalgebra** is meant to be a general-purpose, low-dimensional, linear algebra library, with
|
||
an optimized set of tools for computer graphics and physics. Those features include:
|
||
|
||
* A single parametrizable type `Matrix` for vectors, (square or rectangular) matrices, and slices
|
||
with dimensions known either at compile-time (using type-level integers) or at runtime.
|
||
* Matrices and vectors with compile-time sizes are statically allocated while dynamic ones are
|
||
allocated on the heap.
|
||
* Convenient aliases for low-dimensional matrices and vectors: `Vector1` to `Vector6` and
|
||
`Matrix1x1` to `Matrix6x6`, including rectangular matrices like `Matrix2x5`.
|
||
* Points sizes known at compile time, and convenience aliases: `Point1` to `Point6`.
|
||
* Translation (seen as a transformation that composes by multiplication): `Translation2`,
|
||
`Translation3`.
|
||
* Rotation matrices: `Rotation2`, `Rotation3`.
|
||
* Quaternions: `Quaternion`, `UnitQuaternion` (for 3D rotation).
|
||
* Unit complex numbers can be used for 2D rotation: `UnitComplex`.
|
||
* Algebraic entities with a norm equal to one: `Unit<T>`, e.g., `Unit<Vector3<f32>>`.
|
||
* Isometries (translation ⨯ rotation): `Isometry2`, `Isometry3`
|
||
* Similarity transformations (translation ⨯ rotation ⨯ uniform scale): `Similarity2`, `Similarity3`.
|
||
* Affine transformations stored as a homogeneous matrix: `Affine2`, `Affine3`.
|
||
* Projective (i.e. invertible) transformations stored as a homogeneous matrix: `Projective2`,
|
||
`Projective3`.
|
||
* General transformations that does not have to be invertible, stored as a homogeneous matrix:
|
||
`Transform2`, `Transform3`.
|
||
* 3D projections for computer graphics: `Perspective3`, `Orthographic3`.
|
||
* Matrix factorizations: `Cholesky`, `QR`, `LU`, `FullPivLU`, `SVD`, `Schur`, `Hessenberg`, `SymmetricEigen`.
|
||
* Insertion and removal of rows of columns of a matrix.
|
||
*/
|
||
|
||
// #![feature(plugin)]
|
||
//
|
||
// #![plugin(clippy)]
|
||
|
||
#![deny(non_camel_case_types)]
|
||
#![deny(unused_parens)]
|
||
#![deny(non_upper_case_globals)]
|
||
#![deny(unused_qualifications)]
|
||
#![deny(unused_results)]
|
||
#![deny(missing_docs)]
|
||
#![doc(
|
||
html_favicon_url = "https://nalgebra.org/img/favicon.ico",
|
||
html_root_url = "https://nalgebra.org/rustdoc"
|
||
)]
|
||
#![cfg_attr(not(feature = "std"), no_std)]
|
||
#![cfg_attr(all(feature = "alloc", not(feature = "std")), feature(alloc))]
|
||
|
||
#[cfg(feature = "arbitrary")]
|
||
extern crate quickcheck;
|
||
|
||
#[cfg(feature = "serde-serialize")]
|
||
#[macro_use]
|
||
extern crate serde;
|
||
|
||
#[cfg(feature = "abomonation-serialize")]
|
||
extern crate abomonation;
|
||
|
||
#[cfg(feature = "mint")]
|
||
extern crate mint;
|
||
|
||
#[macro_use]
|
||
extern crate approx;
|
||
#[cfg(feature = "std")]
|
||
extern crate matrixmultiply;
|
||
extern crate num_traits as num;
|
||
#[cfg(feature = "std")]
|
||
extern crate rand_distr;
|
||
|
||
#[cfg(all(feature = "alloc", not(feature = "std")))]
|
||
extern crate alloc;
|
||
|
||
#[cfg(not(feature = "std"))]
|
||
extern crate core as std;
|
||
|
||
#[cfg(feature = "io")]
|
||
extern crate pest;
|
||
#[macro_use]
|
||
#[cfg(feature = "io")]
|
||
extern crate pest_derive;
|
||
|
||
pub mod base;
|
||
#[cfg(feature = "debug")]
|
||
pub mod debug;
|
||
pub mod geometry;
|
||
#[cfg(feature = "io")]
|
||
pub mod io;
|
||
pub mod linalg;
|
||
#[cfg(feature = "sparse")]
|
||
pub mod sparse;
|
||
|
||
pub use crate::base::*;
|
||
pub use crate::geometry::*;
|
||
pub use crate::linalg::*;
|
||
#[cfg(feature = "sparse")]
|
||
pub use crate::sparse::*;
|
||
#[cfg(feature = "std")]
|
||
#[deprecated(
|
||
note = "The 'core' module is being renamed to 'base' to avoid conflicts with the 'core' crate."
