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 traits all at once. For example:

use cgmath::prelude::*;

Re-exports

• 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

• abs_diff_eq
  Approximate equality of using the absolute difference.
• abs_diff_ne
  Approximate inequality of using the absolute difference.
• assert_abs_diff_eq
  An assertion that delegates to abs_diff_eq!, and panics with a helpful error on failure.
• assert_abs_diff_ne
  An assertion that delegates to abs_diff_ne!, and panics with a helpful error on failure.
• assert_relative_eq
  An assertion that delegates to relative_eq!, and panics with a helpful error on failure.
• assert_relative_ne
  An assertion that delegates to relative_ne!, and panics with a helpful error on failure.
• assert_ulps_eq
  An assertion that delegates to ulps_eq!, and panics with a helpful error on failure.
• assert_ulps_ne
  An assertion that delegates to ulps_ne!, and panics with a helpful error on failure.
• relative_eq
  Approximate equality using both the absolute difference and relative based comparisons.
• relative_ne
  Approximate inequality using both the absolute difference and relative based comparisons.
• ulps_eq
  Approximate equality using both the absolute difference and ULPs (Units in Last Place).
• ulps_ne
  Approximate inequality using both the absolute difference and ULPs (Units in Last Place).

Structs

• AbsDiff
  The requisite parameters for testing for approximate equality using a absolute difference based comparison.
• 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 using a relative based comparison.
• Ulps
  The requisite parameters for testing for approximate equality using an ULPs based comparison.
• Vector1
  A 1-dimensional vector.
• Vector2
  A 2-dimensional vector.
• Vector3
  A 3-dimensional vector.
• Vector4
  A 4-dimensional vector.

Traits

• AbsDiffEq
  Equality that is defined using the absolute difference of two numbers.
• Angle
  Angles and their associated trigonometric functions.
• 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.
• RelativeEq
  Equality comparisons between two numbers using both the absolute difference and relative based comparisons.
• 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
• UlpsEq
  Equality comparisons between two numbers using both the absolute difference and ULPs (Units in Last Place) based comparisons.
• 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.
• point1
  The short constructor.
• point2
  The short constructor.
• point3
  The short constructor.
• vec1
  The short constructor.
• vec2
  The short constructor.
• vec3
  The short constructor.
• vec4
  The short constructor.