vector v1.0.0 Vector

A library of two- and three-dimensional vector operations. All vectors are represented as tuples with either two or three elements.

Examples

iex> # Vector Tripple Product Identity
...> a = {2, 3, 1}
...> b = {1, 4, -2}
...> c = {-1, 2, 1}
...> Vector.equal?(
...>   Vector.cross(Vector.cross(a, b), c),
...>   Vector.subtract(Vector.multiply(b, Vector.dot(a, c)), Vector.multiply(a, Vector.dot(b, c))))
true

Link to this section Summary

Functions

Adds two vectors

Returns the basis vector for the given axis

Returns the scalar component for the axis given

Returns the cross product of two vectors AB

Returns the norm (magnitude) of the cross product of two vectors AB

Divide a vector by scalar value s

Returns the dot product of two vectors AB

Compares two vectors for euqality, with an optional tolerance

Multiply a vector by scalar value s

Returns the norm (magnitude) of a vector

Returns the square of the norm norm (magnitude) of a vector

Returns a new coordinate by projecting a given length distance from coordinate start along vector

Reverses a vector

Subtract vector B from vector A. Equivalent to Vector.add(A, Vector.revers(B))

Returns the unit vector parallel ot the given vector. This will raise an ArithmeticError if a zero-magnitude vector is given. Use unit_safe if there is a chance that a zero-magnitude vector will be sent

Returns the unit vector parallel ot the given vector, but will handle the vectors {0, 0} and {0, 0, 0} by returning the same vector

Link to this section Types

Link to this type location()
location() :: {number, number} | {number, number, number}
Link to this type vector()
vector() :: {number, number} | {number, number, number}

Link to this section Functions

Link to this function add(arg1, arg2)
add(vector, vector) :: vector

Adds two vectors

Examples

iex> Vector.add({3, -4}, {2, 1})
{5,-3}
iex> Vector.add({-2, 0, 5}, {0, 0, 0})
{-2, 0, 5}
iex> Vector.add({2, 1, -2}, Vector.reverse({2, 1, -2}))
{0, 0, 0}
Link to this function basis(atom)
basis(atom) :: vector

Returns the basis vector for the given axis

Examples

iex> Vector.basis(:x)
{1, 0, 0}
iex> Vector.basis(:y)
{0, 1, 0}
iex> Vector.component(Vector.basis(:y), :y)
1
Link to this function component(arg, atom)
component(vector, atom) :: number

Returns the scalar component for the axis given

Examples

iex> Vector.component({3, -4}, :y)
-4
iex> Vector.component({-6, 0, 8}, :z)
8
iex> Vector.component({1, -2}, :z)
0
iex> Vector.component(Vector.basis(:x), :z)
0
Link to this function cross(arg1, arg2)
cross(vector, vector) :: vector

Returns the cross product of two vectors AB

Examples

iex> Vector.cross({2, 3}, {1, 4})
{0, 0, 5}
iex> Vector.cross({2, 2, -1}, {1, 4, 2})
{8, -5, 6}
iex> Vector.cross({3, -3, 1}, {4, 9, 2})
{-15, -2, 39}
Link to this function cross_norm(arg1, arg2)
cross_norm(vector, vector) :: number

Returns the norm (magnitude) of the cross product of two vectors AB

Examples

iex> Vector.cross_norm({2, 3}, {1, 4})
5
iex> Vector.cross_norm({1, 4}, {2, 2})
6
iex> Vector.cross_norm({2, 0, -1}, {0, 3, 3})
9.0
iex> Float.floor(:math.pow(Vector.cross_norm({2, 2, -1}, {1, 4, 2}), 2))
125.0
Link to this function divide(arg, s)
divide(vector, number) :: vector

Divide a vector by scalar value s

Examples

iex> Vector.divide({3, -4}, 2.5)
{1.2, -1.6}
iex> Vector.divide({-2, 0, 5}, -2)
{1.0, 0.0, -2.5}
Link to this function dot(arg1, arg2)
dot(vector, vector) :: number