|
||
)]
|
||
pub use base as core;
|
||
|
||
use simba::scalar::SupersetOf;
|
||
use std::cmp::{self, Ordering, PartialOrd};
|
||
|
||
use num::{One, Signed, Zero};
|
||
|
||
use base::allocator::Allocator;
|
||
pub use num_complex::Complex;
|
||
pub use simba::scalar::{
|
||
ClosedAdd, ClosedDiv, ClosedMul, ClosedSub, ComplexField, Field, RealField,
|
||
};
|
||
pub use simba::simd::{SimdBool, SimdComplexField, SimdPartialOrd, SimdRealField};
|
||
|
||
/// Gets the multiplicative identity element.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [`origin`](../nalgebra/fn.origin.html)
|
||
/// * [`zero`](fn.zero.html)
|
||
#[inline]
|
||
pub fn one<T: One>() -> T {
|
||
T::one()
|
||
}
|
||
|
||
/// Gets the additive identity element.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [`one`](fn.one.html)
|
||
/// * [`origin`](../nalgebra/fn.origin.html)
|
||
#[inline]
|
||
pub fn zero<T: Zero>() -> T {
|
||
T::zero()
|
||
}
|
||
|
||
/*
|
||
*
|
||
* Ordering
|
||
*
|
||
*/
|
||
// XXX: this is very naive and could probably be optimized for specific types.
|
||
// XXX: also, we might just want to use divisions, but assuming `val` is usually not far from `min`
|
||
// or `max`, would it still be more efficient?
|
||
/// Wraps `val` into the range `[min, max]` using modular arithmetics.
|
||
///
|
||
/// The range must not be empty.
|
||
#[inline]
|
||
pub fn wrap<T>(mut val: T, min: T, max: T) -> T
|
||
where T: Copy + PartialOrd + ClosedAdd + ClosedSub {
|
||
assert!(min < max, "Invalid wrapping bounds.");
|
||
let width = max - min;
|
||
|
||
if val < min {
|
||
val += width;
|
||
|
||
while val < min {
|
||
val += width
|
||
}
|
||
|
||
val
|
||
} else if val > max {
|
||
val -= width;
|
||
|
||
while val > max {
|
||
val -= width
|
||
}
|
||
|
||
val
|
||
} else {
|
||
val
|
||
}
|
||
}
|
||
|
||
/// Returns a reference to the input value clamped to the interval `[min, max]`.
|
||
///
|
||
/// In particular:
|
||
/// * If `min < val < max`, this returns `val`.
|
||
/// * If `val <= min`, this returns `min`.
|
||
/// * If `val >= max`, this returns `max`.
|
||
#[inline]
|
||
pub fn clamp<T: PartialOrd>(val: T, min: T, max: T) -> T {
|
||
if val > min {
|
||
if val < max {
|
||
val
|
||
} else {
|
||
max
|
||
}
|
||
} else {
|
||
min
|
||
}
|
||
}
|
||
|
||
/// Same as `cmp::max`.
|
||
#[inline]
|
||
pub fn max<T: Ord>(a: T, b: T) -> T {
|
||
cmp::max(a, b)
|
||
}
|
||
|
||
/// Same as `cmp::min`.
|
||
#[inline]
|
||
pub fn min<T: Ord>(a: T, b: T) -> T {
|
||
cmp::min(a, b)
|
||
}
|
||
|
||
/// The absolute value of `a`.
|
||
///
|
||
/// Deprecated: Use [Matrix::abs] or [RealField::abs] instead.
|
||
#[deprecated(note = "use the inherent method `Matrix::abs` or `RealField::abs` instead")]
|
||
#[inline]
|
||
pub fn abs<T: Signed>(a: &T) -> T {
|
||
a.abs()
|
||
}
|
||
|
||
/// Returns the infimum of `a` and `b`.
|
||
#[deprecated(note = "use the inherent method `Matrix::inf` instead")]
|
||
#[inline]
|
||
pub fn inf<N, R: Dim, C: Dim>(a: &MatrixMN<N, R, C>, b: &MatrixMN<N, R, C>) -> MatrixMN<N, R, C>
|
||
where
|
||
N: Scalar + SimdPartialOrd,
|
||
DefaultAllocator: Allocator<N, R, C>,
|
||
{
|
||
a.inf(b)
|
||
}
|
||
|
||
/// Returns the supremum of `a` and `b`.
