nalgebra/src/lib.rs

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/*!
# nalgebra
**nalgebra** is a low-dimensional linear algebra library written for Rust targeting:
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* low-dimensional general-purpose linear algebra (still lacks a lot of features).
* real time computer graphics.
* real time computer physics.
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An on-line version of this documentation is available [here](http://nalgebra.org/doc/nalgebra).
## Using **nalgebra**
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All the functionality of **nalgebra** is grouped in one place: the root module `nalgebra::`. This
module re-exports everything and includes free functions for all traits methods performing
out-of-place operations.
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* You can import the whole prelude using:
```.ignore
use nalgebra::*;
```
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The preferred way to use **nalgebra** is to import types and traits explicitly, and call
Api change: deal with inplace/out of place methods. Before, it was too easy to use an out of place method instead of the inplace one since they name were pretty mutch the same. This kind of confusion may lead to silly bugs very hard to understand. Thus the following changes have been made when a method is available both inplace and out-of-place: * inplace version keep a short name. * out-of-place version are suffixed by `_cpy` (meaning `copy`), and are static methods. Methods applying transformations (rotation, translation or general transform) are now prefixed by `append`, and a `prepend` version is available too. Also, free functions doing in-place modifications dont really make sense. They have been removed. Here are the naming changes: * `invert` -> `inv` * `inverted` -> `Inv::inv_cpy` * `transpose` -> `transpose` * `transposed` -> `Transpose::transpose_cpy` * `transform_by` -> `append_transformation` * `transformed` -> `Transform::append_transformation_cpy` * `rotate_by` -> `apppend_rotation` * `rotated` -> `Rotation::append_rotation_cpy` * `translate_by` -> `apppend_translation` * `translate` -> `Translation::append_translation_cpy` * `normalized` -> `Norm::normalize_cpy` * `rotated_wrt_point` -> `RotationWithTranslation::append_rotation_wrt_point_cpy` * `rotated_wrt_center` -> `RotationWithTranslation::append_rotation_wrt_center_cpy` Note that using those static methods is very verbose, and using in-place methods require an explicit import of the related trait. This is a way to convince the user to use free functions most of the time.
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free-functions using the `na::` prefix:
```.rust
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extern crate nalgebra as na;
use na::{Vec3, Rot3, Rotation};
Api change: deal with inplace/out of place methods. Before, it was too easy to use an out of place method instead of the inplace one since they name were pretty mutch the same. This kind of confusion may lead to silly bugs very hard to understand. Thus the following changes have been made when a method is available both inplace and out-of-place: * inplace version keep a short name. * out-of-place version are suffixed by `_cpy` (meaning `copy`), and are static methods. Methods applying transformations (rotation, translation or general transform) are now prefixed by `append`, and a `prepend` version is available too. Also, free functions doing in-place modifications dont really make sense. They have been removed. Here are the naming changes: * `invert` -> `inv` * `inverted` -> `Inv::inv_cpy` * `transpose` -> `transpose` * `transposed` -> `Transpose::transpose_cpy` * `transform_by` -> `append_transformation` * `transformed` -> `Transform::append_transformation_cpy` * `rotate_by` -> `apppend_rotation` * `rotated` -> `Rotation::append_rotation_cpy` * `translate_by` -> `apppend_translation` * `translate` -> `Translation::append_translation_cpy` * `normalized` -> `Norm::normalize_cpy` * `rotated_wrt_point` -> `RotationWithTranslation::append_rotation_wrt_point_cpy` * `rotated_wrt_center` -> `RotationWithTranslation::append_rotation_wrt_center_cpy` Note that using those static methods is very verbose, and using in-place methods require an explicit import of the related trait. This is a way to convince the user to use free functions most of the time.
