Crate oxygengine_physics_2d::prelude::nalgebra

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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.
  • sparse
    Sparse 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.
  • 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
  • CsCholesky
    The cholesky decomposition of a column compressed sparse matrix.
  • CsMatrix
    A compressed sparse column matrix.
  • CsVecStorage
    A storage of column-compressed sparse matrix based on a Vec.
  • DefaultAllocator
    An allocator based on GenericArray and VecStorage for statically-sized and dynamically-sized matrices respectively.
  • 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.
  • OPoint
    A point in an euclidean space.
  • 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.
  • QR
    The QR decomposition of a general matrix.
  • Quaternion
    A quaternion. See the type alias UnitQuaternion = Unit<Quaternion> for a quaternion that may be used as a rotation.
  • 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 Transform. Its bottom-row is equal to (0, 0 ... 0, 1).
  • TGeneral
    Tag representing the most general (not necessarily inversible) Transform type.
  • TProjective
    Tag representing the most general inversible Transform type.

Traits

  • AbstractRotation
    Trait implemented by rotations that can be used inside of an Isometry or Similarity.
  • ClosedAdd
    Trait alias for Add and AddAssign with result of type Self.
  • ClosedDiv
    Trait alias for Div and DivAssign with result of type Self.
  • ClosedMul
    Trait alias for Mul and MulAssign with result of type Self.
  • ClosedSub
    Trait alias for Sub and SubAssign with result of type Self.
  • ComplexField
    Trait shared by all complex fields and its subfields (like real numbers).
  • CsStorage
    Trait for compressed column sparse matrix storage.
  • CsStorageIter
    Trait for iterable compressed-column matrix storage.
  • CsStorageIterMut
    Trait for mutably iterable compressed-column sparse matrix storage.
  • CsStorageMut
    Trait for compressed column sparse matrix mutable storage.
  • Dim
    Trait implemented by any type that can be used as a dimension. This includes type-level integers and Dynamic (for dimensions not known at compile-time).
  • 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.
  • IsContiguous
    Marker trait indicating that a storage is stored contiguously in memory.
  • IsDynamic
    Trait implemented by Dynamic.
  • IsNotStaticOne
    Trait implemented by Dynamic and type-level integers different from U1.
  • Norm
    A trait for abstract matrix norms.
  • Normed
    Trait implemented by entities scan be be normalized and put in an Unit struct.
  • RawStorage
    The trait shared by all matrix data storage.
  • RawStorageMut
    Trait implemented by matrix data storage that can provide a mutable access to its elements.
  • RealField
    Trait shared by all reals.
  • ReshapableStorage
    A matrix storage that can be reshaped in-place.
  • Scalar
    The basic scalar type for all structures of nalgebra.
  • SimdBool
    Lane-wise generalization of bool for SIMD booleans.
  • SimdComplexField
    Lane-wise generalisation of ComplexField for SIMD complex fields.
  • SimdPartialOrd
    Lane-wise generalization of the standard PartialOrd for SIMD values.
  • SimdRealField
    Lanewise generalization of RealField for SIMD reals.
  • SimdValue
    Base trait for every SIMD types.
  • SliceRange
    A range with a size that may be known at compile-time.
  • Storage
    Trait shared by all matrix data storage that don’t contain any uninitialized elements.
  • StorageMut
    Trait shared by all mutable matrix data storage that don’t contain any uninitialized elements.
  • SubTCategoryOf
    Indicates that Self is a more specific Transform category than Other.
  • SuperTCategoryOf
    Indicates that Self is a more general Transform category than Other.
  • TCategory
    Trait implemented by phantom types identifying the projective transformation type.
  • TCategoryMul
    Traits that gives the Transform category that is compatible with the result of the multiplication of transformations with categories Self and Other.
  • ToConst
  • ToTypenum

Functions

  • absDeprecated
    The absolute value of a.
  • center
    The center of two points.
  • clamp
    Returns a reference to the input value clamped to the interval [min, max].
  • 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 try_convert but without any property checks.
  • convert_unchecked
    Use with care! Same as try_convert but without any property checks.
  • distance
    The distance between two points.
  • distance_squared
    The squared distance between two points.
  • infDeprecated
    Returns the infimum of a and b.
  • inf_supDeprecated
    Returns simultaneously the infimum and supremum of a and b.
  • is_convertible
    Indicates if try_convert will succeed without actually performing the conversion.
  • max
    Same as cmp::max.
  • min
    Same as cmp::min.
  • one
    Gets the multiplicative identity element.
  • partial_clamp
    Clamp value between min and max. Returns None if value is not comparable to min or max.
  • partial_cmp
    Compare a and b using a partial ordering relation.
  • partial_ge
    Returns true iff a and b are comparable and a >= b.
  • partial_gt
    Returns true iff a and b are comparable and a > b.
  • partial_le
    Returns true iff a and b are comparable and a <= b.
  • partial_lt
    Returns true iff a and b are comparable and a < b.
  • partial_max
    Return the maximum of a and b if they are comparable.
  • partial_min
    Return the minimum of a and b if they are comparable.
  • partial_sort2
    Sorts two values in increasing order using a partial ordering.
  • supDeprecated
    Returns the supremum of a and b.
  • 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 out with the inverse of matrix.
  • wilkinson_shift
    Computes the wilkinson shift, i.e., the 2x2 symmetric matrix eigenvalue to its tailing component tnn.
  • wrap
    Wraps val into the range [min, max] using modular arithmetics.
  • zero
    Gets the additive identity element.

Type Aliases