|
||
#[deprecated(note = "use the inherent method `Matrix::sup` instead")]
|
||
#[inline]
|
||
pub fn sup<N, R: Dim, C: Dim>(a: &MatrixMN<N, R, C>, b: &MatrixMN<N, R, C>) -> MatrixMN<N, R, C>
|
||
where
|
||
N: Scalar + SimdPartialOrd,
|
||
DefaultAllocator: Allocator<N, R, C>,
|
||
{
|
||
a.sup(b)
|
||
}
|
||
|
||
/// Returns simultaneously the infimum and supremum of `a` and `b`.
|
||
#[deprecated(note = "use the inherent method `Matrix::inf_sup` instead")]
|
||
#[inline]
|
||
pub fn inf_sup<N, R: Dim, C: Dim>(
|
||
a: &MatrixMN<N, R, C>,
|
||
b: &MatrixMN<N, R, C>,
|
||
) -> (MatrixMN<N, R, C>, MatrixMN<N, R, C>)
|
||
where
|
||
N: Scalar + SimdPartialOrd,
|
||
DefaultAllocator: Allocator<N, R, C>,
|
||
{
|
||
a.inf_sup(b)
|
||
}
|
||
|
||
/// Compare `a` and `b` using a partial ordering relation.
|
||
#[inline]
|
||
pub fn partial_cmp<T: PartialOrd>(a: &T, b: &T) -> Option<Ordering> {
|
||
a.partial_cmp(b)
|
||
}
|
||
|
||
/// Returns `true` iff `a` and `b` are comparable and `a < b`.
|
||
#[inline]
|
||
pub fn partial_lt<T: PartialOrd>(a: &T, b: &T) -> bool {
|
||
a.lt(b)
|
||
}
|
||
|
||
/// Returns `true` iff `a` and `b` are comparable and `a <= b`.
|
||
#[inline]
|
||
pub fn partial_le<T: PartialOrd>(a: &T, b: &T) -> bool {
|
||
a.le(b)
|
||
}
|
||
|
||
/// Returns `true` iff `a` and `b` are comparable and `a > b`.
|
||
#[inline]
|
||
pub fn partial_gt<T: PartialOrd>(a: &T, b: &T) -> bool {
|
||
a.gt(b)
|
||
}
|
||
|
||
/// Returns `true` iff `a` and `b` are comparable and `a >= b`.
|
||
#[inline]
|
||
pub fn partial_ge<T: PartialOrd>(a: &T, b: &T) -> bool {
|
||
a.ge(b)
|
||
}
|
||
|
||
/// Return the minimum of `a` and `b` if they are comparable.
|
||
#[inline]
|
||
pub fn partial_min<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
|
||
if let Some(ord) = a.partial_cmp(b) {
|
||
match ord {
|
||
Ordering::Greater => Some(b),
|
||
_ => Some(a),
|
||
}
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/// Return the maximum of `a` and `b` if they are comparable.
|
||
#[inline]
|
||
pub fn partial_max<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
|
||
if let Some(ord) = a.partial_cmp(b) {
|
||
match ord {
|
||
Ordering::Less => Some(b),
|
||
_ => Some(a),
|
||
}
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to
|
||
/// `min` or `max`.
|
||
#[inline]
|
||
pub fn partial_clamp<'a, T: PartialOrd>(value: &'a T, min: &'a T, max: &'a T) -> Option<&'a T> {
|
||
if let (Some(cmp_min), Some(cmp_max)) = (value.partial_cmp(min), value.partial_cmp(max)) {
|
||
if cmp_min == Ordering::Less {
|
||
Some(min)
|
||
} else if cmp_max == Ordering::Greater {
|
||
Some(max)
|
||
} else {
|
||
Some(value)
|
||
}
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/// Sorts two values in increasing order using a partial ordering.
|
||
#[inline]
|
||
pub fn partial_sort2<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<(&'a T, &'a T)> {
|
||
if let Some(ord) = a.partial_cmp(b) {
|
||
match ord {
|
||
Ordering::Less => Some((a, b)),
|
||
_ => Some((b, a)),
|
||
}
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/*
|
||
*
|
||
* Point operations.
|
||
*
|
||
*/
|
||
/// The center of two points.
|
||
///
|
||
/// # See also:
|
||
///
|
||
/// * [distance](fn.distance.html)
|
||
/// * [distance_squared](fn.distance_squared.html)
|
||
#[inline]
|
||
pub fn center<N: SimdComplexField, D: DimName>(p1: &Point<N, D>, p2: &Point<N, D>) -> Point<N, D>
|
||
where DefaultAllocator: Allocator<N, D> {
|
||
((&p1.coords + &p2.coords) * convert::<_, N>(0.5)).into()
|
||
}
|
||
|
||
/// 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>(
|
||
p1: &Point<N, D>,
|
||
p2: &Point<N, D>,
|
||
) -> N::SimdRealField
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
(&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>,
|
||
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()
|
||
}
|