# Crate bevy_rapier3d::prelude::nalgebra [−][src]

## Expand description

# 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 and the official package manager: cargo.

Simply add the following to your `Cargo.toml`

file:

[dependencies] // TODO: replace the * by the latest version. nalgebra = "*"

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:

#[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.

## Modules

base | [Reexported at the root of this crate.] Data structures for vector and matrix computations. |

geometry | [Reexported at the root of this crate.] Data structures for points and usual transformations (rotations, isometries, etc.) |

linalg | [Reexported at the root of this crate.] Factorization of real matrices. |

## Macros

dmatrix | Construct a dynamic matrix directly from data. |

dvector | Construct a dynamic column vector directly from data. |

matrix | Construct a fixed-size matrix directly from data. |

point | Construct a fixed-size point directly from data. |

unimplemented_or_uninitialized_generic | When “no_unsound_assume_init” is enabled, expands to |

vector | Construct a fixed-size column vector directly from data. |

## Structs

ArrayStorage | A array-based statically sized matrix data storage. |

Bidiagonal | The bidiagonalization of a general matrix. |

Cholesky | The Cholesky decomposition of a symmetric-definite-positive matrix. |

ColPivQR | The QR decomposition (with column pivoting) of a general matrix. |

Complex | A complex number in Cartesian form. |

Const | |

DefaultAllocator | An allocator based on |

DualQuaternion | A dual quaternion. |

Dynamic | Dim of dynamically-sized algebraic entities. |

EuclideanNorm | Euclidean norm. |

FullPivLU | LU decomposition with full row and column pivoting. |

Hessenberg | Hessenberg decomposition of a general matrix. |

Isometry | A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion). |

LU | LU decomposition with partial (row) pivoting. |

LpNorm | Lp norm. |

Matrix | The most generic column-major matrix (and vector) type. |

Orthographic3 | A 3D orthographic projection stored as a homogeneous 4x4 matrix. |

PermutationSequence | A sequence of row or column permutations. |

Perspective3 | A 3D perspective projection stored as a homogeneous 4x4 matrix. |

Point | A point in an euclidean space. |

QR | The QR decomposition of a general matrix. |

Quaternion | A quaternion. See the type alias |

Reflection | A reflection wrt. a plane. |

Rotation | A rotation matrix. |

SVD | Singular Value Decomposition of a general matrix. |

Schur | Schur decomposition of a square matrix. |

Similarity | A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation. |

SliceStorage | A matrix data storage for a matrix slice. Only contains an internal reference to another matrix data storage. |

SliceStorageMut | A mutable matrix data storage for mutable matrix slice. Only contains an internal mutable reference to another matrix data storage. |

SymmetricEigen | Eigendecomposition of a symmetric matrix. |

SymmetricTridiagonal | Tridiagonalization of a symmetric matrix. |

Transform | A transformation matrix in homogeneous coordinates. |

Translation | A translation. |

UDU | UDU factorization. |

UniformNorm | L-infinite norm aka. Chebytchev norm aka. uniform norm aka. suppremum norm. |

Unit | A wrapper that ensures the underlying algebraic entity has a unit norm. |

VecStorage | A Vec-based matrix data storage. It may be dynamically-sized. |

## Enums

TAffine | Tag representing an affine |

TGeneral | Tag representing the most general (not necessarily inversible) |

TProjective | Tag representing the most general inversible |

## Traits

AbstractRotation | Trait implemented by rotations that can be used inside of an |

ClosedAdd | Trait |

ClosedDiv | Trait |

ClosedMul | Trait |

ClosedSub | Trait |

ComplexField | Trait shared by all complex fields and its subfields (like real numbers). |

Dim | Trait implemented by any type that can be used as a dimension. This includes type-level
integers and |