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fn main() {
let a = Vec3::new(1.0f64, 1.0, 1.0);
let mut b = Rot3::new(na::zero());
Api change: deal with inplace/out of place methods. Before, it was too easy to use an out of place method instead of the inplace one since they name were pretty mutch the same. This kind of confusion may lead to silly bugs very hard to understand. Thus the following changes have been made when a method is available both inplace and out-of-place: * inplace version keep a short name. * out-of-place version are suffixed by `_cpy` (meaning `copy`), and are static methods. Methods applying transformations (rotation, translation or general transform) are now prefixed by `append`, and a `prepend` version is available too. Also, free functions doing in-place modifications dont really make sense. They have been removed. Here are the naming changes: * `invert` -> `inv` * `inverted` -> `Inv::inv_cpy` * `transpose` -> `transpose` * `transposed` -> `Transpose::transpose_cpy` * `transform_by` -> `append_transformation` * `transformed` -> `Transform::append_transformation_cpy` * `rotate_by` -> `apppend_rotation` * `rotated` -> `Rotation::append_rotation_cpy` * `translate_by` -> `apppend_translation` * `translate` -> `Translation::append_translation_cpy` * `normalized` -> `Norm::normalize_cpy` * `rotated_wrt_point` -> `RotationWithTranslation::append_rotation_wrt_point_cpy` * `rotated_wrt_center` -> `RotationWithTranslation::append_rotation_wrt_center_cpy` Note that using those static methods is very verbose, and using in-place methods require an explicit import of the related trait. This is a way to convince the user to use free functions most of the time.
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b.append_rotation_mut(&a);
Api change: deal with inplace/out of place methods. Before, it was too easy to use an out of place method instead of the inplace one since they name were pretty mutch the same. This kind of confusion may lead to silly bugs very hard to understand. Thus the following changes have been made when a method is available both inplace and out-of-place: * inplace version keep a short name. * out-of-place version are suffixed by `_cpy` (meaning `copy`), and are static methods. Methods applying transformations (rotation, translation or general transform) are now prefixed by `append`, and a `prepend` version is available too. Also, free functions doing in-place modifications dont really make sense. They have been removed. Here are the naming changes: * `invert` -> `inv` * `inverted` -> `Inv::inv_cpy` * `transpose` -> `transpose` * `transposed` -> `Transpose::transpose_cpy` * `transform_by` -> `append_transformation` * `transformed` -> `Transform::append_transformation_cpy` * `rotate_by` -> `apppend_rotation` * `rotated` -> `Rotation::append_rotation_cpy` * `translate_by` -> `apppend_translation` * `translate` -> `Translation::append_translation_cpy` * `normalized` -> `Norm::normalize_cpy` * `rotated_wrt_point` -> `RotationWithTranslation::append_rotation_wrt_point_cpy` * `rotated_wrt_center` -> `RotationWithTranslation::append_rotation_wrt_center_cpy` Note that using those static methods is very verbose, and using in-place methods require an explicit import of the related trait. This is a way to convince the user to use free functions most of the time.
2013-10-14 16:22:32 +08:00
2014-01-14 16:52:18 +08:00
assert!(na::approx_eq(&na::rotation(&b), &a));
Api change: deal with inplace/out of place methods. Before, it was too easy to use an out of place method instead of the inplace one since they name were pretty mutch the same. This kind of confusion may lead to silly bugs very hard to understand. Thus the following changes have been made when a method is available both inplace and out-of-place: * inplace version keep a short name. * out-of-place version are suffixed by `_cpy` (meaning `copy`), and are static methods. Methods applying transformations (rotation, translation or general transform) are now prefixed by `append`, and a `prepend` version is available too. Also, free functions doing in-place modifications dont really make sense. They have been removed. Here are the naming changes: * `invert` -> `inv` * `inverted` -> `Inv::inv_cpy` * `transpose` -> `transpose` * `transposed` -> `Transpose::transpose_cpy` * `transform_by` -> `append_transformation` * `transformed` -> `Transform::append_transformation_cpy` * `rotate_by` -> `apppend_rotation` * `rotated` -> `Rotation::append_rotation_cpy` * `translate_by` -> `apppend_translation` * `translate` -> `Translation::append_translation_cpy` * `normalized` -> `Norm::normalize_cpy` * `rotated_wrt_point` -> `RotationWithTranslation::append_rotation_wrt_point_cpy` * `rotated_wrt_center` -> `RotationWithTranslation::append_rotation_wrt_center_cpy` Note that using those static methods is very verbose, and using in-place methods require an explicit import of the related trait. This is a way to convince the user to use free functions most of the time.
