Data.Vector

This module provides several small vectors over Double values. All fields are strict and unpacked, so using these should be fairly efficient. Each size of vector is a seperate type. It also provides a few vector constants to save you some typing now and then.

Documentation

type Scalar = Double

The type of Vector fields.

class Vector v where

The Vector class. All vectors are members of this class, and it provides ways to apply functions over vectors. Typically this methods aren't used directly; rather, the other class instances for each vector are implemented in terms of these.

Methods

fromScalar :: Scalar -> v

vmap :: (Scalar -> Scalar) -> v -> v

vzip :: (Scalar -> Scalar -> Scalar) -> v -> v -> v

vfold :: (Scalar -> Scalar -> Scalar) -> v -> Scalar

Instances

Vector Vector3

Vector Vector2

vdot :: Vector v => v -> v -> Scalar

Takes the dot product of two vectors [of the same dimension]. If you remember your highschool linear algebra, the dot product of two vectors V and W is equal to |V| * |W| * cos k, where |V| is the length of vector V, and k is the minimum angle between the two vectors.

vmag :: Vector v => v -> Scalar

Returns the magnitude of a vector (that is, it's length). Note that this is always positive or zero (never negative).

(|*) :: Vector v => Scalar -> v -> v

Multiply a vector by a scalar. This scales the magnitude (length) of the vector, but leaves its length unchanged. (Except in the case of a negative scalar, in which case the vector's direction is reversed.)

The operators |* and *| are identical, just with their arguments flipped.

(*|) :: Vector v => v -> Scalar -> v

Multiply a vector by a scalar. This scales the magnitude (length) of the vector, but leaves its length unchanged. (Except in the case of a negative scalar, in which case the vector's direction is reversed.)

The operators *| and |* are identical, just with their arguments flipped.

vnormalise :: Vector v => v -> v

Adjust a vector so that its length is exactly one. (Or, if the vector's length was zero, it stays zero.)

data Vector2

The type of 2-dimensional vectors. It provides various class instances such as Eq, Num, Show, etc.

Constructors

Vector2

Fields

v2x :: !Scalar

v2y :: !Scalar

Instances

Eq Vector2

Fractional Vector2

Num Vector2

Ord Vector2

Show Vector2

Vector Vector2

vector2X :: Vector2

Constant: The unit-length X vector, (1, 0).

vector2Y :: Vector2

Constant: The unit-length Y vector, (0, 1).

data Vector3

The type of 3-dimensional vectors. Similar to Vector2.

Constructors

Vector3

Fields

v3x :: !Scalar

v3y :: !Scalar

v3z :: !Scalar

Instances

Eq Vector3

Fractional Vector3

Num Vector3

Ord Vector3

Show Vector3

Vector Vector3

vcross :: Vector3 -> Vector3 -> Vector3

Takes the cross product of two [3D] vectors. Again, from highschool linear algebra, the cross product of vector V and W is a new vector P such that |P| = |V| * |W| * sin k (where k is the minimum angle between V and W), and the direction of P is perpendicular to both V and W. For example, vcross vector3X vector3Y = vector3Z. Note also that vcross w v = negate (vcross v w).

vector3X :: Vector3

Constant: The unit-length X vector, (1, 0, 0).

vector3Y :: Vector3

Constant: The unit-length Y vector, (0, 1, 0).

vector3Z :: Vector3

Constant: The unit-length Z vector, (0, 0, 1).