DimAdd | |

DimDiv | |

DimMax | |

DimMin | |

DimMul | |

DimName | Trait implemented exclusively by type-level integers. |

DimNameAdd | |

DimNameDiv | |

DimNameMax | |

DimNameMin | |

DimNameMul | |

DimNameSub | |

DimSub | |

Field | Trait implemented by fields, i.e., complex numbers and floats. |

IsDynamic | Trait implemented by |

IsNotStaticOne | Trait implemented by |

Norm | A trait for abstract matrix norms. |

Normed | Trait implemented by entities scan be be normalized and put in an |

RealField | Trait shared by all reals. |

Scalar | The basic scalar type for all structures of |

SimdBool | Lane-wise generalization of |

SimdComplexField | Lane-wise generalisation of |

SimdPartialOrd | Lane-wise generalization of the standard |

SimdRealField | Lanewise generalization of |

SimdValue | Base trait for every SIMD types. |

SliceRange | A range with a size that may be known at compile-time. |

SubTCategoryOf | Indicates that |

SuperTCategoryOf | Indicates that |

TCategory | Trait implemented by phantom types identifying the projective transformation type. |

TCategoryMul | Traits that gives the |

ToConst | |

ToTypenum |

## Functions

abs | Deprecated The absolute value of |

center | The center of two points. |

clamp | Returns a reference to the input value clamped to the interval |

convert | Converts an object from one type to an equivalent or more general one. |

convert_ref | Converts an object from one type to an equivalent or more general one. |

convert_ref_unchecked | Use with care! Same as |

convert_unchecked | Use with care! Same as |

distance | The distance between two points. |

distance_squared | The squared distance between two points. |

inf | Deprecated Returns the infimum of |

inf_sup | Deprecated Returns simultaneously the infimum and supremum of |

is_convertible | Indicates if |

max | Same as |

min | Same as |

one | Gets the multiplicative identity element. |

partial_clamp | Clamp |

partial_cmp | Compare |

partial_ge | Returns |

partial_gt | Returns |

partial_le | Returns |

partial_lt | Returns |

partial_max | Return the maximum of |

partial_min | Return the minimum of |

partial_sort2 | Sorts two values in increasing order using a partial ordering. |

sup | Deprecated Returns the supremum of |

try_convert | Attempts to convert an object to a more specific one. |

try_convert_ref | Attempts to convert an object to a more specific one. |

try_invert_to | Performs a LU decomposition to overwrite |

wilkinson_shift | Computes the wilkinson shift, i.e., the 2x2 symmetric matrix eigenvalue to its tailing
component |

wrap | Wraps |

zero | Gets the additive identity element. |

## Type Definitions

Affine2 | A 2D affine transformation. Stored as a homogeneous 3x3 matrix. |

Affine3 | A 3D affine transformation. Stored as a homogeneous 4x4 matrix. |

DMatrix | A dynamically sized column-major matrix. |

DMatrixSlice | A column-major matrix slice dynamic numbers of rows and columns. |

DMatrixSliceMut | A column-major matrix slice dynamic numbers of rows and columns. |

DVector | A dynamically sized column vector. |

DVectorSlice | A column vector slice dynamic numbers of rows and columns. |

DVectorSliceMut | A column vector slice dynamic numbers of rows and columns. |

DimDiff | |

DimMaximum | |

DimMinimum | |

DimNameDiff | |

DimNameMaximum | |

DimNameMinimum | |

DimNameProd | |

DimNameQuot | |

DimNameSum | |

DimProd | |

DimQuot | |

DimSum | |

Isometry2 | A 2-dimensional direct isometry using a unit complex number for its rotational part. |

Isometry3 | A 3-dimensional direct isometry using a unit quaternion for its rotational part. |

IsometryMatrix2 | A 2-dimensional direct isometry using a rotation matrix for its rotational part. |

IsometryMatrix3 | A 3-dimensional direct isometry using a rotation matrix for its rotational part. |

Matrix1 | A stack-allocated, column-major, 1x1 square matrix. |

Matrix1x2 | A stack-allocated, column-major, 1x2 matrix. |

Matrix1x3 | A stack-allocated, column-major, 1x3 matrix. |

Matrix1x4 | A stack-allocated, column-major, 1x4 matrix. |

Matrix1x5 | A stack-allocated, column-major, 1x5 matrix. |

Matrix1x6 | A stack-allocated, column-major, 1x6 matrix. |

Matrix1xX | A heap-allocated, row-major, matrix with 1 rows and a dynamic number of columns. |