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}
```
## Features
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**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:
* Vectors with predefined static sizes: `Vec1`, `Vec2`, `Vec3`, `Vec4`, `Vec5`, `Vec6`.
* Vector with a user-defined static size: `VecN`.
* Points with static sizes: `Pnt1`, `Pnt2`, `Pnt3`, `Pnt4`, `Pnt5`, `Pnt6`.
* Square matrices with static sizes: `Mat1`, `Mat2`, `Mat3`, `Mat4`, `Mat5`, `Mat6 `.
* Rotation matrices: `Rot2`, `Rot3`
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* Quaternions: `Quat`, `UnitQuat`.
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* Isometries (translation rotation): `Iso2`, `Iso3`
* Similarity transformations (translation rotation uniform scale): `Sim2`, `Sim3`.
* 3D projections for computer graphics: `Persp3`, `PerspMat3`, `Ortho3`, `OrthoMat3`.
* Dynamically sized heap-allocated vector: `DVec`.
* Dynamically sized stack-allocated vectors with a maximum size: `DVec1` to `DVec6`.
* Dynamically sized heap-allocated (square or rectangular) matrix: `DMat`.
* Linear algebra and data analysis operators: `Cov`, `Mean`, `qr`, `cholesky`.
* Almost one trait per functionality: useful for generic programming.
## **nalgebra** in use
Here are some projects using **nalgebra**.
Feel free to add your project to this list if you happen to use **nalgebra**!
* [nphysics](https://github.com/sebcrozet/nphysics): a real-time physics engine.
* [ncollide](https://github.com/sebcrozet/ncollide): a collision detection library.
* [kiss3d](https://github.com/sebcrozet/kiss3d): a minimalistic graphics engine.
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* [nrays](https://github.com/sebcrozet/nrays): a ray tracer.
*/
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#![deny(non_camel_case_types)]
#![deny(unused_parens)]
#![deny(non_upper_case_globals)]
#![deny(unused_qualifications)]
#![deny(unused_results)]
#![warn(missing_docs)]
#![doc(html_root_url = "http://nalgebra.org/doc")]
extern crate rustc_serialize;
extern crate rand;
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extern crate num;
extern crate generic_array;
#[cfg(feature="arbitrary")]
extern crate quickcheck;
use std::cmp;
use std::ops::{Neg, Mul};
use num::{Zero, One};
pub use traits::{
Absolute,
AbsoluteRotate,
ApproxEq,
Axpy,
Basis,
BaseFloat,
BaseNum,
Bounded,
Cast,
Col,
ColSlice, RowSlice,
Cov,
Cross,
CrossMatrix,
Det,
Diag,
Dim,
Dot,
EigenQR,
Eye,
FloatPnt,
FloatVec,
FromHomogeneous,
Indexable,
Inv,
Iterable,
IterableMut,
Mat,
Mean,
Norm,
NumPnt,
NumVec,
Orig,
Outer,
POrd,
POrdering,
PntAsVec,
Repeat,
Rotate, Rotation, RotationMatrix, RotationWithTranslation, RotationTo,
Row,
Shape,
SquareMat,
ToHomogeneous,
Transform, Transformation,
Translate, Translation,
Transpose,
UniformSphereSample
};
pub use structs::{
Identity,
DMat, DMat1, DMat2, DMat3, DMat4, DMat5, DMat6,
DVec, DVec1, DVec2, DVec3, DVec4, DVec5, DVec6,
Iso2, Iso3,
Sim2, Sim3,
Mat1, Mat2, Mat3, Mat4,
Mat5, Mat6,
Rot2, Rot3,
VecN, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6,
Pnt1, Pnt2, Pnt3, Pnt4, Pnt5, Pnt6,
Persp3, PerspMat3,
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Ortho3, OrthoMat3,
Quat, UnitQuat
};
pub use linalg::{
qr,
householder_matrix,
cholesky,
hessenberg
};
mod structs;
mod traits;
mod linalg;
mod macros;
// mod lower_triangular;
// mod chol;
/// Change the input value to ensure it is on the range `[min, max]`.
