Crate cgmath

A low-dimensional linear algebra library, targeted at computer graphics.

Trait overview

In order to make a clean, composable API, we divide operations into traits that are roughly based on mathematical properties. The main ones that we concern ourselves with are listed below:

• VectorSpace: Specifies the main operators for vectors, quaternions, and matrices.
• MetricSpace: For types that have a distance function implemented.
• InnerSpace: For types that have a dot (or inner) product - ie. vectors or quaternions. This also allows for the definition of operations that are based on the dot product, like finding the magnitude or normalizing.
• EuclideanSpace: Points in euclidean space, with an associated space of displacement vectors.
• Matrix: Common operations for matrices of arbitrary dimensions.
• SquareMatrix: A special trait for matrices where the number of columns equal the number of rows.

Other traits are included for practical convenience, for example:

• Array: For contiguous, indexable arrays of elements, specifically vectors.
• ElementWise: For element-wise addition, subtraction, multiplication, division, and remainder operations.

The prelude

Importing each trait individually can become a chore, so we provide a prelude module to allow you to import the main trait all at once. For example:

use cgmath::prelude::*;

Re-exports

pub extern crate mint;

pub extern crate num_traits;

Modules

conv	Constrained conversion functions for assisting in situations where type inference is difficult.
prelude	This module contains the most common traits used in cgmath. By glob-importing this module, you can avoid the need to import each trait individually, while still being selective about what types you import.

Macros

assert_relative_eq
assert_relative_ne
assert_ulps_eq
assert_ulps_ne
relative_eq	Predicate for testing the approximate equality of two values.
relative_ne	Predicate for testing the approximate inequality of two values.
ulps_eq	Predicate for testing the approximate equality of two values using a maximum ULPs (Units in Last Place).
ulps_ne	Predicate for testing the approximate inequality of two values using a maximum ULPs (Units in Last Place).

Structs

Basis2	A two-dimensional rotation matrix.
Basis3	A three-dimensional rotation matrix.
Decomposed	A generic transformation consisting of a rotation, displacement vector and scale amount.
Deg	An angle, in degrees.
Euler	A set of Euler angles representing a rotation in three-dimensional space.
Matrix2	A 2 x 2, column major matrix
Matrix3	A 3 x 3, column major matrix
Matrix4	A 4 x 4, column major matrix
Ortho	An orthographic projection with arbitrary left/right/bottom/top distances
Perspective	A perspective projection with arbitrary left/right/bottom/top distances
PerspectiveFov	A perspective projection based on a vertical field-of-view angle.
Point1	A point in 1-dimensional space.
Point2	A point in 2-dimensional space.
Point3	A point in 3-dimensional space.
Quaternion	A quaternion in scalar/vector form.
Rad	An angle, in radians.
Relative	The requisite parameters for testing for approximate equality.
Ulps	The requisite parameters for testing for approximate equality.
Vector1	A 1-dimensional vector.
Vector2	A 2-dimensional vector.
Vector3	A 3-dimensional vector.
Vector4	A 4-dimensional vector.

Traits

Angle	Angles and their associated trigonometric functions.
ApproxEq	Equality comparisons based on floating point tolerances.
Array	An array containing elements of type Element
BaseFloat	Base floating point types
BaseNum	Base numeric types with partial ordering
Bounded	Numbers which have upper and lower bounds
ElementWise	Element-wise arithmetic operations. These are supplied for pragmatic reasons, but will usually fall outside of traditional algebraic properties.
EuclideanSpace	Points in a Euclidean space with an associated space of displacement vectors.
InnerSpace	Vectors that also have a dot (or inner) product.
Matrix	A column-major matrix of arbitrary dimensions.
MetricSpace	A type with a distance function between values.
One	Defines a multiplicative identity element for Self.
Rotation	A trait for a generic rotation. A rotation is a transformation that creates a circular motion, and preserves at least one point in the space.
Rotation2	A two-dimensional rotation.
Rotation3	A three-dimensional rotation.
SquareMatrix	A column-major major matrix where the rows and column vectors are of the same dimensions.
Transform	A trait representing an affine transformation that can be applied to points or vectors. An affine transformation is one which
Transform2
Transform3
VectorSpace	Vectors that can be added together and multiplied by scalars.
Zero	Defines an additive identity element for Self.

Functions

dot	Dot product of two vectors.
frustum	Create a perspective matrix from a view frustum.
ortho	Create an orthographic projection matrix.
perspective	Create a perspective projection matrix.
vec1	The short constructor.
vec2	The short constructor.
vec3	The short constructor.
vec4	The short constructor.