Matrix2 | A stack-allocated, column-major, 2x2 square matrix. |

Matrix2x1 | A stack-allocated, column-major, 2x1 matrix. |

Matrix2x3 | A stack-allocated, column-major, 2x3 matrix. |

Matrix2x4 | A stack-allocated, column-major, 2x4 matrix. |

Matrix2x5 | A stack-allocated, column-major, 2x5 matrix. |

Matrix2x6 | A stack-allocated, column-major, 2x6 matrix. |

Matrix2xX | A heap-allocated, row-major, matrix with 2 rows and a dynamic number of columns. |

Matrix3 | A stack-allocated, column-major, 3x3 square matrix. |

Matrix3x1 | A stack-allocated, column-major, 3x1 matrix. |

Matrix3x2 | A stack-allocated, column-major, 3x2 matrix. |

Matrix3x4 | A stack-allocated, column-major, 3x4 matrix. |

Matrix3x5 | A stack-allocated, column-major, 3x5 matrix. |

Matrix3x6 | A stack-allocated, column-major, 3x6 matrix. |

Matrix3xX | A heap-allocated, row-major, matrix with 3 rows and a dynamic number of columns. |

Matrix4 | A stack-allocated, column-major, 4x4 square matrix. |

Matrix4x1 | A stack-allocated, column-major, 4x1 matrix. |

Matrix4x2 | A stack-allocated, column-major, 4x2 matrix. |

Matrix4x3 | A stack-allocated, column-major, 4x3 matrix. |

Matrix4x5 | A stack-allocated, column-major, 4x5 matrix. |

Matrix4x6 | A stack-allocated, column-major, 4x6 matrix. |

Matrix4xX | A heap-allocated, row-major, matrix with 4 rows and a dynamic number of columns. |

Matrix5 | A stack-allocated, column-major, 5x5 square matrix. |

Matrix5x1 | A stack-allocated, column-major, 5x1 matrix. |

Matrix5x2 | A stack-allocated, column-major, 5x2 matrix. |

Matrix5x3 | A stack-allocated, column-major, 5x3 matrix. |

Matrix5x4 | A stack-allocated, column-major, 5x4 matrix. |

Matrix5x6 | A stack-allocated, column-major, 5x6 matrix. |

Matrix5xX | A heap-allocated, row-major, matrix with 5 rows and a dynamic number of columns. |

Matrix6 | A stack-allocated, column-major, 6x6 square matrix. |

Matrix6x1 | A stack-allocated, column-major, 6x1 matrix. |

Matrix6x2 | A stack-allocated, column-major, 6x2 matrix. |

Matrix6x3 | A stack-allocated, column-major, 6x3 matrix. |

Matrix6x4 | A stack-allocated, column-major, 6x4 matrix. |

Matrix6x5 | A stack-allocated, column-major, 6x5 matrix. |

Matrix6xX | A heap-allocated, row-major, matrix with 6 rows and a dynamic number of columns. |

MatrixCross | The type of the result of a matrix cross product. |

MatrixMN | Deprecated An owned matrix column-major matrix with |

MatrixN | Deprecated An owned matrix column-major matrix with |

MatrixSlice | A matrix slice. |

MatrixSlice1 | A column-major 1x1 matrix slice. |

MatrixSlice1x2 | A column-major 1x2 matrix slice. |

MatrixSlice1x3 | A column-major 1x3 matrix slice. |

MatrixSlice1x4 | A column-major 1x4 matrix slice. |

MatrixSlice1x5 | A column-major 1x5 matrix slice. |

MatrixSlice1x6 | A column-major 1x6 matrix slice. |

MatrixSlice1xX | A column-major matrix slice with 1 row and a number of columns chosen at runtime. |

MatrixSlice2 | A column-major 2x2 matrix slice. |

MatrixSlice2x1 | A column-major 2x1 matrix slice. |

MatrixSlice2x3 | A column-major 2x3 matrix slice. |

MatrixSlice2x4 | A column-major 2x4 matrix slice. |

MatrixSlice2x5 | A column-major 2x5 matrix slice. |

MatrixSlice2x6 | A column-major 2x6 matrix slice. |

MatrixSlice2xX | A column-major matrix slice with 2 rows and a number of columns chosen at runtime. |

