Crate jumpy::core::physics::collisions::rapier::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:

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.
  • 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 ArrayStorage and VecStorage for statically-sized and dynamically-sized matrices respectively.
  • DualQuaternion
    A dual quaternion.
  • Dyn
    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.
  • Scale
    A scale which supports non-uniform scaling.
  • Schur
    Schur decomposition of a square matrix.
  • Similarity
    A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.
  • 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.
  • ViewStorage
    A matrix data storage for a matrix view. Only contains an internal reference to another matrix data storage.
  • ViewStorageMut
    A mutable matrix data storage for mutable matrix view. Only contains an internal mutable reference to another matrix data storage.

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.

Constants§

  • U0
    The constant dimension 0 .
  • U1
    The constant dimension 1.
  • U2
    The constant dimension 2 .
  • U3
    The constant dimension 3 .
  • U4
    The constant dimension 4 .
  • U5
    The constant dimension 5 .
  • U6
    The constant dimension 6 .
  • U7
    The constant dimension 7 .
  • U8
    The constant dimension 8 .
  • U9
    The constant dimension 9 .
  • U10
    The constant dimension 10 .
  • U11
    The constant dimension 11 .
  • U12
    The constant dimension 12 .
  • U13
    The constant dimension 13 .
  • U14
    The constant dimension 14 .
  • U15
    The constant dimension 15 .
  • U16
    The constant dimension 16 .
  • U17
    The constant dimension 17 .
  • U18
    The constant dimension 18 .
  • U19
    The constant dimension 19 .
  • U20
    The constant dimension 20 .
  • U21
    The constant dimension 21 .
  • U22
    The constant dimension 22 .
  • U23
    The constant dimension 23 .
  • U24
    The constant dimension 24 .
  • U25
    The constant dimension 25 .
  • U26
    The constant dimension 26 .
  • U27
    The constant dimension 27 .
  • U28
    The constant dimension 28 .
  • U29
    The constant dimension 29 .
  • U30
    The constant dimension 30 .
  • U31
    The constant dimension 31 .
  • U32
    The constant dimension 32 .
  • U33
    The constant dimension 33 .
  • U34
    The constant dimension 34 .
  • U35
    The constant dimension 35 .
  • U36
    The constant dimension 36 .
  • U37
    The constant dimension 37 .
  • U38
    The constant dimension 38 .
  • U39
    The constant dimension 39 .
  • U40
    The constant dimension 40 .
  • U41
    The constant dimension 41 .
  • U42
    The constant dimension 42 .
  • U43
    The constant dimension 43 .
  • U44
    The constant dimension 44 .
  • U45
    The constant dimension 45 .
  • U46
    The constant dimension 46 .
  • U47
    The constant dimension 47 .
  • U48
    The constant dimension 48 .
  • U49
    The constant dimension 49 .
  • U50
    The constant dimension 50 .
  • U51
    The constant dimension 51 .
  • U52
    The constant dimension 52 .
  • U53
    The constant dimension 53 .
  • U54
    The constant dimension 54 .
  • U55
    The constant dimension 55 .
  • U56
    The constant dimension 56 .
  • U57
    The constant dimension 57 .
  • U58
    The constant dimension 58 .
  • U59
    The constant dimension 59 .
  • U60
    The constant dimension 60 .
  • U61
    The constant dimension 61 .
  • U62
    The constant dimension 62 .
  • U63
    The constant dimension 63 .
  • U64
    The constant dimension 64 .
  • U65
    The constant dimension 65 .
  • U66
    The constant dimension 66 .
  • U67
    The constant dimension 67 .
  • U68
    The constant dimension 68 .
  • U69
    The constant dimension 69 .
  • U70
    The constant dimension 70 .
  • U71
    The constant dimension 71 .
  • U72
    The constant dimension 72 .
  • U73
    The constant dimension 73 .
  • U74
    The constant dimension 74 .
  • U75
    The constant dimension 75 .
  • U76
    The constant dimension 76 .
  • U77
    The constant dimension 77 .
  • U78
    The constant dimension 78 .
  • U79
    The constant dimension 79 .
  • U80
    The constant dimension 80 .
  • U81
    The constant dimension 81 .
  • U82
    The constant dimension 82 .
  • U83
    The constant dimension 83 .
  • U84
    The constant dimension 84 .
  • U85
    The constant dimension 85 .
  • U86
    The constant dimension 86 .
  • U87
    The constant dimension 87 .
  • U88
    The constant dimension 88 .
  • U89
    The constant dimension 89 .
  • U90
    The constant dimension 90 .
  • U91
    The constant dimension 91 .
  • U92
    The constant dimension 92 .
  • U93
    The constant dimension 93 .
  • U94
    The constant dimension 94 .
  • U95
    The constant dimension 95 .
  • U96
    The constant dimension 96 .
  • U97
    The constant dimension 97 .
  • U98
    The constant dimension 98 .
  • U99
    The constant dimension 99 .
  • U100
    The constant dimension 100 .
  • U101
    The constant dimension 101 .
  • U102
    The constant dimension 102 .
  • U103
    The constant dimension 103 .
  • U104
    The constant dimension 104 .
  • U105
    The constant dimension 105 .
  • U106
    The constant dimension 106 .
  • U107
    The constant dimension 107 .
  • U108
    The constant dimension 108 .
  • U109
    The constant dimension 109 .
  • U110
    The constant dimension 110 .
  • U111
    The constant dimension 111 .
  • U112
    The constant dimension 112 .
  • U113
    The constant dimension 113 .
  • U114
    The constant dimension 114 .
  • U115
    The constant dimension 115 .
  • U116
    The constant dimension 116 .
  • U117
    The constant dimension 117 .
  • U118
    The constant dimension 118 .
  • U119
    The constant dimension 119 .
  • U120
    The constant dimension 120 .
  • U121
    The constant dimension 121 .
  • U122
    The constant dimension 122 .
  • U123
    The constant dimension 123 .
  • U124
    The constant dimension 124 .
  • U125
    The constant dimension 125 .
  • U126
    The constant dimension 126 .
  • U127
    The constant dimension 127 .

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).
  • Dim
    Trait implemented by any type that can be used as a dimension. This includes type-level integers and Dyn (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
  • DimRange
    A range with a size that may be known at compile-time.
  • 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 Dyn.
  • IsNotStaticOne
    Trait implemented by Dyn 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.
  • SliceRangeDeprecated
    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§