# Crate cgmath

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 traits 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.

## 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.
• 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.
• Vectors that also have a dot (or inner) product.
• 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.
• The short constructor.
• The short constructor.
• The short constructor.