MatrixSlice3 | A column-major 3x3 matrix slice. |

MatrixSlice3x1 | A column-major 3x1 matrix slice. |

MatrixSlice3x2 | A column-major 3x2 matrix slice. |

MatrixSlice3x4 | A column-major 3x4 matrix slice. |

MatrixSlice3x5 | A column-major 3x5 matrix slice. |

MatrixSlice3x6 | A column-major 3x6 matrix slice. |

MatrixSlice3xX | A column-major matrix slice with 3 rows and a number of columns chosen at runtime. |

MatrixSlice4 | A column-major 4x4 matrix slice. |

MatrixSlice4x1 | A column-major 4x1 matrix slice. |

MatrixSlice4x2 | A column-major 4x2 matrix slice. |

MatrixSlice4x3 | A column-major 4x3 matrix slice. |

MatrixSlice4x5 | A column-major 4x5 matrix slice. |

MatrixSlice4x6 | A column-major 4x6 matrix slice. |

MatrixSlice4xX | A column-major matrix slice with 4 rows and a number of columns chosen at runtime. |

MatrixSlice5 | A column-major 5x5 matrix slice. |

MatrixSlice5x1 | A column-major 5x1 matrix slice. |

MatrixSlice5x2 | A column-major 5x2 matrix slice. |

MatrixSlice5x3 | A column-major 5x3 matrix slice. |

MatrixSlice5x4 | A column-major 5x4 matrix slice. |

MatrixSlice5x6 | A column-major 5x6 matrix slice. |

MatrixSlice5xX | A column-major matrix slice with 5 rows and a number of columns chosen at runtime. |

MatrixSlice6 | A column-major 6x6 matrix slice. |

MatrixSlice6x1 | A column-major 6x1 matrix slice. |

MatrixSlice6x2 | A column-major 6x2 matrix slice. |

MatrixSlice6x3 | A column-major 6x3 matrix slice. |

MatrixSlice6x4 | A column-major 6x4 matrix slice. |

MatrixSlice6x5 | A column-major 6x5 matrix slice. |

MatrixSlice6xX | A column-major matrix slice with 6 rows and a number of columns chosen at runtime. |

MatrixSliceMut | A mutable matrix slice. |

MatrixSliceMut1 | A column-major 1x1 matrix slice. |

MatrixSliceMut1x2 | A column-major 1x2 matrix slice. |

MatrixSliceMut1x3 | A column-major 1x3 matrix slice. |

MatrixSliceMut1x4 | A column-major 1x4 matrix slice. |

MatrixSliceMut1x5 | A column-major 1x5 matrix slice. |

MatrixSliceMut1x6 | A column-major 1x6 matrix slice. |

MatrixSliceMut1xX | A column-major matrix slice with 1 row and a number of columns chosen at runtime. |

MatrixSliceMut2 | A column-major 2x2 matrix slice. |

MatrixSliceMut2x1 | A column-major 2x1 matrix slice. |

MatrixSliceMut2x3 | A column-major 2x3 matrix slice. |

MatrixSliceMut2x4 | A column-major 2x4 matrix slice. |

MatrixSliceMut2x5 | A column-major 2x5 matrix slice. |

MatrixSliceMut2x6 | A column-major 2x6 matrix slice. |

MatrixSliceMut2xX | A column-major matrix slice with 2 rows and a number of columns chosen at runtime. |

MatrixSliceMut3 | A column-major 3x3 matrix slice. |

MatrixSliceMut3x1 | A column-major 3x1 matrix slice. |

MatrixSliceMut3x2 | A column-major 3x2 matrix slice. |

MatrixSliceMut3x4 | A column-major 3x4 matrix slice. |

MatrixSliceMut3x5 | A column-major 3x5 matrix slice. |

MatrixSliceMut3x6 | A column-major 3x6 matrix slice. |

MatrixSliceMut3xX | A column-major matrix slice with 3 rows and a number of columns chosen at runtime. |

MatrixSliceMut4 | A column-major 4x4 matrix slice. |

MatrixSliceMut4x1 | A column-major 4x1 matrix slice. |

MatrixSliceMut4x2 | A column-major 4x2 matrix slice. |

MatrixSliceMut4x3 | A column-major 4x3 matrix slice. |

MatrixSliceMut4x5 | A column-major 4x5 matrix slice. |

MatrixSliceMut4x6 | A column-major 4x6 matrix slice. |

MatrixSliceMut4xX | A column-major matrix slice with 4 rows and a number of columns chosen at runtime. |