#[inline(always)]
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(always)]
pub fn max<T: Ord>(a: T, b: T) -> T {
cmp::max(a, b)
}
/// Same as `cmp::min`.
#[inline(always)]
pub fn min<T: Ord>(a: T, b: T) -> T {
cmp::min(a, b)
}
/// Returns the infimum of `a` and `b`.
#[inline(always)]
pub fn inf<T: POrd>(a: &T, b: &T) -> T {
POrd::inf(a, b)
}
/// Returns the supremum of `a` and `b`.
#[inline(always)]
pub fn sup<T: POrd>(a: &T, b: &T) -> T {
POrd::sup(a, b)
}
/// Compare `a` and `b` using a partial ordering relation.
#[inline(always)]
pub fn partial_cmp<T: POrd>(a: &T, b: &T) -> POrdering {
POrd::partial_cmp(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a < b`.
#[inline(always)]
pub fn partial_lt<T: POrd>(a: &T, b: &T) -> bool {
POrd::partial_lt(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a <= b`.
#[inline(always)]
pub fn partial_le<T: POrd>(a: &T, b: &T) -> bool {
POrd::partial_le(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a > b`.
#[inline(always)]
pub fn partial_gt<T: POrd>(a: &T, b: &T) -> bool {
POrd::partial_gt(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a >= b`.
#[inline(always)]
pub fn partial_ge<T: POrd>(a: &T, b: &T) -> bool {
POrd::partial_ge(a, b)
}
/// Return the minimum of `a` and `b` if they are comparable.
#[inline(always)]
pub fn partial_min<'a, T: POrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
POrd::partial_min(a, b)
}
/// Return the maximum of `a` and `b` if they are comparable.
#[inline(always)]
pub fn partial_max<'a, T: POrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
POrd::partial_max(a, b)
}
/// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to
/// `min` or `max`.
#[inline(always)]
pub fn partial_clamp<'a, T: POrd>(value: &'a T, min: &'a T, max: &'a T) -> Option<&'a T> {
POrd::partial_clamp(value, min, max)
}
//
//
// Constructors
//
//
/// Create a special identity object.
///
/// Same as `Identity::new()`.
#[inline(always)]
pub fn identity() -> Identity {
Identity::new()
}
/// Create a zero-valued value.
///
/// This is the same as `std::num::zero()`.
#[inline(always)]
pub fn zero<T: Zero>() -> T {
Zero::zero()
}
/// Tests is a value is iqual to zero.
#[inline(always)]
pub fn is_zero<T: Zero>(val: &T) -> bool {
val.is_zero()
}
/// Create a one-valued value.
///
/// This is the same as `std::num::one()`.
#[inline(always)]
pub fn one<T: One>() -> T {
One::one()
}
//
//
// Geometry
//
//
/// Returns the trivial origin of an affine space.
#[inline(always)]
pub fn orig<P: Orig>() -> P {
Orig::orig()
}
/// Returns the center of two points.
#[inline]
pub fn center<N: BaseFloat, P: FloatPnt<N, V>, V: Copy + Norm<N>>(a: &P, b: &P) -> P {
let _2 = one::<N>() + one();
(*a + *b.as_vec()) / _2
}
/*
* FloatPnt
*/
/// Returns the distance between two points.
#[inline(always)]
pub fn dist<N: BaseFloat, P: FloatPnt<N, V>, V: Norm<N>>(a: &P, b: &P) -> N {
a.dist(b)
}
/// Returns the squared distance between two points.
