Crate cgmath [] [src]

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::*;

Reexports

pub extern crate num_traits;
pub use approx::*;

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.

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.

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.

Array

An array containing elements of type Element

BaseFloat

Base floating point types

BaseInt

Base integer types

BaseNum

Base numeric types with partial ordering

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.

PartialOrd

A trait providing a partial ordering.

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 frustrum.

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.