MatrixSliceMut5 | A column-major 5x5 matrix slice. |

MatrixSliceMut5x1 | A column-major 5x1 matrix slice. |

MatrixSliceMut5x2 | A column-major 5x2 matrix slice. |

MatrixSliceMut5x3 | A column-major 5x3 matrix slice. |

MatrixSliceMut5x4 | A column-major 5x4 matrix slice. |

MatrixSliceMut5x6 | A column-major 5x6 matrix slice. |

MatrixSliceMut5xX | A column-major matrix slice with 5 rows and a number of columns chosen at runtime. |

MatrixSliceMut6 | A column-major 6x6 matrix slice. |

MatrixSliceMut6x1 | A column-major 6x1 matrix slice. |

MatrixSliceMut6x2 | A column-major 6x2 matrix slice. |

MatrixSliceMut6x3 | A column-major 6x3 matrix slice. |

MatrixSliceMut6x4 | A column-major 6x4 matrix slice. |

MatrixSliceMut6x5 | A column-major 6x5 matrix slice. |

MatrixSliceMut6xX | A column-major matrix slice with 6 rows and a number of columns chosen at runtime. |

MatrixSliceMutMN | A column-major matrix slice with |

MatrixSliceMutN | A column-major matrix slice with |

MatrixSliceMutXx1 | A column-major matrix slice with a number of rows chosen at runtime and 1 column. |

MatrixSliceMutXx2 | A column-major matrix slice with a number of rows chosen at runtime and 2 columns. |

MatrixSliceMutXx3 | A column-major matrix slice with a number of rows chosen at runtime and 3 columns. |

MatrixSliceMutXx4 | A column-major matrix slice with a number of rows chosen at runtime and 4 columns. |

MatrixSliceMutXx5 | A column-major matrix slice with a number of rows chosen at runtime and 5 columns. |

MatrixSliceMutXx6 | A column-major matrix slice with a number of rows chosen at runtime and 6 columns. |

MatrixSliceXx1 | A column-major matrix slice with a number of rows chosen at runtime and 1 column. |

MatrixSliceXx2 | A column-major matrix slice with a number of rows chosen at runtime and 2 columns. |

MatrixSliceXx3 | A column-major matrix slice with a number of rows chosen at runtime and 3 columns. |

MatrixSliceXx4 | A column-major matrix slice with a number of rows chosen at runtime and 4 columns. |

MatrixSliceXx5 | A column-major matrix slice with a number of rows chosen at runtime and 5 columns. |

MatrixSliceXx6 | A column-major matrix slice with a number of rows chosen at runtime and 6 columns. |

MatrixSum | The type of the result of a matrix sum. |

MatrixVec | Deprecated Renamed to VecStorage. |

MatrixXx1 | A heap-allocated, column-major, matrix with a dynamic number of rows and 1 columns. |

MatrixXx2 | A heap-allocated, column-major, matrix with a dynamic number of rows and 2 columns. |

MatrixXx3 | A heap-allocated, column-major, matrix with a dynamic number of rows and 3 columns. |

MatrixXx4 | A heap-allocated, column-major, matrix with a dynamic number of rows and 4 columns. |

MatrixXx5 | A heap-allocated, column-major, matrix with a dynamic number of rows and 5 columns. |

MatrixXx6 | A heap-allocated, column-major, matrix with a dynamic number of rows and 6 columns. |

OMatrix | An owned matrix column-major matrix with |

OVector | An owned D-dimensional column vector. |

Point1 | A statically sized 1-dimensional column point. |

Point2 | A statically sized 2-dimensional column point. |

Point3 | A statically sized 3-dimensional column point. |

Point4 | A statically sized 4-dimensional column point. |

Point5 | A statically sized 5-dimensional column point. |

Point6 | A statically sized 6-dimensional column point. |

Projective2 | An invertible 2D general transformation. Stored as a homogeneous 3x3 matrix. |