#[inline(always)]
pub fn sqdist<N: BaseFloat, P: FloatPnt<N, V>, V: Norm<N>>(a: &P, b: &P) -> N {
a.sqdist(b)
}
/*
* Translation<V>
*/
/// Gets the translation applicable by `m`.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Vec3, Iso3};
///
/// fn main() {
/// let t = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
/// let trans = na::translation(&t);
///
/// assert!(trans == Vec3::new(1.0, 1.0, 1.0));
/// }
/// ```
#[inline(always)]
pub fn translation<V, M: Translation<V>>(m: &M) -> V {
m.translation()
}
/// Gets the inverse translation applicable by `m`.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Vec3, Iso3};
///
/// fn main() {
/// let t = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
/// let itrans = na::inv_translation(&t);
///
/// assert!(itrans == Vec3::new(-1.0, -1.0, -1.0));
/// }
/// ```
#[inline(always)]
pub fn inv_translation<V, M: Translation<V>>(m: &M) -> V {
m.inv_translation()
}
/// Applies the translation `v` to a copy of `m`.
#[inline(always)]
pub fn append_translation<V, M: Translation<V>>(m: &M, v: &V) -> M {
Translation::append_translation(m, v)
}
/*
* Translate<P>
*/
/// Applies a translation to a point.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Pnt3, Vec3, Iso3};
///
/// fn main() {
/// let t = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
/// let p = Pnt3::new(2.0, 2.0, 2.0);
///
/// let tp = na::translate(&t, &p);
///
/// assert!(tp == Pnt3::new(3.0, 3.0, 3.0))
/// }
/// ```
#[inline(always)]
pub fn translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
m.translate(p)
}
/// Applies an inverse translation to a point.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Pnt3, Vec3, Iso3};
///
/// fn main() {
/// let t = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
/// let p = Pnt3::new(2.0, 2.0, 2.0);
///
/// let tp = na::inv_translate(&t, &p);
///
/// assert!(na::approx_eq(&tp, &Pnt3::new(1.0, 1.0, 1.0)))
/// }
#[inline(always)]
pub fn inv_translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
m.inv_translate(p)
}
/*
* Rotation<V>
*/
/// Gets the rotation applicable by `m`.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Vec3, Rot3};
///
/// fn main() {
/// let t = Rot3::new(Vec3::new(1.0f64, 1.0, 1.0));
///
/// assert!(na::approx_eq(&na::rotation(&t), &Vec3::new(1.0, 1.0, 1.0)));
/// }
/// ```
#[inline(always)]
pub fn rotation<V, M: Rotation<V>>(m: &M) -> V {
m.rotation()
}
/// Gets the inverse rotation applicable by `m`.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Vec3, Rot3};
///
/// fn main() {
/// let t = Rot3::new(Vec3::new(1.0f64, 1.0, 1.0));
///
/// assert!(na::approx_eq(&na::inv_rotation(&t), &Vec3::new(-1.0, -1.0, -1.0)));
/// }
/// ```
#[inline(always)]
pub fn inv_rotation<V, M: Rotation<V>>(m: &M) -> V {
m.inv_rotation()
}
// FIXME: this example is a bit shity
/// Applies the rotation `v` to a copy of `m`.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Vec3, Rot3};
///
/// fn main() {
/// let t = Rot3::new(Vec3::new(0.0f64, 0.0, 0.0));
/// let v = Vec3::new(1.0, 1.0, 1.0);
/// let rt = na::append_rotation(&t, &v);
///
/// assert!(na::approx_eq(&na::rotation(&rt), &Vec3::new(1.0, 1.0, 1.0)))
/// }
/// ```
#[inline(always)]
pub fn append_rotation<V, M: Rotation<V>>(m: &M, v: &V) -> M {
Rotation::append_rotation(m, v)
}
// FIXME: this example is a bit shity
/// Pre-applies the rotation `v` to a copy of `m`.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{Vec3, Rot3};
///
/// fn main() {
/// let t = Rot3::new(Vec3::new(0.0f64, 0.0, 0.0));
/// let v = Vec3::new(1.0, 1.0, 1.0);
/// let rt = na::prepend_rotation(&t, &v);
///
/// assert!(na::approx_eq(&na::rotation(&rt), &Vec3::new(1.0, 1.0, 1.0)))
/// }
/// ```
#[inline(always)]
pub fn prepend_rotation<V, M: Rotation<V>>(m: &M, v: &V) -> M {
Rotation::prepend_rotation(m, v)
}
/*
* Rotate<V>
*/
/// Applies a rotation to a vector.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{BaseFloat, Rot3, Vec3};
///
/// fn main() {
/// let t = Rot3::new(Vec3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
/// let v = Vec3::new(1.0, 0.0, 0.0);
///
/// let tv = na::rotate(&t, &v);
///
/// assert!(na::approx_eq(&tv, &Vec3::new(0.0, 1.0, 0.0)))
/// }
/// ```
#[inline(always)]
pub fn rotate<V, M: Rotate<V>>(m: &M, v: &V) -> V {
m.rotate(v)
}
/// Applies an inverse rotation to a vector.
