## Expand description

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 num_traits;`

## Modules

- Constrained conversion functions for assisting in situations where type inference is difficult.
- 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

- Approximate equality of using the absolute difference.
- Approximate inequality of using the absolute difference.
- An assertion that delegates to
`abs_diff_eq!`

, and panics with a helpful error on failure. - An assertion that delegates to
`abs_diff_ne!`

, and panics with a helpful error on failure. - An assertion that delegates to
`relative_eq!`

, and panics with a helpful error on failure. - An assertion that delegates to
`relative_ne!`

, and panics with a helpful error on failure. - An assertion that delegates to
`ulps_eq!`

, and panics with a helpful error on failure. - An assertion that delegates to
`ulps_ne!`

, and panics with a helpful error on failure. - Approximate equality using both the absolute difference and relative based comparisons.
- Approximate inequality using both the absolute difference and relative based comparisons.
- Approximate equality using both the absolute difference and ULPs (Units in Last Place).
- Approximate inequality using both the absolute difference and ULPs (Units in Last Place).

## Structs

- The requisite parameters for testing for approximate equality using a absolute difference based comparison.
- A two-dimensional rotation matrix.
- A three-dimensional rotation matrix.
- A generic transformation consisting of a rotation, displacement vector and scale amount.
- An angle, in degrees.
- A set of Euler angles representing a rotation in three-dimensional space.
- A 2 x 2, column major matrix
- A 3 x 3, column major matrix
- A 4 x 4, column major matrix
- An orthographic projection with arbitrary left/right/bottom/top distances
- A perspective projection with arbitrary left/right/bottom/top distances
- A perspective projection based on a vertical field-of-view angle.
- A point in 1-dimensional space.
- A point in 2-dimensional space.
- A point in 3-dimensional space.
- A quaternion in scalar/vector form.
- An angle, in radians.
- The requisite parameters for testing for approximate equality using a relative based comparison.
- The requisite parameters for testing for approximate equality using an ULPs based comparison.
- A 1-dimensional vector.
- A 2-dimensional vector.
- A 3-dimensional vector.
- A 4-dimensional vector.

## Traits

- Equality that is defined using the absolute difference of two numbers.
- Angles and their associated trigonometric functions.
- An array containing elements of type
`Element`

- Base floating point types
- Base numeric types with partial ordering
- Numbers which have upper and lower bounds
- Element-wise arithmetic operations. These are supplied for pragmatic reasons, but will usually fall outside of traditional algebraic properties.
- Points in a Euclidean space with an associated space of displacement vectors.
- A column-major matrix of arbitrary dimensions.
- A type with a distance function between values.
- Defines a multiplicative identity element for
`Self`

. - Equality comparisons between two numbers using both the absolute difference and relative based comparisons.
- 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.
- A two-dimensional rotation.
- A three-dimensional rotation.
- A column-major major matrix where the rows and column vectors are of the same dimensions.
- A trait representing an affine transformation that can be applied to points or vectors. An affine transformation is one which
- Equality comparisons between two numbers using both the absolute difference and ULPs (Units in Last Place) based comparisons.
- Vectors that can be added together and multiplied by scalars.
- Defines an additive identity element for
`Self`

.

## Functions

- Dot product of two vectors.
- Create a perspective matrix from a view frustum.
- Create an orthographic projection matrix.
- Create a perspective projection matrix.
- The short constructor.
- The short constructor.
- The short constructor.
- The short constructor.