Projective3 | An invertible 3D general transformation. Stored as a homogeneous 4x4 matrix. |

Rotation2 | A 2-dimensional rotation matrix. |

Rotation3 | A 3-dimensional rotation matrix. |

RowDVector | A dynamically sized row vector. |

RowOVector | An owned D-dimensional row vector. |

RowSVector | A statically sized D-dimensional row vector. |

RowVector | A matrix with one row and |

RowVector1 | A stack-allocated, 1-dimensional row vector. |

RowVector2 | A stack-allocated, 2-dimensional row vector. |

RowVector3 | A stack-allocated, 3-dimensional row vector. |

RowVector4 | A stack-allocated, 4-dimensional row vector. |

RowVector5 | A stack-allocated, 5-dimensional row vector. |

RowVector6 | A stack-allocated, 6-dimensional row vector. |

SMatrix | A statically sized column-major matrix with |

SMatrixSlice | A column-major matrix slice with dimensions known at compile-time. |

SMatrixSliceMut | A column-major matrix slice with dimensions known at compile-time. |

SVector | A statically sized D-dimensional column vector. |

SVectorSlice | A column vector slice with dimensions known at compile-time. |

SVectorSliceMut | A column vector slice with dimensions known at compile-time. |

Similarity2 | A 2-dimensional similarity. |

Similarity3 | A 3-dimensional similarity. |

SimilarityMatrix2 | A 2-dimensional similarity using a rotation matrix for its rotation part. |

SimilarityMatrix3 | A 3-dimensional similarity using a rotation matrix for its rotation part. |

SquareMatrix | A square matrix. |

Transform2 | A 2D general transformation that may not be invertible. Stored as a homogeneous 3x3 matrix. |

Transform3 | A 3D general transformation that may not be inversible. Stored as a homogeneous 4x4 matrix. |

Translation1 | A 1-dimensional translation. |

Translation2 | A 2-dimensional translation. |

Translation3 | A 3-dimensional translation. |

Translation4 | A 4-dimensional translation. |

Translation5 | A 5-dimensional translation. |

Translation6 | A 6-dimensional translation. |

U0 | |

U1 | |

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UnitComplex | A 2D rotation represented as a complex number with magnitude 1. |

UnitDualQuaternion | A unit quaternions. May be used to represent a rotation followed by a translation. |

UnitQuaternion | A unit quaternions. May be used to represent a rotation. |

UnitVector1 | A stack-allocated, 1-dimensional unit vector. |

UnitVector2 | A stack-allocated, 2-dimensional unit vector. |

UnitVector3 | A stack-allocated, 3-dimensional unit vector. |

UnitVector4 | A stack-allocated, 4-dimensional unit vector. |

UnitVector5 | A stack-allocated, 5-dimensional unit vector. |

UnitVector6 | A stack-allocated, 6-dimensional unit vector. |

Vector | A matrix with one column and |

Vector1 | A stack-allocated, 1-dimensional column vector. |

Vector2 | A stack-allocated, 2-dimensional column vector. |

Vector3 | A stack-allocated, 3-dimensional column vector. |

Vector4 | A stack-allocated, 4-dimensional column vector. |

Vector5 | A stack-allocated, 5-dimensional column vector. |

Vector6 | A stack-allocated, 6-dimensional column vector. |

VectorN | Deprecated An owned matrix column-major matrix with |

VectorSlice | A column vector slice with dimensions known at compile-time. |

VectorSlice1 | A 1D column vector slice. |

VectorSlice2 | A 2D column vector slice. |

VectorSlice3 | A 3D column vector slice. |

VectorSlice4 | A 4D column vector slice. |

VectorSlice5 | A 5D column vector slice. |

VectorSlice6 | A 6D column vector slice. |

VectorSliceMut | A column vector slice with dimensions known at compile-time. |

VectorSliceMut1 | A 1D column vector slice. |

VectorSliceMut2 | A 2D column vector slice. |

VectorSliceMut3 | A 3D column vector slice. |

VectorSliceMut4 | A 4D column vector slice. |

VectorSliceMut5 | A 5D column vector slice. |

VectorSliceMut6 | A 6D column vector slice. |

VectorSum | The type of the result of a matrix sum. |