///
/// ```rust
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/// extern crate nalgebra as na;
/// use na::{BaseFloat, Rot3, Vec3};
///
/// fn main() {
/// let t = Rot3::new(Vec3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
/// let v = Vec3::new(1.0, 0.0, 0.0);
///
/// let tv = na::inv_rotate(&t, &v);
///
/// assert!(na::approx_eq(&tv, &Vec3::new(0.0, -1.0, 0.0)))
/// }
/// ```
#[inline(always)]
pub fn inv_rotate<V, M: Rotate<V>>(m: &M, v: &V) -> V {
m.inv_rotate(v)
}
/*
* RotationWithTranslation<LV, AV>
*/
/// Rotates a copy of `m` by `amount` using `center` as the pivot point.
#[inline(always)]
pub fn append_rotation_wrt_point<LV: Neg<Output = LV> + Copy,
AV,
M: RotationWithTranslation<LV, AV>>(
m: &M,
amount: &AV,
center: &LV) -> M {
RotationWithTranslation::append_rotation_wrt_point(m, amount, center)
}
/// Rotates a copy of `m` by `amount` using `m.translation()` as the pivot point.
#[inline(always)]
pub fn append_rotation_wrt_center<LV: Neg<Output = LV> + Copy,
AV,
M: RotationWithTranslation<LV, AV>>(
m: &M,
amount: &AV) -> M {
RotationWithTranslation::append_rotation_wrt_center(m, amount)
}
/*
* RotationTo
*/
/// Computes the angle of the rotation needed to transfom `a` to `b`.
#[inline(always)]
pub fn angle_between<V: RotationTo>(a: &V, b: &V) -> V::AngleType {
a.angle_to(b)
}
/// Computes the rotation needed to transform `a` to `b`.
#[inline(always)]
pub fn rotation_between<V: RotationTo>(a: &V, b: &V) -> V::DeltaRotationType {
a.rotation_to(b)
}
/*
* RotationMatrix<LV, AV, R>
*/
/// Builds a rotation matrix from `r`.
#[inline(always)]
pub fn to_rot_mat<N, LV, AV, R, M>(r: &R) -> M
where R: RotationMatrix<N, LV, AV, Output = M>,
M: SquareMat<N, LV> + Rotation<AV> + Copy,
LV: Mul<M, Output = LV>
{
// FIXME: rust-lang/rust#20413
r.to_rot_mat()
}
/*
* AbsoluteRotate<V>
*/
/// Applies a rotation using the absolute values of its components.
#[inline(always)]
pub fn absolute_rotate<V, M: AbsoluteRotate<V>>(m: &M, v: &V) -> V {
m.absolute_rotate(v)
}
/*
* Transformation<T>
*/
/// Gets the transformation applicable by `m`.
#[inline(always)]
pub fn transformation<T, M: Transformation<T>>(m: &M) -> T {
m.transformation()
}
/// Gets the inverse transformation applicable by `m`.
#[inline(always)]
pub fn inv_transformation<T, M: Transformation<T>>(m: &M) -> T {
m.inv_transformation()
}
/// Gets a transformed copy of `m`.