Returns the dot product of two vectors AB

Examples

iex> Vector.dot({2, 3}, {1, 4})
14
iex> Vector.dot({1, 4}, {2, 2})
10
iex> Vector.dot({2, 0, -1}, {0, 3, 3})
-3
Link to this function equal?(a, b, tolerance \\ 0.0)
equal?(vector, vector, number) :: boolean

Compares two vectors for euqality, with an optional tolerance

Examples

iex> Vector.equal?({3, -4}, {3, -4})
true
iex> Vector.equal?({3, -4}, {3.0001, -3.9999})
false
iex> Vector.equal?({3, -4}, {3.0001, -3.9999}, 0.001)
true
iex> Vector.equal?({3, -4, 1}, {3.0001, -3.9999, 1.0}, 0.001)
true
Link to this function multiply(arg, s)
multiply(vector, number) :: vector

Multiply a vector by scalar value s

Examples

iex> Vector.multiply({3, -4}, 2.5)
{7.5, -10.0}
iex> Vector.multiply({-2, 0, 5}, -2)
{4, 0, -10}
Link to this function norm(arg)
norm(vector) :: number

Returns the norm (magnitude) of a vector

Examples

iex> Vector.norm({3, 4})
5.0
iex> Vector.norm({-1, 0})
1
iex> Vector.norm({0, -2, 0})
2
Link to this function norm_squared(arg)
norm_squared(vector) :: number

Returns the square of the norm norm (magnitude) of a vector

Examples

iex> Vector.norm_squared({3, 4})
25
iex> Vector.norm_squared({1, 0})
1
iex> Vector.norm_squared({2, 0, -1})
5
iex> Vector.norm_squared({-2, 3, 1})
14
Link to this function project(vector, start, distance)
project(vector, location, number) :: location

Returns a new coordinate by projecting a given length distance from coordinate start along vector

Examples

iex> Vector.project({3, -4}, {-1, 1}, 4)
{1.4, -2.2}
iex> Vector.project({-6, 0, 8}, {1, -2, 0.4}, 2.5)
{-0.5, -2.0, 2.4}
iex> Vector.project({-2, 1, 3}, {0, 0, 0}, 2.5) |> Vector.norm()
2.5
Link to this function reverse(arg)
reverse(vector) :: vector

Reverses a vector

Examples

iex> Vector.reverse({3, -4})
{-3, 4}
iex> Vector.reverse({-2, 0, 5})
{2, 0, -5}
iex> Vector.cross_norm({-2, 3, 5}, Vector.reverse({-2, 3, 5}))
0
Link to this function subtract(a, b)
subtract(vector, vector) :: vector

Subtract vector B from vector A. Equivalent to Vector.add(A, Vector.revers(B))

Examples

iex> Vector.subtract({3, -4}, {2, 1})
{1,-5}
iex> Vector.subtract({-2, 0, 5}, {-3, 1, 2})
{1, -1, 3}

Returns the unit vector parallel ot the given vector. This will raise an ArithmeticError if a zero-magnitude vector is given. Use unit_safe if there is a chance that a zero-magnitude vector will be sent.

Examples

iex> Vector.unit({3, 4})
{0.6, 0.8}
iex> Vector.unit({8, 0, 6})
{0.8, 0.0, 0.6}
iex> Vector.unit({-2, 0, 0})
{-1.0, 0.0, 0.0}
iex> Vector.unit({0, 0, 0})
** (ArithmeticError) bad argument in arithmetic expression
Link to this function unit_safe(v)
unit_safe(vector) :: vector

Returns the unit vector parallel ot the given vector, but will handle the vectors {0, 0} and {0, 0, 0} by returning the same vector

Examples

iex> Vector.unit_safe({3, 4})
{0.6, 0.8}
iex> Vector.unit_safe({0, 0})
{0, 0}
iex> Vector.unit_safe({0, 0, 0})
{0, 0, 0}