Crate math_utils

Math types and traits

Re-exports

pub use vek::approx;

pub use vek::num_traits;

pub use vek;

Modules

coordinate

Tagged coordinate types

geometry

Geometry utilities

Macros

impl_numcast_fields

Structs

Affine2

2D affine space

Affine3

3D affine space

Affine4

4D affine space

AffineMap

Homomorphism of an affine spaces: a combination of a linear map and a translation

Affinity

Affine isomorphism

AngleWrapped

Unsigned wrapped angle restricted to $[0, 2\pi)$

AngleWrappedSigned

Signed wrapped angle restricted to $(-\pi, \pi]$

Angles3

(Euler angles) representation of a 3D orientation. Internally the angles are wrapped to $[0, 2\pi)$.

Deg

Degrees

Euclidean2

2D euclidean space

Euclidean3

3D euclidean space

Euclidean4

4D euclidean space

LinearAuto

Invertible linear endomorphism

LinearIso

Invertible linear map

Matrix2

2x2 matrix.

Matrix3

3x3 matrix.

Matrix4

4x4 matrix.

NonNegative

Non-negative scalars (may be zero)

NonZero

Non-zero scalars

NonZero2

2D non-zero vector

NonZero3

3D non-zero vector

NonZero4

4D non-zero vector

NormalSigned

Scalars in the closed interval [-1, 1]

Normalized

Scalars in the closed unit interval [0, 1]

Point2

2D position

Point3

3D position

Point4

4D position

Pose3

Representation of a 3D position + orientation

Positive

Strictly positive scalars (non-zero)

Projectivity

Isomorphism of projective spaces (a.k.a. homography or projective collineation)

Quaternion

Quaternions are a convenient representation for rotations in 3D spaces.

Rad

Radians

Rotation2

Orthogonal 2x2 matrix with determinant +1, i.e. a member of the circle group $SO(2)$ of special orthogonal matrices

Rotation3

Orthogonal 3x3 matrix with determinant +1, i.e. a member of the 3D rotation group $SO(3)$ of special orthogonal matrices

Turn

Turns

Unit2

2D unit vector

Unit3

3D unit vector

Unit4

4D unit vector

Vector2

Vector type suited for 2D spatial coordinates.

Vector3

Vector type suited for 3D spatial coordinates.

Vector4

Vector type suited for homogeneous 3D spatial coordinates.

Versor

Unit quaternion representing an orientation in $\mathbb{R}^3$

Enums

Axis2

X or Y axis

Axis3

X, Y, or Z axis

Axis4

X, Y, Z, or W axis

Octant

3D octant

Quadrant

2D quadrant

Sign

Negative, zero, or positive

SignedAxis1

Positive or negative X axis

SignedAxis2

Positive or negative X or Y axis

SignedAxis3

Positive or negative X, Y, or Z axis

SignedAxis4

Positive or negative X, Y, Z, or W axis

Constants

COMPONENT_INDEX_W

3

COMPONENT_INDEX_X

0

COMPONENT_INDEX_Y

1

COMPONENT_INDEX_Z

2

Traits

AdditiveGroup

Interface for a group with identity represented by zero, and operation defined by + and -

AdditiveMonoid

Set with identity represented by zero and (associative) binary operation defined by +

AffineSpace

Space of Point and Vector (translations)

Angle

Interface for angle units

Dot

Scalar product (bilinear form) on a Module

EuclideanSpace

AffineSpace with translations in a (Euclidean) real inner product space

Exp

Exponential function

Field

A (commutative) Ring where $1 \neq 0$ and all non-zero elements are invertible

FixedMatrix2

Convert to fixed precision 2x2 matrix

FixedMatrix3

Convert to fixed precision 3x3 matrix

FixedMatrix4

Convert to fixed precision 4x4 matrix

FixedPoint2

Convert to fixed precision 2D point

FixedPoint3

Convert to fixed precision 3D point

FixedPoint4

Convert to fixed precision 4D point

FixedVector2

Convert to fixed precision 2D vector

FixedVector3

Convert to fixed precision 3D vector

FixedVector4

Convert to fixed precision 4D vector

Group

Set with identity, inverses, and (associative) binary operation

GroupAction

(Right) action of a group on a set

InnerProductSpace

Bilinear form on a VectorSpace

Integer

Ring of integers

LinearMap

Module homomorphism

MaybeSerDes

Adds serde Serialize and DeserializeOwned constraints.

MetricSpace

Set of points with distance function

MinMax

Provides min, max, and clamp that are not necessarily consistent with those from Ord. This is provided because f32 and f64 do not implement Ord, so this trait is defined to give a uniform interface with Ord types.

Module

Additive group combined with scalar multiplication

MultiplicativeGroup

Interface for a group with identity represented by one, operation defined by * and /

MultiplicativeMonoid

Set with identity represented by one and (associative) binary operation defined by *

NormedVectorSpace

VectorSpace with vector length/magnitude function

Point

Point types convertible to and from a vector type, with difference function that follows from the free and transitive group action

ProjectiveSpace

Projective completion (homogeneous coordinates)

Real

Field with special functions and partial ordering

Ring

Interface for a (partially ordered) ring as a combination of an additive group and a distributive multiplication operation

SignedExt

Function returning number representing sign of self

Sqrt

Square root function

Trig

Trigonometric functions

VectorSpace

Module with scalars taken from a Field

Functions

report_sizes

Print the sizes of some types