#[inline(always)]
pub fn append_transformation<T, M: Transformation<T>>(m: &M, t: &T) -> M {
Transformation::append_transformation(m, t)
}
/*
* Transform<V>
*/
/// Applies a transformation to a vector.
#[inline(always)]
pub fn transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
m.transform(v)
}
/// Applies an inverse transformation to a vector.
#[inline(always)]
pub fn inv_transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
m.inv_transform(v)
}
/*
* Dot<N>
*/
/// Computes the dot product of two vectors.
#[inline(always)]
pub fn dot<V: Dot<N>, N>(a: &V, b: &V) -> N {
Dot::dot(a, b)
}
/*
* Norm<N>
*/
/// Computes the L2 norm of a vector.
#[inline(always)]
pub fn norm<V: Norm<N>, N: BaseFloat>(v: &V) -> N {
Norm::norm(v)
}
/// Computes the squared L2 norm of a vector.
#[inline(always)]
pub fn sqnorm<V: Norm<N>, N: BaseFloat>(v: &V) -> N {
Norm::sqnorm(v)
2013-05-19 01:04:03 +08:00
}
/// Gets the normalized version of a vector.
#[inline(always)]
pub fn normalize<V: Norm<N>, N: BaseFloat>(v: &V) -> V {
Norm::normalize(v)
}
/*
* Det<N>
*/
/// Computes the determinant of a square matrix.
#[inline(always)]
pub fn det<M: Det<N>, N>(m: &M) -> N {
Det::det(m)
}
/*
* Cross<V>
*/
/// Computes the cross product of two vectors.
#[inline(always)]
pub fn cross<LV: Cross>(a: &LV, b: &LV) -> LV::CrossProductType {
Cross::cross(a, b)
}
/*
* CrossMatrix<M>
*/
/// Given a vector, computes the matrix which, when multiplied by another vector, computes a cross
/// product.
#[inline(always)]
pub fn cross_matrix<V: CrossMatrix<M>, M>(v: &V) -> M {
CrossMatrix::cross_matrix(v)
}
/*
* ToHomogeneous<U>
*/
/// Converts a matrix or vector to homogeneous coordinates.
#[inline(always)]
pub fn to_homogeneous<M: ToHomogeneous<Res>, Res>(m: &M) -> Res {
ToHomogeneous::to_homogeneous(m)
}
/*
* FromHomogeneous<U>
*/
/// Converts a matrix or vector from homogeneous coordinates.
///
/// w-normalization is appied.
#[inline(always)]
pub fn from_homogeneous<M, Res: FromHomogeneous<M>>(m: &M) -> Res {
FromHomogeneous::from(m)
}
/*
* UniformSphereSample
*/
/// Samples the unit sphere living on the dimension as the samples types.
///
/// The number of sampling point is implementation-specific. It is always uniform.
#[inline(always)]
2015-01-08 04:16:56 +08:00
pub fn sample_sphere<V: UniformSphereSample, F: FnMut(V)>(f: F) {
UniformSphereSample::sample(f)
}
//
//
// Operations
//
//
/*
* AproxEq<N>
*/
/// Tests approximate equality.
#[inline(always)]
pub fn approx_eq<T: ApproxEq<N>, N>(a: &T, b: &T) -> bool {
ApproxEq::approx_eq(a, b)
}
/// Tests approximate equality using a custom epsilon.
#[inline(always)]
pub fn approx_eq_eps<T: ApproxEq<N>, N>(a: &T, b: &T, eps: &N) -> bool {
ApproxEq::approx_eq_eps(a, b, eps)
}
/*
* Absolute<A>
*/
/// Computes a component-wise absolute value.
#[inline(always)]
pub fn abs<M: Absolute<Res>, Res>(m: &M) -> Res {
Absolute::abs(m)
}
/*
* Inv
*/
/// Gets an inverted copy of a matrix.
#[inline(always)]
pub fn inv<M: Inv>(m: &M) -> Option<M> {
Inv::inv(m)
}
/*
* Transpose
*/
/// Gets a transposed copy of a matrix.
#[inline(always)]
pub fn transpose<M: Transpose>(m: &M) -> M {
Transpose::transpose(m)
}
/*
* Outer<M>
*/
/// Computes the outer product of two vectors.
#[inline(always)]
pub fn outer<V: Outer>(a: &V, b: &V) -> V::OuterProductType {
Outer::outer(a, b)
}
/*
* Cov<M>
*/
/// Computes the covariance of a set of observations.
#[inline(always)]
pub fn cov<M: Cov<Res>, Res>(observations: &M) -> Res {
Cov::cov(observations)
}
/*
* Mean<N>
*/
/// Computes the mean of a set of observations.
#[inline(always)]
pub fn mean<N, M: Mean<N>>(observations: &M) -> N {
Mean::mean(observations)
}
/*
* EigenQR<N, V>
*/
/// Computes the eigenvalues and eigenvectors of a square matrix usin the QR algorithm.
#[inline(always)]
pub fn eigen_qr<N, V, M>(m: &M, eps: &N, niter: usize) -> (M, V)
where V: Mul<M, Output = V>,
M: EigenQR<N, V> {
EigenQR::eigen_qr(m, eps, niter)
}
//
//
// Structure
//
//
/*
* Eye
*/
/// Construct the identity matrix for a given dimension
#[inline(always)]
pub fn new_identity<M: Eye>(dim: usize) -> M {
Eye::new_identity(dim)
}
/*
* Repeat
*/
/// Create an object by repeating a value.
///
/// Same as `Identity::new()`.
#[inline(always)]
pub fn repeat<N, T: Repeat<N>>(val: N) -> T {
Repeat::repeat(val)
}
/*
* Basis
*/
/// Computes the canonical basis for a given dimension.
#[inline(always)]
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pub fn canonical_basis<V: Basis, F: FnMut(V) -> bool>(f: F) {
Basis::canonical_basis(f)
}
/// Computes the basis of the orthonormal subspace of a given vector.
#[inline(always)]
2015-01-08 04:16:56 +08:00
pub fn orthonormal_subspace_basis<V: Basis, F: FnMut(V) -> bool>(v: &V, f: F) {
Basis::orthonormal_subspace_basis(v, f)
}
/// Gets the (0-based) i-th element of the canonical basis of V.
#[inline]
pub fn canonical_basis_element<V: Basis>(i: usize) -> Option<V> {
Basis::canonical_basis_element(i)
}
/*
* Row<R>
*/
/*
* Col<C>
*/
/*
* Diag<V>
*/
/// Gets the diagonal of a square matrix.
#[inline(always)]
pub fn diag<M: Diag<V>, V>(m: &M) -> V {
m.diag()
}
/*
* Dim
*/
/// Gets the dimension an object lives in.
///
/// Same as `Dim::dim::(None::<V>)`.
#[inline(always)]
pub fn dim<V: Dim>() -> usize {
Dim::dim(None::<V>)
}
/// Gets the indexable range of an object.
#[inline(always)]
pub fn shape<V: Shape<I>, I>(v: &V) -> I {
v.shape()
}
/*
* Cast<T>
*/
/// Converts an object from one type to another.
///
/// For primitive types, this is the same as the `as` keywords.
/// The following properties are preserved by a cast:
///
/// * Type-level geometric invariants cannot be broken (eg. a cast from Rot3<f64> to Rot3<i64> is
/// not possible)
/// * A cast to a type with more type-level invariants cannot be done (eg. a cast from Mat<f64> to
/// Rot3<f64> is not possible)
/// * For primitive types an unbounded cast is done using the `as` keyword (this is different from
/// the standard library which makes bound-checking to ensure eg. that a i64 is not out of the
/// range of an i32 when a cast from i64 to i32 is done).
/// * A cast does not affect the dimension of an algebraic object. Note that this prevents an
/// isometric transform to be cast to a raw matrix. Use `to_homogeneous` for that special purpose.
#[inline(always)]
pub fn cast<T, U: Cast<T>>(t: T) -> U {
Cast::from(t)
}
/*
* Indexable
*/